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SExI-FS Final.cdr - World Agroforestry Centre

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1. Figure 24 Roots visualization 3 4 Evaluate Species The species setting behavior can be tested using Evaluate option Right click the species item on the Project tree windows and select Evaluate menu The species setting can be modified here and tested by growing a tree in an isolated environment or using a static defined hemiphot The defined hemiphot is act as hemiphot captured by the tree as it grow On the real simulation this hemiphot will changes dynamically as the surrounding environment This static hemiphot is used to see the plasticity response of the species To edit the hemiphot click the Legend bar below or fill in manually the light field then click on the Hemiphot canvas Y ou can save the hemiphot for further use To start testing the species click on the Evaluate button and fill in the number of iteration click Ok The growth process of the tree will show on 3D visualization SExI FS User Guide Projects Project gi Setting e Ermironmaent E Light Capture ip Farbiity Map a Topography wv Scania Species C mponernl A Evaluate A Specie ee ea Species B tree Pict Spoke L Lala Ops rar Dee rimini Spares Deamipion L ger C der Ye Bre M LA T Beer Chances niil Du pa Lis Crea Purah ETES teen Demers 1300 Eire Feapaty ri b bod Mirage Vixb nI 14 DOG D ind sath Pepe DEC Aris figs OS TU DEFIE i CEH Furl UA eer god DBs c 1258 naw pag q Hagn alin H
2. In addition systematic mortality is assumed once tree crown size has reached 5 of normal crown size By default annual survival probability is a function of current growth rate relative to max growth rate given current size i e it does not take into account senescence as tree approaches maxi mum size Senescence may be incorporated simply by using growth rate relative to species absolute maximum growth rate rather than growth rate relative to max growth rate at current size Alternatively tree size relative to species maximum could be considered as an additional predictor Thetrees that don t survive enter the tree fall module Thetree fall module deals with secondary damage dueto tree fall The direction of fall is random Any tree smaller that 0 9 times the height of the falling tree and which is located in the area of potential damage is damaged Area of potential damage is a sector defined by the direction of tree fall and the crown width of fallen tree and initial position of tree The latter might be replaced by a probability value function of CF that would look like 1 EXP SRCF1 CF 34 SExI FS User Guide Figure 65 Diagram of tree fall sectoral damage Potentially damaged trees less than half the size of thefalling tree are either killed in a proportion equal to a parameter referred to as secondary mortality probability parameters or damaged Tree damage here means a deterioration of crown form ca 50 decrease of
3. Spatially Explicit Individual based Forest Simulator User Guide and Software Version 2 1 0 Degi Harja and Gregoire Vinc nt World Agroforestry Centre ICRAF and Institut de Recherche pour le D veloppement IRD SExI FS Spatially Explicit Individual based Forest Simulator User Guide and Software Version 2 1 0 Degi Harja and Gregoire Vinc nt World Agroforestry Centre ICRAF and Institut de Recherche pour le D veloppement IRD 2008 Correct citation Harja D and Vinc nt G 2008 Spatially Explicit Individual based Forest Simulator User Guide and Software World Agroforestry Centre ICRAF and Institut de Recherche pour le D veloppement IRD Disclaimer and Copyright The activities related to the work reported in this document were implemented with the support of World Agroforestry Centre ICRAF Institut de Recherche pour le D veloppement IRD and Common Fund for Commodities CFC The opinions expressed herein are those of the authors and do not necessarily reflect the views of ICRAF IRD and CFC 2008 World Agroforestry Centre ICRAF Southeast Asia Regional Office JI CIFOR Situ Gede Sindang Barang Bogor 16115 PO Box 161 Bogor 16001 Indonesia Tel 62 251 625415 fax 62 251 625416 Email icraf indonesia cglar org http www worldagroforestrycentre org sea ISBN 979 3198 39 2 Design amp layout by Josef Arinto and Vidya Fitrian Tree sketch by J asnari Acknowledgements
4. I yeu ward t chang somefing on pnus soneen click the Previaus baian dera ili TTE ERSTE om LL 4i Le S E Pa il Ene Mi YOu may cance Ms imnstallalian ad any me Ere clicking the Canter burfian un Figure 1 Introduction Step 2 Choose install folder Write down the installation folder or press Choose button to show the folder selection dialog Press the N ext button to continue Figure 2 Step 3 Choose shortcut folder Write down the shortcut folder or usethe other available options Press the N ext button to continue Figure 3 0 SO e SEXI FS User Guide o6 LA gt EN 20 ei pra Lj y PEENES E EE Figure 2 Choose install folder B Where wouid you Mer to create product icons Ina mew Program Group nian existing Program Group ces In the Start Hami Qn the Desktop C Tether Quick Launch Bar C or Figure 3 Choose shortcut folder hes SExI FS User Guide a 3 Qo Step 4 Pre Installation summary This shows the summary of the installation setting Press Install button to start the installation Product Name SEX FS install Folder C Program FilessEx FS eee Pro UT ae a ayeee Shortcut Folder C Documents and Settings mutyoutamiStart MenuiPrograms SEsi FS Disk Space Information for Installation Target Required 106 155 666 bytes Available 7 220 277 2468 bytes Figure 4 Pre installation s
5. completely opaque in which casethe growth SExI FS User Guide modifier for the only growing VB would be equal to the effective light of that particular azimuth average effective light 2 number of azimuths Such extreme cases are however not possible with the default parameterization due to built in correlation between the levels of light perceived by adjacent VBs overlapping of sectors Finally extreme departure from the mean value are only likely to occur when a large majority of VBs perceive very low light levels which is necessarily associated to low CP and low overall growth and hence individual growth of VBs should remain within reasonable boundaries Let G i be the standard growth rate equal for all azimuth computed in previous step Let L i be the sectoral light associated to VBazimuth i The following algorithm is used to adjust G i to L i Step 1 Effective light level L i is first computed for each VB direction as If L i gt optilum then L i optilum else L i 2 i Step 2 For all VB present not halted by collision and receiving sufficient light see section 5 2 4 on step 1 for details and notably additional condition that limits the total crown surface that may be lost in one time step through shedding due to low light G i the modified growth rate is computed as If L i A V G L i G i G i 14flexi 1 AVG L i L 1 sensi IF L i AVG L i G i 2M ax G i 1 flexi 1
6. for dbh CP interaction using the same PSP data as above It turns out that the interaction between both predictors is statistically highly significant and that smaller trees are indeed more sensitive than larger trees to sub opti mal CP scores N ote that the above procedure may eventually yield robust estimates only for abundant species H ence it is preferable whenever possible to develop potential growth curve by repeated measurement of isolated trees or low density stands Experience also indicates that sensitivity to shading is poorly captured in PSP data often there is no clear species specific response indicating that additional information should be used to estimate check Minilum and Optilum parameter values minimum and optimum light levels for growth For lesser abundant species one option is to repeatedly measure purposefully sampled trees Sample should whenever possible include open grown trees Crown Position 5 Sample should only include trees with optimal or near optimal crown shape CF gt 4 and cover a range of diameters Trees should be sampled in similar edapho climatic environment If a decent sample of trees is available across a range of CP classes shade response CP effect on growth can be meaningfully esti mated Alternative complementary options include using scarce published literature and local ecological knowledge about the species of interest The latter may notably yield useful ranking between species both in
7. A number of organizations and individuals provided assistance to make this work successful The authors would like to thank Dr Laxman Joshi Dr Gede Wibawa Elok Ponco Mulyoutami Janudianto Diah Wulandari Aniq Fadhillah Josef Arinto Vidya Fitrian IPB Computer Science students and consultant Tiza Asterinadewi Arum M adarum Ifnu Bima Fatkhan Riza Nugraha ICRAF site office staff Ratna Akiefnawati Jasnari Ilahang Budi Cangkurawok Endri Martini IT support Usman Muchlish and Ahmad Taufik The Smallholder Rubber Agroforestry System Project The Smallholder Rubber Agroforestry System SRA S Project in Indonesia and Thailand 2004 2008 is funded by the Common Fund for Commodities CFC and supervised by the International Rubber Study Group IRSG The project purpose is to increase smallholder rubber productivity and to contribute to overall sustainability of natural rubber production The project aims to improve productivity through integrating high yielding clonal rubber in smallholder agroforestry systems reduce production costs during the immature growth phase of rubber plants provide more affordable alternatives to small scale rubber farmers other than monoculture and to maintain biodiversity and environmental sustainability At the final stage of the project appropriate rubber technology for farmers lessons and recommendations from the project activities are being documented and distributed to rubber producing countries in Asia a
8. Guide J Qj 45 And is plotted below Growth reduction due to tapping 0 50 100 150 200 250 300 350 Tapping days per year Figure 60 Growth reduction as function of number of tapping days hevea default calibration in SEXI 5 1 3 Height Increment A reference allometric function relates tree height to tree dbh height dbhP Height sosaHussAAS E Figure 61 Height DBH function Thus height increment which is the function of DBH increment is height inc a dbh dbh _ incr P dbh And the height increment corrected by the elongation factor is height inc elong height incr c break _ function SEXI FS User Guide 46 Where cis the elongation factor c 1 flexi cCP Where e flexi is a parameter which measures the ratio of height growth rates under the most contrasted light gradients 0 and 1 e CP is the crown position index between O and 1 e sensi is a measure of how responsive the species is to shading sensi 1 e g 2 typical of a shade avoiding species and sensi lt 1 e g 0 5 of a shade tolerant species and the break function which is simply meant to ensure a smooth height growth reduction when approaching asymptotic height is defined as follow TENE height break e whereh is current height hmax is asymptotic height and k curvature parameter that is taken to be 20 for all species br hc 0 5 0 0 20 25 30 35 20 hc hMax Figure 62 Hei
9. are able to grow and produce new foliage at solar irradiances where branches on dominant trees die Thus branches are sufficiently interdependent that a positive carbon budget by itself does not ensure branch survival branch position relative to other branches on the same tree Is also important Sprugel et all 2002 Furthermore the increased growth of non shaded branches in trees where only two branches were shaded suggests that resources were preferentially allocated to branches in more favourable positions H enriksson 2001 H ence we expect that local deformation of a crown for example the opportunistic development of a part of the crown in response to local abundance of light side gap row planting etc will be better modeled as a combination of the overall growth potential modulated by local gradients B A wholetree active shade avoidance response under low light notably lateral shading by which crown growth is reoriented towards height at the expense of lateral growth and which is commonly observed under high tree population density or low light levels This response may result from a combination of biological mechanisms Relative or absolute increase of growth in height may also be a response of internal competition of allocation of growth potential within the crown as a decreasing gradient of light or space availability from apex to base is common H ence the distinction made here between global or local response is somewhat arbitrary
10. b button The animation shows the changes of trees from step to step of iteration 36 SExI FS User Guide 4 3 Tree Data Tree data output can be viewed through the M enu bar or Project popup menu It shows all the tree data history Figure 48 Next you can either download the data to be processed with some statistical software or directly view the plot and distribution using the available chart tools LS Projecti amp mE SIM_AGETREE ID AGE K DH HEIGHT CPINDEX CFINDEX CR_RADILIS R DEPTH 078 lot 0918 5 0 5 115 d 74 11554 og LE 1 41 ME T 71270003 118554 17 T 787319548 13 1g F 718548 54 18 712 319545 TE 142 f 4 14 Pia j rd 6i Wl 4 T i P 1454 T A a 17137000 TT 548 E 1270003 18548 1319548 715700030 TN d T 43 41 Ed Za f LIL P eT kl t i E F 1 zr LM id it d FLA ill Figure 48 Tree data There are three types of charts that can be used to analyze the data Bar Chart Line Chart and Scatter Plot 4 3 1 Bar chart Select the variable on the left panel and move it to the x and axis panel on the right By default the y axis is the number of trees based on the x variable class Y ou can also group the data by moving some of the variable to Group variable list The Bounds setting is the number of x axis class Qo SEXI FS User Guide 310 Set EE ET LA E TES ot hus Variable Setting amp o DIE HEDRE igma DBH Figure 49
11. crown volume This is achieved by shedding half of the VBs on one side of the crown 5 1 8 Reference Tree Reference tree is a tree which grows in an optimum environment isolated The tree is grown for a number of years and its various features dbh height crown size etc are stored in an array The relation between dbh and other dimensions of reference tree is sometimes referred to as normal relation When computing reference dimension value for a particular dbh local Lagrange interpolation method is used The interpolated polynomial is calculated from the 3 closest value indexes This procedure is meant to avoid large interpolation error on curve shape by linear section interpolation Thefact that only 3 values are used for interpolation should avoid Runge oscillations which can become problematic with high degree polynomial interpolation e g Http sonia madani club fr Cloaque Arithmurgistan Interpolation lagrange html 5 2 STReTCH Module 5 2 1 Introduction Statement of objectives Despite a widerange of development strategies architectural models sensu Hall et al 1979 all trees face the same fundamental constraints in terms of light capture and notably need to strike a balance between investment in support structure and assimilatory organs The objective of the Stretch moduleis to propose a generic SExI FS User Guide model to represent crown shape flexibility in response to light and space limitations indep
12. exact altitude of tree base when trees are positioned on an existing topography map y p4 P3 PE TE pt Pl x y z P2 y y P3 x y z3 P4 x Yas Z4 Pt x y z De Nemec PT en Pt is tree location and P1 P2 P3 P4 are topography data Then Zz 1 aX1 b y t a l bxk abz L az 25h p 22 where x x x y S y E y X5 X Ya Ya 3 2 5 Scenario Setting The scenario module is viewed as a flowchart model Figure 20 Scenario setting Theflow will be executed on each iteration for all thetrees The charts are editable The available Processes include only Cut Tree and Yield Harvest future version may include more Processes in the scenario The Condition chart controls the flow condition based on thetree variable 3 3 Species Settings Figure 20 Scenario setting SExI FS User Guide h i PE a Do Puti oc DD Cia here p ndi ihe cei Cr D lire Di F Faili To add a species to the project highlight the Species Component section on Projects window Figure 21 Thefirst time add a species the Properties window will show an empty species list Figure 22 Click add button to add species component to the list Or you can load the previous saved species list by pressing load button m at agraj Scanaria Ames a y n es 3pe cias YYY aperies 3 Tree Fiol Figure 21 Species component section pe
13. is shown by the vertical projection of the crown If there are only one radius information r1 the leftmost the vertical projection will be a circular shape but if there are more then one radius information the vertical projection will look like on following the graph in Figure 36 the rightmost graph use 5 radius information The horizontal and vertical projection information of the tree geometry is then converted into 3D shape object Es Crown Curie i ES Crown Depth F MESME un i rj 3 i E m 2 i E J m I i 3 EE PoE X fpi X A EC if fus i IL DR E ee ee eS i 3 i i 1 I u srl ELLES LIT i I pog 4 Iz z 3 bes t E t 4 Er s r cor T 1 us 3 SS eS ee 2 nm nn dE a r ij p L Figure 36 Horizontal and vertical projection of tree geometry 29 30 SExI FS User Guide The geometry information of the trees can be inserted manually using the table interface shown in Figure 37 The table is also able to load a text data file tab separated with the format shown below lid X y spesies dbh height cr depth cr curve cr radius rot 1 16 5 38 25 alpukat 0 10668 95 6 2 4 5 1 8 2 0 2 19 7 39 5 alpukat 017834 17 12 8 33 5 0 3 381 37 8 durian 0057322 5 15 1 1 1 3 4 0 Cj apt tire EJ lien Pil Qu trees Pi uM Comtun Comics Loss j i Sg Chet e 1 MM spun amp ET Hi on T a 4 i Um TELE i Xn T j i E T Leur Coesiruciad Treas Figure 37 Construct trees 3 7 Running the
14. on this format e Tree Species trs Tree species file is save on this file type with XML content format e Hemiphot hem H emi phot image is save on this file type with XML content format 83 EL in titut de mech chers IBS nuam hg iiim logo pon meni
15. term of growth rate and shade tolerance 6 3 2 Below Ground Crowding Index BGCI Usually BGCI is correlated to above ground indices CP and CF and in species rich PSP it may be difficult to show statistically significant growth reduction which is not yet captured by CP and CF indices In some particular cases e g limited number of species and expected contrasted competitiveness for below ground resources such as water it may be possibleto actually estimate BGCI from repeated measurements What wetry to estimate and which is supposedly different between species in the present case is the influential zone of each species In other words we assume equal sensitivity to resource shortage but differential resource capture efficiency represented by a relatively larger or smaller influential zone Thus the basic idea is to explore for the different species a range of species specific and size dependent influential zones SExI FS User Guide The general model to be fitted for each species is DBH_Inc Pot_inc CP CF Htapping 8GCl In the most general case assuming that only CF is species independent fitting the above model for a particular target species requires estimating 3 pot inc 5 CP as categorical 1 tapping n lambda species specific IZ scaling factor 8 n parameters In addition CF common to all species needs to be estimated too Although this is certainly feasible it cannot be done using procedures available in Standard
16. the crown envelope Extension of the subtending vectors is affected by local light and space availability as determined by species specific parameters Crown deformation algorithm is detailed in the STReTCH module Section 5 2 below 5 1 5 Latex Production So far only latex yield of rubber and fruit production has been implemented The relationship between size DBH and maximum latex yield is considered to be linear Vinge a 2999 4 SExI FS User Guide Latex production is considered to decrease after a certain number of tapping incisions due to bark consumption and diseases etc By default the decrease in latex production is set to start after 2000 days of tapping Say ten years of Intensive tapping and latex flow will completely dry up after 8000 days of tapping Then prediction of actual latex production after corrected by frequency of tapping f f 2000 latex act latex 1 6000 2 and O if 28000 days Fruit production and timber production can be specified as a function of tree size through the user interface 5 1 6 Recruitment Species defer in their preferred light environment for establishment This light preference is captured by a probability distribution function which can be esti mated by the experimentally determined frequency distribution of saplings per light classes A beta distribution is used which is defined as f x 2G n 4w G n G w x 1 x with O x lt 1 n 0
17. the parameters related to tree geometry This directly stems from the fact that competition is simulated by means of spatial interactions so that anything that alters either the shape the size or the relative position of the trees have direct impact on the outcome of the competition and therefore on the growth dynamic These elementary influences are usually SExI FS User Guide straightforward but their effect at different times and scales are difficult to predict without simulating because of the numerous feedback loops at work and the non linear dynamics of the system To illustrate this let s examine very simple cases By simulating growth in a mono specific stand of regularly spaced trees planted at increasing densities we observe the following response Planting at medium density translates into growth in height of the trees in the center of the plot being superior to that of border trees which is a response to the increasingly limited access to light of the trees in the center of the plot When planting density is increased further though growth in height of the trees in the center of the plot becomes less than their neighbors the level of competition is so high that these trees get overtopped and suppressed by border trees in more favorable position with respect to access to light Another simple test shows that ability to respond to low light availability by enhanced growth tn height a response which occurs at the expense of grow
18. trees and forests An architectural analysis Berlin Springer Verlag Henriksson J 2001 Differential shading of branches or wholetrees survival growth and reproduction Oecologia 126 4 482 486 Horn H S 1971 The adaptive geometry of trees Princeton University Press Princeton Lacointe A Deleens E Ameglio T Saint Joanis B Lelarge C Vandame M Song G C Daudet F A 2004 Testing the branch autonomy theory a 13C 14C double labelling experiment on differentially shaded branches Plant Cell and Environment 27 9 1159 1168 Montgomery R A Chazdon R L 2001 Forest structure canopy architecture and light transmittance in tropical wet forests Ecology 82 10 2707 2718 M orataya R Galloway G Berninger F Kanninen M 1999 Foliage biomasssapw ood area and volume relationships of Tectona grandis L f and Gmelina arborea Roxb silvicultural implications Forest Ecology and M anagement 113 2 3 231 239 Press W H Teukolsky S A Vetterling W T Flannery B P 1992 Numerical recipes in C 2nd ed the art of scientific computing Cambridge University Press p 994 Putz F E Parker G G Archibald R M 1984 M echanical A brasion and Intercrown Spacing American Midland Naturalist 112 24 28 ol SExI FS User Guide Ritchie G A 1997 Evidence for red far red signaling and photomorphogenic growth response in Douglas fir PSeudotuga menzii seedlings Tree Physiology 17 161 168 Rudnicki M Lieffers V J Silins U 2003 St
19. variation of soil fertility can also be simulated A soil fertility map can be entered manually for each cell of a grid covering the plot or read from a text file Missing data are interpolated using bilinear 3 dimensional interpolation Press et al 1992 Fertility values fall between Oto 1 a fertility of one meaning there is no local soil fertility related limitation in addition to the overall fertility level defined in the step above Thefertility experienced by atree will then depend on tree position in the plot Fertility index used for computing reduction in growth of a particular tree is simply the average value over the cells included in the tree s influential zone All cells which center is included in the crown projection are used in mean fertility calculation METERS Dis SR f X S i Change Figure 59 Fertility Map e Tree Production Effect Tapping of rubber trees slows tree growth Annual DBH increment decreases with increasing tapping frequency Research on rubber trees shows that after 200 days of tapping DBH increments decrease by about 50 see review in Grist et al 1998 and data in Vincent et al Submitted for A groforestry System However the decrease is not simply proportional the simple fact that trees are tapped albeit lightly seem to induced a strong decrease in dbh increment The default function used is GrowthReduction 1 Exp number of tapping days per year 365 0 5 g SEXI FS User
20. 2 SExI FS User Guide Fertility values vary between 0 and 1 a fertility of one meaning there is no soil fertility related limitation e Fertility Based On Root Zone If true the fertility experienced by a tree will be computed as the average of cells fertility value of cells within the tree root influential zone Otherwise the fertility information will be taken at the exact cell location of the tree e Plot Fertility Index This is an index of soil fertility of the plot between 0 and 1 e Soil Fertility Cell Width The fertility map cell width m e Soil Fertility Cell Height The fertility map cell height m e Fertility Map Click on the input field to open the fertility map editor 3 2 2 Light Capture Setting There are three categories of parameters to be documented in order to set up the light capture module light model spatial environment and light interception options Figure 15 Properties Laghst Capture LIEN Lion hited Humber of amp mums 15 hHumbar gf metlnahamns ie Mumbar of Aueithrs Amin is Me horcontal component of a direction compass dirazbon rrsaasurgd around ma torgan fom the Morin point Toward me East Le clockwise if 5 usualty medsLired m dagress a yet iti Figure 15 Light Capture Setting SExI FS User Guide s Haeba of Inclinatians Target Postion Figure 16 Horizon Projection of Beams Vector Figure 17 Vertical Projection of Beams Vector here the number of inclination 6
21. 24 c4 E ut Da sado ide nouer cui s pd 26 JO CONSU TOG rers esp tE e Erre EREA a aA S E eE a 29 3 7 Running the Simulation 30 4 SIMULA ON O UIDHL i cac cocer c o9 3 OR CE on 2 Pen QC UR C eee 31 4 1 Vertical Projection Plot 31 42 3D VISUAIZAUON cien e eric wc bon e w ord a ave as danse en aes 34 AS A NES SD Soir S35 RE AR RUE OR doET aee ae RRDECR e P ee ae es 36 5 Documentel llcsq33a4 2 P1UCVDUPR tone ee sm tan revint 39 5 1 Model Description and M ain Algorithms 39 5 2 STRETCH Module 54 6 Calibration Procedures 69 6 1 Allometric Data 69 6 2 Data Processing Sa a nd orar has oui 73 OS GONA ARS a a eek oe 76 References an ae dan ee eee 81 Vol ee ee CHECA CELO EE Qe 83 SExI FS User Guide 1 General Information 1 1 Overview The SEXxI forest simulator focuses on tree tree interactions in a mixed multi species agroforest The high level of structural complexity of such traditional agroforestry systems defies classical forestry approaches when it comes to optimizing management practices To cope with this complexity farmers have adopted a tree by tree management approach which is closer to gardening than to any usual tropical forestry or estate crop management model Individual tree care a
22. 50 SExI FS User Guide Step 3 Identifying cells that will hostthe recruits Select cells to be colonized in current time step if any For each light class the number of recruits is known and equal to the total area of that light class x recruitment rate The random allocation of those recruit to particular cells is done according to a parameter which reflects the relative bias towards preferential establishment in empty cells hence controls spatial regularity in recruitment and may be set to 1 by default assuming that only empty cells will be considered as potential location for new recruits Conversely if is set to Oall cells within a particular light class will be selected with the same probability H ence as overall density per light dass governs the total recruitment rate this will result in a spatially totally random distribution of seedlings within a light class provided that the draw is done on the whole set of cells for each individual See last section for details of the proposed algorithm section 5 2 3 b and section 5 2 6 Step 4 Determine to which species a recruit belongs Wenow have identified the individual cells that will carry a recruit and the number of recruits per cell For each recruit wethen randomly draw the species to which it belongs using thefollowing procedure Let F betherelative weighted frequency of the species i i e the relative effective abundance of species contributing to regeneration inside t
23. Bar Chart 4 3 2 Line chart On the line chart you can define the X and Y variable from the available variable list And define the calculation method M ode in case the Y value is more the one per C category The calculation method available is average sum and count Variable Setting iP Project amp ni Ht IM AGE Hoe SPECIES EESTI TREE ib W i Im DEH cx noe J Bspeciess ho ai Wsesces M el jus CR RADHIS AN Be ICR DEPTH i e La IT Lom cancer Figure 50 Line chart SEXI FS User Guide 4 3 2 Scatter plot The X and Y axis can be set for by variable from the variable list Bspecies1 Bspecies3 species Figure 51 Scatter plot SExI FS User Guide 39 5 Documentation 5 1 Model description and main algorithms 5 1 1 Main loop The loop is run on a yearly time step It starts with an initialization step the initial trees are recorded into the module as individual objects N ext the trees crown attributes Crown Form Index CF and Crown Position Index CP are updated Crown Form is an index of how well developed a crown is and Crown Position is an index of light availability Simulation data is then recorded after this step Tree growth is then computed diameter height and crown volume increment At each step in time for each tree a survival test is made Finally at stand level a recruitment test is conducted BEY Tree Level Process i Plot Level Proce
24. D ata We assume we havetwo tree population samples measured in contrasted conditions i e isolated or in dense stands Wefurther assume that the dense stand sub population may be considered representative of the most extreme conditions i e we capture most of the species possible range of growth conditions In casethe height dbh relationship of either of the two subpopulations shows a strong dispersion an envelop curve analysis could be used e g stochastic frontier functions may be used SExI FS User Guide 15 instead of standard regression see free software at http www uq edu au economics cepa software htm but has not used in the present study We use the data collected by ICRAF by mid 2004 for 6 species for which sample size seems suitable Lansium domesticum H evea brasiliensis Durio zibethinus Archidendron jiringa Alstonia angustiloba P araserianthes falcataria M ethodology Step 1 graphical analysis and data transformation Assuming that the dbh height relationship may be correctly described using the following relationship height a dbh b data are first log transformed and plotted using linear smoother We visually check that the log transformation is fine graphical analysis of residuals may help pinpoint possible problem such as heteroscedascity or unwished pattern in the residuals Step 2 first parameter estimates For most species it can be seen that the regression lines of the two sub populations ar
25. H ence overall light level is the environmental cue used in SEXxI to model vertical stretching of tree A number of casual observations suggest that crown riseis accelerated by increased light gradient e g durian with low branches until it reaches the upper canopy and emerges shorter rubber trees with reasonable crown depth under dense stand of rubber trees themselves having the crown reduced to the most extreme top of the tree This would illustrate a change in growth strategy growth allocation pattern in response to gap opening for example In the proposed implementation of the model increased slenderness will force crown rise 5 2 3 Crown shape modeling a Analytical framework Crown development is decomposed into vertical extension and horizontal extension of VBs Virtual Branches and light may affect each directional component differently Growth of an individual VB will depend on 1 Overall growth potential Individual VB growth will depend on the overall potential crown volume increment associated with dbh increment which notably depends on overall light limitation The relationship between crown volume increment and dbh increment is controlled by h dbh and dbh CW power relationships 2 Species crown profile default implementation is half ellipsoid in order to maintain the general shape of crown profile ellipsoidal conical paraboloid of revolution etc in the absence of deformation due to competition the growth o
26. L 1 AVG L 1 sensi 0 The above formulation is consistent with the way flexi and sensi are used to implement whole tree response to shading Flexi essentially controlling the maximum departure from reference here symmetric growth and sensi an index of sensitivity to shading either local or global 61 SExI FS User Guide n TU oe S DE oes Pu enum k z T a X RE ae oi d E M Wu NER e Mus db d nu lh Ayre are FE v a nts nh f ne i Re EA ET d RE XN E NR yy i a qe z P 4 Dx vs Yo i Jii hs i Museo Stak aed EO ds OE PU Pe PED Dl i OR oes 1 er 3 is F DX e r y n na E E Ligh tRAt io ng ay ghtrat in 0 8 Figure 66 Percentage increase in VB extension in Figure 67 Percentage change decrease in growth high light microsites as a function of sensitivity and rate of vertex as a function of light ratio local light light ratio average light local light flexi 1 average light and sensitivity when local light is less than average light flexi 1 Finally if VB is inside neighboring crown i e has intruded a neighbouring crown G i is set to zero no growth through neighbor s crown envelope 5 2 4 Branch shedding Branch shedding always starts with lower most VB in any azimuth l A first test for VB survival is made prior to VB growth If VB sectoral light level is below a certain threshold then it is dropped Threshold light level at which lower most VBs are shed is set to be equal to minim
27. Simulation cp 0 6 0 6 0 8 To start running the simulation highlight the Project Root section on Project window The Properties window will show the project properties and the Run 0 4 0 6 0 3 button Figure 12 Click the Run button and enter the number of iterations click Ok The simulation will run for the specified number of iterations years While the simulation is running you can see the progress bar that indicates progress of simulation CT 0x Humber of iteration years OK Cancel Figure 38 Running simulation SExI FS User Guide 31 4 Simulation Output You can explore the simulation output by either inspecting the tree plotting in Two Dimension 2D and Three Dimension 3D graphic or plotting the tree data on statistical chart 4 1 Vertical Projection Plot The vertical projection plot is showing a 2D view of tree crowns vertical projection Figure 39 You can monitor the dynamic growth of the tree and its crown through this plot The plot management also can be done through this plot Enui Figure 39 Vertical projection plot 4 1 1 Plot Options Right click on the plot area you will find menus for configuring the plot Zoomin Magnify the plot O Pam Outline B Overlay Opaque Show info Transparent E Hemiphot Show hemispherical photograph Shwo 9 Shaded model for the selected location amp Zoom Out Zooming out the plot amp P
28. Zone Modifier npetition r act Label Species name identity Species Component Theinitial diameter for newly recruited trees default is 1 cm dbh e Crown Porosity A measure of crown transparency here the crown is considered as partially transparent 0 1 e Survival Probability The annual survival probability value of a completely suppressed plant SExI FS User Guide no growth In addition a systematic mortality is assumed once 5 of reference tree crown size has been reached See Documentation chapter for more details M ortality M odifier Mortality Modifier modulates the shape of survival probability curve as growth rate is reduced higher m values imply higher mortality rates at identical growth rate Default value is 15 See Documentation chapter for more details 2 Mortality Probability 2 Mortality Probability is the probability that a tree dies from a neighbouring tree fall 0 1 if it lies in the sector affected by tree fall Default value is 50 see Documentation chapter for further computational details Adult Size The DBH at which a tree species reaches sexual maturity determines start of recruitment for non pioneer species 3 3 2 DBH Function The evolution of DBH over time t is modeled by a classical Chapman Richards function dbh dbh_max i e Approximating DBH annual increment with the first derivative of DBH with respect to time t one can express dbh increment as a function o
29. aigh A 16 naogp Hargra B D 4 En Heighl Wing cere fil HE q Emran abiiy ome ey MNE le m Lars awe Spee ce D a Figure 25 Evaluate species Ms fS HEJ Fie Praject Tree Pd Hele 5B HEE PHASX o waa Projects roe E a F E Presacti mainiti prises Societ t a6 Gang _ omm Geeciae 1 gt Lignt come Spariat Dewcripson iar i 0 P07 377 wrap Vapegragiw amag PETA umanu B Y i Diii Li a Sacha Component t died TIT D ipaciocs 5600 E Apatiit A Wpecisg E Trag Pict TO UU Lond 1 170 pni 1g conn 0 4500 4n o0 1 1800 135400 1220 1 DE 0 300 05050 1 0000 EN Figure 26 Evaluate species using hemi phot modification j kar i 5 ae Li toad 27 250 26 SExI FS User Guide 3 5 Tree Planting Once you have set up the species component for your simulation you need to plant trees Highlight the Tree Plot component in the Project window the Properties window will show an empty tree table Figure 27 To start planting trees you Should move to Tree Planting tab or you can click the button click here to plant trees inside the empty tree table Properties Properties zs iree Plot Irae Plot Project Ej Eee rr Plant m Construci Flam Lit Congiu 7 Trees T Planting Ternglate Ti ezs adi m Manu Rand Paien Gi click here to plant trees Apply Template Trees Figure 27 Tree table tab Figure 28 Tree planting tab Planting trees can start wit
30. aint Vertical projection paint model So O Cove 2 SExI FS User Guide Outline Outline paint model Opaque Opaque paint model Transparent Transparent paint model Shaded Shaded paint model Show Info Show information label of each tree on the plot Species ID DBH etc Overlay Overlay the layer plot Light Map Overlay the light map layer Root Map Overlay the root map layer Figure 40 Plot menu Figure 41 shows the hemiphot for some location selected on the plot and Figure 42 is the overlay of light map Figure 43 Show info of tree tree ID overlay with root map A Vertical View 1 Forest Simul c 3 DECITRE 1 we secs Lort e Calculate Figure 42 Light map Figure 41 Hemiphot Qo SExI FS User Guide 330 Figure 43 Show info of tree tree ID overlay with root map Figure 44 Paint type for thetree clockwise from top left outline opaque transparent and shaded Shows various paint type for vertical projection of the crown Figure 44 Paint type for the tree clockwise from top left outline opaque transparent and shaded SEXI FS User Guide 34 B Project j M Cu ines E uenipho E res Bierrgpisct Fut EL T R Show 10 ipe 2 r i Tye D 2 Pr oper tirs Figure 45 Tree selection menu x Cut Tree s Cutting removing the selected tree s from the plot This can be assumed as a ma
31. and is made for operational purposes Vertical light gradient of increasing intensity towards the top of the canopy is not only common under dense planting where overhead light is abundant whilelateral light is very much restricted but also in the forest understory where a similar gradient though probably less pronounced may prevail in many cases M ontgomery and Chazdon 2001 H ence new leaves are produced where light resource is most abundant a local response which translates into a global deformation of the crown only the upper most part of the crown receives adequate light to maintain active growth and therefore elongation of crown occurs The strategy of compression in the understorey and accelerated growth under gap as described in Sterck 1999 for example would indicate that for canopy species SExI FS User Guide whose juveniles start to grow in the understorey the relevant signal to trigger accelerated growth in height might be the light gradient rather than the light level It has been shown that poplar trees can alter their growth rates under modified red far red ratio and noticeably increase their relative growth in height Gilbert et al 1995 This may be a widespread response to shading Ritchie 1997 Our measurements of hundreds of trees belonging to a dozen species growing either in dense plots while receiving overhead light or overtopped in the understory reveal very similar overall h dbh alteration ICRAF unpublished
32. and structure governs the crown collisions of lodgepole pine Can J For Res 33 7 1238 1244 Sprugel D G 2002 When branch autonomy fails Milton s Law of resource availability and allocation Tree Physiology 22 15 16 1119 1124 Sterck F J 1999 Crown development in tropical rain forest trees in gaps and understorey Plant Ecology 143 1 89 98 Van Noordwijk M 1999 Functional branch analysis to derive allometric equations In Murdiyarso D Van Noordwijk M Suyamto D A 1999 Modelling global change impacts on the soil environment Report of Training Workshop 5 13 M ay 1998 Bogor IC SEA Report No 6 BIOTROP GCTE ICSEA pp 77 80 Vincent G Azhima F Joshi L Healey J R submitted Are permanent rubber agroforests an alternative to cyclical rubber cultivation An agro ecological perspective A groforestry Systems Vincent G Wibawa G Manurung G 2000 Inter tree rubber yield and growth variability A comparison of plantations and agroforests in Sumatra Indonesia Indonesian Rubber Conference and International Rubber Research Development Board Annual Symposium Bogor Indonesian Rubb Res Inst SExI FS User Guide Appendix This manual is also complement with CD which contains some file as listed below e Simulation s A full simulation file included the tree and plot data e Simulation data txt Statistical data output is saved on this format e Simulation setting xml Predefined simulation setting is save
33. anu edu au associated mensuration shape htm equation SExI FS User Guide 67 In fact the model should be able to compute cross sectional area of stem at any height based on any kind of stem profile if such information is provided by user This could beimplemented simply using numerical approximation to compute deltadb h and delta h in the Stretch module SExI FS User Guide 6 Calibration Procedures Below are some guidelines and examples on how to collect tree data to be used for calibrating the SEXI FS model with emphasis on the STReTCH module crown deformation 6 1 Allometric Data The purpose Is here to define relationship between various tree dimensions and how those allometric relationships are affected by tree environment 6 1 1 Tree selection Trees from the following three categories are purposefully sampled over the whole range of diameter of interest eg 5 to 50 cm dbh all trees should have a CF score gt 3 The three categories considered are e Isolated trees e Co dominant trees in dense stands usually pure stands i e CP224 e Suppressed trees CP 2 6 1 2 Tree parameters to be measured e Tree height h e Height of crown base hcb e Height of maximum crown width hmcw e Height of maximum crown width oc may coincide with height of crown S p di base The height of maximum crown heb f 7 CalLeiss width a shape parameter isused 4 er Altimeter _ to compute crown volume Figur
34. arameter governing the ability of a crown to adjust to lateral anisotropy of resources due to difficulties involved in standardizing such measures O ne favourable situation which may occur with planted Species would make use of crown deformation response of trees growing under different planting patterns i e inter row and on the row inter tree distances Rather we makethe assumption that flexibility in tree height adjustment ratio of k value in the height dbh relationship under contrasted vertical gradient is a good proxy for theability of a species to adjust its crown expansion under lateral anisotropic distribution of light 6 3 Growth Data Permanent sample plot data are used to derive the following parameters e Species potential growth function site specific e Species sensitivity to shading e Species sensitivity to tapping e Species influential zone determining BGCI 6 3 1 Potential growth function Standard procedures are used to analyse data from Permanent Sample Plot see for example Alder and Synnot 1992 Vincent et al 2001 for an introduction to such methods Predictors used in the GLM include size crown indices and tapping regime Rare species 10 individuals monitored are grouped into a miscellaneous grey species for the data analysis purpose Once factors effect are esti mated potential growth is computed after correcting for CF CP Tapping index and possibly BGCI Below Ground Crowding Index Corrected dbh i
35. ce area of the convex envelop of the crown The difference betw een actual and normal crown size may result from encroachment from neighboring crowns subopti mal light level or asymmetric development of the crown The asymmetric development of the crown is explained in the section presenting the STRETCH module below crown _ surface _ actual crown surface normal Figure 57 An asymmetric development of crown shown on the model SExI FS User Guide 43 c Belowground Crowding Index Below ground competition is based on the following simple assumptions 1 Root influential zone IZ of a tree is proportional to its size and symmetric in shape circular 2 A crowding index is computed for any tree based on the overlap of neighbours IZ with target tree influential zone 3 M ore competitive species have relatively larger IZ i e higher resource capture efficiency 4 Overall below ground crowding index effect on growth is site specific dependent on overall level of resources The relationship used to relate growth reduction to below ground crowding index is illustrated in the graph below wheres is the site index fertility value In 0 5 me S f BGCT 1 f BGCTI 2 Growth reducer 0 031 9 0 BGCI Below Ground Crowding Index Figure 58 Relationship used in SExi to compute growth reduction as a function of BGCI 4 SExI FS User Guide 44 d Fertility Local
36. ce in light perceived by neighbouring V Bs b TheAlgorithm Vertical stretching of crown Compute vertical and horizontal growth component of VBs of reference tree based on species specific shape and actual overall growth reducers Computation of stem height and dbh increments are described in section 2 3 H eight Increment Those values are then used to compute crown stretching by computing VB increments based on crown profile Half ellipsoid profile vi a VB incr ver cos theta height inc vii a VB inc hor sin theta CW increment theta is the angle of VB with vertical and CW increment is calculated in the following way i e replacing the experimental bilinear relationship between dbh and CW with a power function to avoid discontinuity Step 1 Using the parameters of the esti mated linear relation between CW and dbh which holds for dbh gt 5 cm compute x1 y1 x2 y2 the coordinates of the points of the curve CW dbh where X1 0 05 y120 05 b 4a x22dbhmax y2 dbhmax b a SExI FS User Guide 50 Step 2 Compute the corresponding A and B parameter values of the power function such that CW 2A dbh B A logbll logl y2 log x1 log x2 log x2 log y1 log x1 log y 2 B e log x1 log x2 Step 3 Compute the crown width increment as the expected crown increment for the normal tree given the current dbh hence CW increment A dbh Hncr B dbh B If the tip of a VB is inside a neighboring c
37. crown surface Pl cr cr Pl cd cr e arcsin e where cd stands for crown depth total height height of crown base and cr is crown radius half of crown width see http mathforum org library drmath view 51743 html for derivation of the formula of Surface area of an ellipsoid Then estimated surface or volume is fitted to dbh a loglinear fit is usually satisfactory as total leaf area is expected to scale linearly with stem cross sectional area e g Morataya et al 1999 A gain we expect this relationship to vary little between groups which can betested by ANCOVA and data for the various groups should be pooled for this adjustment to increase robustness of parameters esti mates N ote multilayer trees sensu H orn 1971 which arerarein our data sets arelikely to show a more consistent linear fit between crown volumeand dbh rather than crown surface This may be explored using the estimated volume of crown computed as 1 3 Pi cwa cwb CD half ellipsoid where cwa and cwb is crown width measured twice perpendicular see tree parameter measured on section 6 1 2 6 2 3 Estimation procedure of the flexi parameter O bjectives Weare interested in assessing the change in the slope derivative of the height dbh relationship observed in trees of various species when grown either isolated or in dense stands In the SExI FS model this corresponds to the flexi parameter precisely the ratio of the derivatives is equal to flexi 1
38. d using sub vertical photographs towards the sky Best time to take good quality photographs Is early morning or under heavily overcast skies no direct sunlight Low branches can make pictures of the entire crown difficult or impossible as we can t move back far enough to capture the whole crown In that case it is recommended to beginners to take a series of 71 2 SExI FS User Guide pictures of parts of the crown in a systematic pattern Once experienced selection of a reoresentative part of crown in the field is amore efficient way of doing In most cases selection of a representative portion of crown which can be the entire crown once it has been delineated on the photograph but is more commonly restricted to half a crown excluding the D A all tree trunk will be done by ERE oF xw cropping part of the digitised Figure 75 Crown porosity of Pterospermum javanicum A image on the computer Shorea javanica Koord et Valeton B Parkia speciosa Hassk C and Lansium domesticum Correa D Once a representative portion of the crown has been selected and cropped the picture is converted into black and white bitmap format in order to assess the percentage of visible sky Image thresholding deciding which level of grey defines the limit between black and white i e between tree parts and the sky is the critical step M ost image processing software offer facilities that allow instant comparison between the original image a
39. e 70 H eight measurement e Crown width Crown diameter is measured in two perpendicular directions Crown projection 69 10 SExI FS User Guide diameter is first measured along maximum crown width axis and then perpendicularly to this first direction The average Is used for crown width Figure 71 For the purpose of recording the whole stand into SExI FS and get more accurate prediction of crown width the radius projection of crown can be measured with more then 4 direction Figure 72 shows how the eight radiuses are measured while also keeping the relative direction angle info Figure 71 Crown width measurement Figure 72 Crown radius measurement Crown Position CP The crown position index which depends on the relative position of the crown within the canopy reflects the light conditions prevailing ata particular moment Figure 73 Crown Position scale is defined as follows Alder and Synnott 1992 5 Emergent Crown plan exposed vertically and free from lateral competition at least within the 90 inverted cone subtended by the crown base 4 Full overhead light Crown plan fully exposed vertically but adjacent to other crowns of equal or greater height within the 90 cone 3 Some overhead light Crown partially exposed vertically but partly vertically shaded by other crowns 2 Some side light Crown plan entirely vertical ly shaded but exposed to some direct Figure 73 Dawkins crown position classificatio
40. e almost parallel and we therefore choose to analyse data using a GLM where sub population differ only in terms of their intercept i e assuming homogeneous slope In one case Paraserianthes this assumption is clearly not met but this may be due the data set used as a single very dense evene aged plot was sampled From the model above we Table 1 Estimates of flexi parameter for 6 species used in estimate three parameters SExI FS model for each species al a2 and b Species group Log ga X Sensi 1 And the ratio of the Lansium isolated 0 582 1 78961408 derivatives are equal to the dense plot 0 932 2 53958327 1 42 ratios of the al and a2 Durio isolated 0 399 1 49033362 parameters if b are dense plot 0 799 2 2233165 1 49 identical leading to the Archidendron isolated 0 84 2 31636698 estimates for the different dense plot 1 41 4 0959554 1 77 species reported in Table 1 Hevea isolated 0 963 2 61954333 dense plot 1 275 3 57870141 1 37 Rerunning the equal model Sengon isolated 0 853 2 34667633 without those two outliers dense plot 1 441 4 22491862 1 80 yielded similar estimates Alstonia isolated 0 006 0 99401796 for sensi Marked with an dense plot 0 268 1 30734714 1 32 asterisk in table beside SExI FS User Guide N ote on crown deformation parameterisation crown asymmetry resulting from neighborhood competition 1s commonly observable and has been measured Brisson 2001 H owever we have not yet attenpted to directly measure the p
41. e seen from the algorithm below and illustrated in the figures Thealgorithm Let H i j bea VBTs height at inclination index i and azimuth index j Assuming that each VBTs has height and horizontal distance from axis 0is the lowest VBT for each azimuth direction The following algorithm iterate the VBTs through the inclination index on the two following series of VBTs per azimuth directions H la JC and H Ib Jc 1 Step a For each increments of la and Ib start from a 0 and b 0 find Min H 11 JC H 12 Jc 1 store the result as one of triangle element If the lowest VBT is in series then a else b4 increase one step Find next element Min H i1 JC H I2 Jc 1 store it VBTs with the same index as the second element of triangle Step b If the two stored triangle element is on the same series of azimuth then the third element should bethe lowest element on opponent series Else increase the i of the lowest VBT series and find next Min H i1 Jc H i2 Jc 1 as the third element of triangle Store the last two elements of the previous triangle as the elements for the next triangle If there is more than 1 VBT left in both series then Go to step b SExI FS User Guide Else put the last VBT as the third element and Repeat from step a for the next j azimuth direction index j N ote the algorithm below is used for triangulation of semi irregular V Bs location previous crown type algor
42. e species Figure 34 The plot preview will immediately show up Figure 35 ah gt aber Plat x EF Proiectt be ah OM sperienz Pares n Widih Foto n Heg E Pii emgpiiie Figure 34 M ultiple species planting pattern Figure 35 Multiple species planting pattern preview SExI FS User Guide The tree pattern location and species can still be edited trough the tree table on the right of the plot pattern After creating the pattern click Plant Template button to create the template trees And click the Apply Template Trees button to finish the plantation 3 6 Construct Tree Users are able to reconstruct an established plot into SExI FS The geometry structure is as follow 1 X thex position of the tree base m 2 Y they position of the tree base m 3 Species the species label if the label is match with the one in the species list then it will be linked otherwise new species definition will be created DBH the diameter at breast height of the tree m H eight the height of the tree m CR Depth crown depth m CR Curve crown curve m CR Radius crown radius in vertical projection can be more then one value separated by semicolon m 9 Rotation arotation of the vertical projection of the crown geometry degree 10 CP crown position index 0 1 1l CF crown form index 0 1 o NoVA Figure 36 shows the parameters description of the tree geometry The definition of crown radius
43. ence given a weight of 0 5 both when computing density and basal area N ote in case of regular planting which for example may bethe case for rubber plantation the elementary plot may be delineated as a rectangle which is quicker in thefield including all 8 neighbouring trees two on thelineand thethree trees on each neighbouring planting line In that case the plot area is simply defined as 9 times average planting distance For all trees within a circular plot thefollowing three variables are recorded tree species tree diameter whether the tree neighbouring tree crown is in contact with target tree crown is Boolean 6 2 Data processing 6 2 1 DBH Crown diameter DBH and crown diameter are related by 30 linear regression Data from the various o Duku groups are pooled to establish this Durian relationship It is useful however to check _ n that groups do not differ significantly E20 Am biologically meaningfully rather than 5 statistically If scaling appears not to be isometric log log regression may be used m assuming a power relation between crown O width and stem diameter 6 2 2 DBH Crown surface o Assuming a half ellipsoid approximation E irm om di of the crown profile we then compute the i Figure 76 Girth Crown diameter relations approximate crown surface as SExI FS User Guide e 1 cr cr cd cd 0 5 if cd gt cr crown surface PI cd cd Pl cr cr e4n 1 e 1 e yelse
44. endent of the detailed tree architecture We reckon that a proper crown model should in particular be able to allow for the simulation of anumber of typical development trajectories Responses expected to be covered by the crown mode include e Flexible growth allocation ether towards lateral crown expansion or towards growth in height depending on the prevailing light environment Ex a sapling growing slowly with limited crown development in the understorey until a gap occurs in the canopy above it the successive release in growth rush towards the light and the subsequent vigorous lateral expansion of the tree crown once the tree has reached the upper canopy or possibly its death if the canopy gap closes by lateral growth before the tree makes it to the top e The model should be able to reproducethe change in crown ratio crown depth total tree height as well as the changein height dbh allometry coefficients observed for trees under different planting densities e The model should also be able to simulate the asymmetric growth resulting from row planting which allows an efficient occupation of space without significant decrease in overall tree growth rate cf low sensitivity of rubber dbh increment to planting pattern for a given planting density In the Stretch approach the crown is represented by a growing deformable solid This expanding polyhedron is defined by a set of vectors later referred to as Virtual Branche
45. f any VB is afunction of its relative position in the crown Dbh CW is entered by user as a bilinear relationship linear from 0 to 0 05 m dbh and then from 0 05 to max dbh but is re implemented as a power function to avoid discontinuity problems 57 SExI FS User Guide 3 Vertical stretching resulting from reallocation of growth from lateral expansion to height increase a response to the light gradient it is constrained by species specific plasticity flexi Vertical stretching of crown is done by co limiting its lateral extension through associated limitation in dbh increment assuming that total stem biomass scales isometrically with the product of stem cross sectional area and tree height Crown size is further reduced shedding lower VBs via the relationship linking maximum crown volume to dbh established for free growing trees 4 A local deformation factor The impact of local light level spatial heterogeneity of the incoming light light anisotropy is modeled by modulating the horizontal extension as a function of the relative to average illumination of light sector associated to each VB The degree of crown plasticity is assumed to be identical to flexi and is hence species specific Some additional species specific parameter might be necessary to refine species differences This flexibility can be adjusted through the amplitude of the sectoral light used to define the local light level the larger the sector the lesser the differen
46. f current dbh as follows 1 dbh init E dbh inc dbh init c k dbh max See Documentation chapter for detail The parameter of c and k can be obtained from N on linear regression of DBH DBH increment plot Calibration Procedures on Chapter 6 3 3 3 Height Allometry A reference allometric function relates tree height to tree dbh height a dbi Height A is parameter name for o alpha and Height B is parameter name for p beta 21 SExI FS User Guide Where H eight M ax Absolute is species maximum possible height 3 3 4 Crown Allometry The crown width is linearly related to tree dbh by the following function Crown Width A B DBH The parameters Crown Width A and Crown Width B refer to A and B in the above formula See Documentation chapter for detail 3 3 5 Light Sensitivity The parameters here definethe light stress factor of thetree growth e Minimum Light Level The minimum light level for a tree to grows e Optimum Light Level The optimum light level for a tree to grows The curve below shows the light stress factor derived from the parameters Light Stress CP Q min opt 1 CP is Crown Position an index a measure of light ratio receipt by a tree e Flexi isa parameter which measures the ratio of height growth rates under the most contrasted light conditions between 0 and 1 e Sensi is a measure of how sensitive the species is to shading sensi gt 1 e g 2 typical of a s
47. g default configuration or a pre defined XML configuration file The XML configuration file can be created by saving a modified project as a configuration file see Figure 7b thus thefile can be modified externaly using XML or text editor If default project option is chosen the plot sizeinput dialog will show up Figure 9 Set the simulation Plot Size and click ok Create Simulation Pre i x Wirth ori 100 Heigl my 100 mr Configuration File i al Figure 9 Plot sizeinput for default project Cancel b a Figure 8 New simulation project options New project options tree will be showed on the Projects window Figure 10 50 0 APS SEXI FS User Guide SExI FS Edpatzady Expacite irdividual baapd Forest Simuisioe cons New Simulation Project Figure 10 N ew project on main window 3 2 Project Setting Each project group consists of selectable section items for setting up the general environment species and plantation plot Figure 11 Highlighting each project sections will show their property options on the Properties window Figure 12 If the Properties window is closed you can double click the Section items to display it again r p k mL T St colin e Environment ge Light Capture Ili Fertility Map E Topography Scenana Species Component B tree Piot Figure 11 Project tree items t Properties amp 3 35 Project1 Label Projec
48. ght Break Function hc current height Enhanced height growth is achieved at the expense of dbh increment Assuming that total stem biomass scales isometrically with the product of stem cross sectional area and tree height the maximum possible height increment is then limited by actual dbh increment SExI FS User Guide Ah dbh 2h Adbh dbh 2Adbh Ah dbh h Adbh Adbh Ah dbh height _ inc _ max N ote that max_height increment is independent of tree current slenderness Then actual height increment is Height inc actual 2Min height inc elong height inc max Adjusting the actual dbh increment as the factor of slenderness e if height inc actual height_inc_max then dbh inc actual 0 e If height inc actual height inc max then Dbh inc 2 dbh h s Ah h Adbh 2Adbh h dbh Ah dbh Ah h s Ahc dbh h s dbh Ahc _ ac h s Ah c Wheres is the slenderness coefficient current height height of reference tree grown in the open dbh Adbh h Ah refer to dbh dbh inc height and height inc of reference tree and hc and Ahc stand for current height and height increment of actual tree 5 1 4 Crown Growth A tree crown is represented as a deformable solid Crown deformation can be global in response to increased shading or local in responseto radial anisotropy of incident light or spatial constraint Local deformation is mediated via a set of vectors stemming from crown base and subtending
49. h creating the template trees Figure 28 The spatial arrangement along which trees are planted is ether random manually specified for each tree or created by repeating a user defined regular planting pattern 3 5 1 Manual Planting To plant the trees manually press the M anual Manual Plant x button on Tree Planting tab Figure 29 species JA Speciest The manual planting dialog will show up Figure 29 Select the tree species and click Plant Plant Template Cancel Template Figure 29 Manual planting dialog SExI FS User Guide The tree plot will show up it remains hidden until then and you start to plant the trees by clicking on the plot A tree will be planted on the location you click Figure 30 To stop the planting model right click the mouse And to plant other tree species repeat the above procedure E Projects hcl here to plat Figure 30 Manual planting plot After creating the plantation template click the Apply Template Trees button below the template table Figure 28 The template trees will be cleared and the real trees are added to the plot 3 5 2 Randomize Planting To use the randomized template for tree planting Random Plant d press the Random button on Tree Planting tab Species DE Spectest Figure 28 The random planting dialog will show Mdr el up Figure 31 Select the species and set the number Random Sae of trees to be planted You can specify the random Plani 1esmpla
50. hade avoiding species and sensi 1 e g 0 5 of a shadetolerant species SExI FS User Guide 3 3 6 Regeneration e Beta Shape 1 Beta distribution function parameter 1 e Beta Shape 2 Beta distribution function parameter 2 e Immigration rate 6 0 theta is the relative weight of a species frequency in regional community versus Its frequency in the local community It is used to compute the effective contribution to local recruitment of any given species e Relative Abundance The relative abundance of the species in the meta community regional flora See documentation chapter for more details 3 3 7 Belowground e Root Influential Zone M odifier Species specific factor of root influential zone from default 20 DBH meters Index Of Root Anchoring calculated as Dv2 dbh2 where dbh is tree diameter at breast height 1 3 m height and Dv is the diameters of all vertical roots van Noordwijk 1999 Akinnifesi et al 2004 e Index Of Root Binding of Soil calculated as Dh2 dbh2 where Dh is the diameters of all horizontal roots Van Noordwijk 1999 Akinnifesi et al 2004 e Imperata Competition Factor Modifier factor for Imperata competitions The Index of Root Anchoring and Binding is a new added module Currently these parameters are used for the 3D visualization purpose only Figure 24 Future implementation will include this root module for belowground competition and soil Stabilization model 23 24 SExI FS User Guide
51. he plot By definition E 1 Let F betherelative effective abundance of species contributing to regeneration insidethe plot F is defined as 0 E nsa T 1 0 F tocal F JONES 1 0 F vu where 1 gt 9i gt 0 can be viewed as a measure of a species efficiency of dispersal Suppose that there are M light classes and let Aij be the relative abundance of species i in light class By definition vi A 1 j We further note Lj the relative frequency of recruits which fall into class j hence 2 which is determined in steps 2 and 3 j SExI FS User Guide We then compute the probability of recruiting a sapling of species in a cell belonging to light class j as Rij R PS i L j PC S i N L Jj P L j N oting that P S i N L amp j P S i P L j S i Fi Aij we obtain F Aj j 7 Step 5 Fine location of individual saplings within cells We have now defined for each cell the number of recruits and to which species they belong Wethen locate those randomly within their cell Parameters specific to the recruitment step Species specific parameters e Relative species abundance in overall community Each species in a scenario is attributed a weighting factor such that the ratio of this weight to the sum of weights over all species is equal to the relative abundance of that species in the metapopulation By default a new species is created with a weight of one e Species dispe
52. here the number of azimuth 8 a Light M odel Light Model settings control the level of detail used for exploring the sky vault i e the number of light beams and their weighting The number of inclinations and azimuths defines the number of beams The parameters of the light model are e Number of Azimuth Azimuth is the horizontal component of a direction compass direction measured around the horizon from the North point toward the East i e Clockwise e Number of Inclinations Inclination is the angular distance of the orbital plane from the plane of reference usually planet s equator or the ecliptic e Lowest Zenithal Angle Lowest Zenithal Angle defines the lowest angle considered for light calculation in radian e Interaction Distance The interaction area is limited by the Distance of Interaction setting The trees outside the radius of interaction distance and are not included in light attenuation calculation for target tree e Inclination weighted model There are three models you can choose from 1 SOC Standard Overcast Sky This model weights each direction according to surface of sky vault fraction SExI FS User Guide moreover assuming a decrease in light intensity from zenith to horizon using the formula Light x o x I 2 sin J 2 UOC Uniform Overcast Sky This model weights each direction according to the relative surface of the sky vault explored by each beam 3 Homogeneous This option gives e
53. in the SLIM section 5 1 7 Mortality Survival probability is computed from two parameters Min survival probability and m Min survival probability is the survival probability value of a completely suppressed plant no growth m is a parameter affecting curvature of the relationship between growth rate and survival probability This formulation is equivalent to a logistic model which is strictly equivalent mathematically speaking Log sp 1 sp 2ax4b equivalent to sp 1 1 exp ax b By default x should rather be a measure of relative growth rate instead of growth rate relative to max growth rate given current size as this would incorporate senescence However note that this will most probably not by easy to calibrate for all tree size and may haveto be refined one way would beto have size as a explicit predictor in addition to relative growth rate Survival probability increases with the ratio between actual and maximum growth rate r B dbh inc E dbh inc max sp MIN_ sp 1 min sp p Where m is mortality modifier SExI FS User Guide 23 sp 0 9 15 r Sp min m r min la min 1 sp 0 8 15 r o 9f 0 9 5 1 n a Survival probability 0 8 0 8 0 0 2 0 4 0 6 0 8 1 0 r 1 Growth rate relative to free growing Figure 64 Relationship used in SExI to relate survival probability to growth rate relative to free growing tree of similar size
54. ithm And it s quite robust a af B i ie A E I amp 4 i l rd ized p Y gt go nr g e la j Figure 68 Left figure shows the initial VBTs connection subpart of a crown VBTs right figure shows the VBTs connection after a VBT shed at i 0 and j 1 the series of VBTs at j1 then re indexed for i hi X JA 7 a wj Jo h Jz Figure 69 Connection after a VBT shed along the same line 5 2 7 Algorithm for crown volume computation Volume of the crown is calculated as the sum of all connected tetrahedra one face of which is a triangle of the crown envelope as a result of the triangulation described above Each triangle is then connected to the center of crown base added to each triangle as one other vertex to form a tetrahedron 66 SExI FS User Guide Then tetrahedron volume is calculated using the formula below Let the tetrahedron be specified by its polyhedron vertices at X y Z where 1 4 Then the volume is given by X Yi 4 1 B 1 X5 Yo 2 1 Ve 3 X4 V4 B 1 X4 Ya Z4 1 http mathworld wolfram com Tetrahedron html 5 2 8 Crown deformation and the pipe model theory We may need to explore further the application of the pipe model in order to link more formally crown volume and dbh values To maintain consistency between overall crown volume and tree diameter we further assume that leaf area and stem cross sectional area are linearly related This allomet
55. kbox is selected the crown is considered as partially transparent transparency Is also referred to as crown porosity in the following If Crown Permeability is not selected it is assumed to be totally opaque e Trunk Interception If Trunk Interception checkbox is selected the trunk is considered to intercept the light If Trunk Interception is not selected it s neglected 32 3 Fertility Map Setting Soil fertility is set manually for each cell of a grid covering the plot Missing data are interpolated using bilinear 3 dimensional interpolation Press et al 1992 Fertility values vary between 0 and 1 a fertility of one meaning there is no soil fertility related limitation r Friis go arjit E Wd Fee Mu NGO fi Figure 18 Fertility map setting To show the fertility map highlight the Fertility M ap project item on Projects windows check the Enable Soil Fertility checkbox on Properties window and click the Fertility M ap button below the table Figure 18 You can modify the fertility by either changing the fertility value on the table or by clicking the cells of the fertility map Change the fertility index value below the map and then click on the map The legend color shows the gradation of index value between 0 and 1 you can also click the legend color for changing the fertility index value SExI FS User Guide The fertility map can be saved and used for other simulation project 3 2 4 Topography Setti
56. lable on the Internet It can be downloaded freely from http www worldagroforestry org sea Products AFM odels SEX SExI FS is targeted to be platform independent It s developed using Java Programming Language It will be ableto run on any platform that supports Java Virtual Machine JVM Theinformation about Java Programming Languages and Java Virtual Machine can be accessed through http java sun com 1 3 The Minimum Requirement The minimum requirements to run the 3D visualization of SEXxI FS are 1 60M B Hard disk space Included JVM 2 VGA card with 3D graphics accelerator 3 128M B of RAM 4 PII 600M Hz or equivalent The minimum requirements to run SEXI FS without 3D Visualization are 1 60M B Hard disk space 2 32MB of RAM 3 Pentium PC 133M hz SExI FS User Guide ne x y c o p 2 Getting Started There are two installation packages with built up Java Virtual Machine JVM and without If you don t have a Java virtual machine installed on your computer be sure to get the package that includes one 2 1 Installation Theinstallation steps are as follow Step 1 Introduction It s displays general information about the software Press the N ext button to continue LIRE SP lei xd Introduction insalate ell gusde vou thraugh Ihe mabsitaton of SEHFE lite sirang recorrerenaied thar you quit all programs before tining Siih this Stellan Chck ine Hed button in proceed io the next Screen
57. n in Alder and Synnot 1992 SExI FS User Guide light due to a gap or edge of overhead canopy 1 No direct light Crown plan entirely shaded vertically and laterally Crown Form CF The Crown Form index tries to capture the photosynthetic potential of a tree It is an architectural characteristic and will tend to reflect the development history of the tree Figure 74 Crown Form scale is defined as follows Alder and Synnott 1992 5 Perfect The best size and development generally seen wide circular in plan symmetrical 4 Good Very near ideal sylviculturally satisfactory but with some slight defect of symmetry or some dead branch tips 3 Tolerable J ust sylviculturally satisfactory distinctly asymmetrical or thin but apparently capable of improvement if given more space 2 Poor Distinctly unsatisfactory with extensive dieback strong asymmetry and few branches but probably capable of surviving 1 Very Poor Definitely degenerating or suppressed or badly damaged and probably incapable of increasing its growth rate or responding to liberation A 4 E COMPLETE CIRCLE REGULAR GELE TOLERABLE FOCA EAT POOR PERFECT Boon HALF CAWN LESS THAN HALF CROWN OME D FEW BRANCHES Figure 74 Dawkins crown form classification in Alder and Synnot 1992 e Crown porosity isolated dominant co dominant trees Crown porosity to light is defined as the percentage of sky visible from below the crown and is simply assesse
58. ncrement is used to adjust the dbh ince dbh using a Chapman Richard function with standard non linear regression procedures Using precisely the method described above on PSP sample plot for rubber and comparing the growth rate as a function of size obtained from Sembawa plantings we can observe that the patterns are not consistent Essentially data from PSP provide an estimate of maximum potential growth which is strictly decreasing with tree size whereas data from Sembawa density trial indicate that maximum growth rate may be attained later in case of low density 6x6 planting pattern SExI FS User Guide 0 04 0 03 oc oc O O Z O 0 02 I en SPACE C o 3x3 0 01 Aj x 3x4 r 4x4 A 5x5 v 6x6 0 00 0 00 0 05 0 10 0 15 0 20 DBH Figure 77 PSP standardised dbh increment data Figure 78 Density trial annual dbh increment in m per year computed for CF 5 CP 3 and no tapping in cm per year plot average values tapping starts around 0 15 cm dbh This strictly decreasing growth rate with sizefound in analysing the PSP data instead of the expected typical increase and decrease in growth rate is probably at least partly dueto thefact that the monitoring starts at about the size when the rubber reaches its maximum growth Early growth needed in the model if we want to simulate growth starting at diameters less than 0 05 m cannot be directly esti mated from PSP data but need to rely on additional measurements this was done by u
59. nd Africa The project is led by the World Agroforestry Centre ICRAF in collaboration with the Indonesian Rubber Research Institute Indonesia Prince of Songkla University Thailand Centre de Coop ration Internationale en Recherche Agronomique pour le Developpement CIRAD France University of Helsinki Finland and Kasetsart University Thailand The Spatially Explicit Individual based Forest Simulator SExI FS software was developed under various projects in collaboration between World Agroforestry Centre ICRAF and Institut de Recherche pour le D veloppement IRD The current version of the model is adapted for smallholder rubber based agroforestry system under the SRAS project This manual includes the latest version of the software Content 1 General Information nes ns sas ss chasses CERRAR ORC Rn 1 INNO l L2 He SEXES SON atu ipta ictor v odo Md d EORR don ae dae 3 1 3 The Minimum Requirement 3 2 Getting Startegucesassssskkhsar bes Sigur ERA EGG ER Kg da P En RA 5 AMI AO ee ss mes 5 2 2 RUNNING SEXI FS cuc a aa aura cor nds onto due 8 3 USES MONO cas dc a n on der doom 9 3 1 Create New Simulation Project 9 22 Project SN a da bos dau bea OP E has a toile 9 3 3 Species SCLUTIOS sna ee ts boats CR RERO REN bag anata Ges 19 3 4 Evaluate Species 24 3 5 TFeG PNA 1 3 30952 1
60. nd regular tending takes the form of seedlings transplanting selective cleaning and felling adjusted harvesting intensity Farmers approach appears to bein line with two basic tenets of biology first individuals are all different with behavior and physiology that result from a unique combination of genetic and environmental influence and second interactions are inherently local Based on the same premises a computer model was developed to explore different management scenarios The model uses an object oriented approach where each tree is represented by an instance of a generic class of tree The simulated object trees mimicking real trees interact through modifying their neighbors environment These modifications are mediated through two major resources space and light A 3D representation of a one hectare plot of forest serves as the grounds for the simulation of this competition The major objective of such a model is to get a coherent dynamic representation of a complex system where complexity refers here to the assemblage of locally interacting individuals with different properties more than to the complexity of the elementary processes involved The model provides insight on what arethe critical processes and parameters of the dynamic of the system It should also allow exploring prospective management scenarios help assessing the relevance of present management techniques etc M odel sensitivity tests confirm the importance of
61. nd the classified image which provide some control over the quality of the thresholding step N ote crown porosity cannot be measured on trees growing in theunderstorey This may be problematic as there areindications that tree porosity is responsiveto tree growth environment and may besignificantly lower in shaded trees than trees fully exposed to light 6 1 3 Tree growth environment When relating tree dimensions to its growth environment care should to betaken in making sure that the current environment does reflect the growth environment of the tree which may have changed over time through self thinning tree fall creating gaps differential growth rates in height affecting CP etc Local density and local basal area are recorded by measuring the trees growing in the vicinity of the target tree A tree is recorded if its dbh is gt 5 cm SExI FS User Guide 73 A circular plot with radius rmax around the target tree is defined with rmax max r1 r2 Where r1 is defined as the maximum crown width of target tree and r2 equals the distance to the furthest tree in physical contact with target tree If rmax r1 then local density is simply computed as total number of trees divided by plot area Pi rmax 2 by and local basal area as the sum of all cross sectional areas of individual trees divided by plot area If rmax r2 then local the furthest tree which defines the plot radius is counted as half inside and half outside the plot and h
62. ng A particular topographic settings can be specified But enabling this option will disable the torus space model The area outside the border will be considered as an empty space E Mi Pratt Vrapas Tis in F iiiki dg iy e v Bibi l ger eph gi if Li u c m hmg Tem i a j 2ib Ei view B nn m pr rm sc is ating Figure 19 Topography setting To add the topography information you can insert one by one the altitude data to the table Or load the file that consists of altitude data The file can be as tabulated data format with one line of header Each line of data should consist of three values X Y and Altitude The unit is meter m The example of the format data is as follow X Y Altitude O 0 25 0 5 20 693 0 10 18 255 0 15 17 062 0 20 16 492 The altitude at any location on the plot will be interpolated using bilinear 3 dimensional interpolation Press et al 1992 based on the available topography information The topography can be check using 3D visualization by clicking the View button below the table The data can still be modified and click Refresh button to update the visualization 17 SExI FS User Guide The 3D Visualization object can be dragged using to view the other angle The toolbar below the 3D panel can be used to changes the projection Perspective or Parallel Zooming the slider and view the exact object side combo box Bilinear interpolation Press et al 1992 is used to determine
63. nual plot management Y ou may cut the trees for logging purpose or others Figure 45 show the simulation plot after 10 years of simulation using default parameters Y ou can select and cut the trees and run the simulation again for a number of iteration Tree Hemiphot Show hemispherical photograph model as viewed by the selected tree Show 3D View the 3D visualization of the trees 4 2 3D Visualization You can explore the tree in 3D Graphics Make sure that you have minimum requirement for viewing the 3D graphics see section 1 3 Minimum Requirement Select the trees and right click then select the Show 3D option The 3D visualization will show up Figure 46 You show the 3D visualization without selecting the trees to show the whole plot SExI FS User Guide a 3 a mira je as Figure 47 Virtual Control Figure 46 3D visualization The 3D view options are as follow Crown View the crown Branches View the branches amp Leaves View the artificial leaves visualization Wireframe Show in wireframe mode Solid Show in solid mode Textured Show the textured object Morphing Show a smooth change between animation steps You can control the angle view of the 3D visualization using the virtual control shown on Figure 47 Or you can directly use your mouse to rotate the 3D object on 3D window In this 3D visualization you can play the animation by pressing the Play
64. o use the more detailed light calculation to compute available light at ground level By default the light calculation for each grid cell on the light map uses Simple Vertical Light Calculation The plot is divided into a grid of cells default size 5 by 5 m For each cell at each time step a coarse index of light availability is computed based on overhead light of target cell and 8 immediate neighbors a single vertical direction originating from center of cell is explored for each cell The average of canopy openness on each grid cell is used in the Figure SEINE Sampie recruitment process to assess suitability of light regime The elaborate light map uses the hemispherical photograph method which can capture a more realistic light penetration to the ground This option will require more computation time but is necessary for proper simulation of the recruitment process 3 2 1 2 Belowground e Belowground Competition Enable Belowground competition option to simulate below ground competition between neighboring trees The parameters for root influential zone are explained in section 3 3 7 e Imperata Set this to true for enabling the Imperata obnoxious weed competition e Enable Soil Fertility Set this to true for enabling the Soil Fertility map Soil fertility is set manually for each cell of a grid covering the plot or read from a text file Missing data are interpolated using bilinear 3 dimensional interpolation Press et al 199
65. ological constraints such as pest pressure diseases etc not yet implemented QOO Oo D a Light Stress SExI FS User Guide Light stress is related to light capture i e crown position index value in a species specific way Growth Reduction Factor 0 8 0 6 0 4 0 2 Shade Tolerant Intermediate Light Demanding 0 0 0 0 0 2 0 4 0 6 0 8 1 0 Light Index CP Figure 54 Typical shape of the relation between light index and growth reduction factor for different levels of shade tolerance Min Minimum level for growth to occur Opt Optimum level for growth CP stands for Crown Position which is an index of access to light The computation of this index is explained in details in section 3 2 2 Light Capture Setting In short Crown Position is computed based on a virtual hemispherical photograph that would betaken at tree crown base the target tree crown itself being completely transparent Figure 55 H emispherical Photograph left compare with the model calculated right in high resolution method SEXI FS User Guide 42 i z Li y uri Er ie C hei P Pi a FATE pe TTE uaa us Rs Figure 56 Low resolution H emiphot shows a CP 0 398 on range O 1 b Crown Form CF Crown Form is an index based on the ratio of actual crown size to normal crown size of atree with same DBH Thecrown sizeis defined by the surface area or alternatively the surfa
66. p is set to 5 equal to number of inclination in the light model medium precision Orientations of VBs is randomized by choosing the first VB randomly N ote N umber of V Bs and sectoral light resolution is not accessibleto user Sectoral map calculation algorithm outline If number of sectoral Map azimuths is less than number of light model azimuths or number of sectoral Map inclinations is less then number of light model inclinations for each sector of sectoral light map find all light model sectors which intersect with the sector of sectoral light map Then set the value for the selected sector of sectoral light map as the average of intersected light model sectors value Else Set the sector value of sectoral light map to the value of the closest sector of light model For each of the 15 1 15 VB directions excluding vertical VBs we compute an index of efficient lighting for each direction and the average value of the index Note that this is done for all directions whether there is or not a corresponding VB alive Theratio of this light level to the average light level is used to adjust the horizontal component of growth for each growing VB N ote that whether there are V Bs missing or halted does not affect the deformation of the remaining Vbs Also note that the growth modifier may theoretically reach values as high as the number of directions This would happen in case all directions but one have effective light of zero
67. qual weight to each direction sampled e Default Light Capture Position These are the position within a tree where the light hemi phot is captured and used as light info for the subject tree The available position options are l Tree apex 2 Crown center 3 Crown base 4 Crown onethird 5 ree base b Spatial environment Torus Space If selected then the plot is assumed to be toric in such case the plot has no borders as the trees from one side of the plot act as neighbors for the trees on the opposite side If not selected then the plot is limited by the border N ote that the area outside the border is considered as an open area In geometry a torus pl tori is a doughnut shaped surface of revolution generated by revolving a circle about an axis coplanar with the circle The sphereis a special case of the torus obtained when the axis of rotation is a diameter of the circle If the axis of rotation does not intersect the circle thetorus has a holein the middle and resembles a ring doughnut a hula hoop or an inflated tire Theother case when the axis of rotation is a chord of the circle produces a sort of squashed sphere resembling a round cushion Torus was the Latin word for a cushion of this shape Topography If topography is selected the plot will using the topography data if any elsethe plot is assumed to be flat 15 6 SExI FS User Guide c Interception e Crown Permeability If Crown Permeability chec
68. ric relationship based on the functional relation between sapwood area and leaf area is expected to be robust M orataya et al 1999 and hold under the following provisions a Stem diameter is measured just below crown instead of breast height b Relationship ts location specific under different evaporative demand this relation may be significantly altered Then LA is further broken down into crown volume and leaf area density per unit volume Assuming LAD to remain stable across time and space within a particular tree this implies that we can extend the allometric relation between stem diameter and LA to stem diameter below crown and crown volume or crown surface if we consider that leaves are predominantly located on a thin layer on the outer most side of the crown This relation is used to enforce branch shedding under extreme deformation elongation of tree in response to light gradient i e as crown volume is constrained the lower most branches are shed A tapering equation could be used to link dbh and diameter below crown so that the assumption of linear relation between stem cross sectional area and leaf area would be more robust In first approximation a conical truncated shape may be used based on data collected by Hubert de Foresta in Krui for example for the part between diameter at breast height and diameter at crown base height but see also for a discussion of the various approaches that may be used http sres
69. rown the horizontal component of growth of that VB is set to 0 but height increment is still applied to ensure decent crown profile Conical profile Assumptions identical to above implicit assumption dbh 2dcbh To maintain conical profile we compute the expected displacement absolute increment of all VBTips as a function of height growth and lateral extension of crown base Let H bethe crown depth length and L the expected not necessarily equal to actual crown radius at crown base for previous dbh before current time step increment then expected V B length of angle with vertical is sin L cos H 1 let L 2aL height increment and H expected crown radius at crown base for new dbh previous dbh dbh inc then expected new length of VB with angle with vertical is l 2 sin L cos H 1 and the current increment in length of VB of angle is computed as l l Where L a dbh b 2 SEXI FS User Guide 60 Lateral deformation of crown Based on the sky map and the light model adjust VB inc hor only for anisotropy of incoming light At this stage we assume that the number of VBs per tree is fixed and set to the following Default number of VBs on vertical direction is 15 6 degrees each and 15 Vbs for lateral direction 12 Degrees Then the default number of azimuths of the sectoral light map is set to 15 same as the number of VBs for a given indination The number of inclinations of the sectoral light ma
70. rsal limitation 1 0 reflects species dispersal limitation should be close to 0 for pioneer species and may be close to 0 for strongly aggregated species Overall parameters e a relative preference for empty cal default alpha 1 This is implemented in the following way Cels are given a weight of 1 o 1 where Lu is Lif call is occupied and Oif itis empty If o 0 then each cal is drawn randomly from the complete set of cells if o Zl then each cell is drawn randomly from the subset of empty cells note that after each draw the cells are re weighted to reflect change in occupancy Practically for 0 lt a lt 1 cells are placed on a line in an arbitrary order from O to sum of cell weights Cell i and call i 1 being separated by a distance equal to weight of cell i L Then a random number between 0 and Sum of weights is drawn and the recruit is allocated to the 51 SExI FS User Guide cal whose associated interval contains the value obtained randomly the call corresponding to the first graduation larger than the random number drawn e maximum sapling density The default value is set to 5000 per ha but may be changed according to local data and developmental stage considered for the recruitment step The light map used in the recruitment module is computed for a 1x 1m grid using the similar light calculations as for trees light index i e the so called detailed light map as opposed to the simple light map as described
71. s all stemming from the crown base The growth rate of those Virtual Branches VB is a function of local light conditions local response and their relative position to capturethe crown elongation a species specific characteristic The way in which VBs are affected by local light conditions or constrained by their relative position within the crown is species dependent 5 2 2 Ecological basis Biological Principles While overall growth as captured by the dbh increment will decrease under sub optimal or supra optimal light levels crown shape may also be affected by sub optimal or anisotropic light and in return affect overall growth performance Two major mechanisms may contribute to crown shape alteration under specific light conditions 29 50 SExI FS User Guide A Local asymmetric competition between branches within a tree The so called branch autonomy theory states that the local carbon balance between production and demand for growth and respiration determines the fate of the branch and notably whether it will be shed However there Is increasing evidence that such a simple view is not tenable H enriksson 2001 Sprugel 2002 Lacointe et al 2004 Notably it was shown that the light level at which a branch will be shed depends on the relative light level to the rest of the crown rather than the absolute level of light experienced Even though dominant trees have more resources to allocate branches on suppressed trees
72. s into 5 light classes The segmentation uses intervals equal to one fifth of the available light range K means clustering algorithm into homogeneous light classes or quantile based segmentation could be used as an alternative not yet tested Step 2 Determining the number of recruits For each light class determine recruitment rate from a recruitment function assuming that recruitment rate is a function of degree of saturation of the stand carrying capacity maximum sapling density which is itself limited by light availability Median value of light class is used to estimate carrying capacity per light class The default function used assumes that maxi mum density is proportional to the available light or its proxy canopy openness CO Default parameterisation uses sets maximum density in high light i e CO 1 to 5000 individuals per ha It is further assumed that sapling density will be 0 if CO 0 Recruitment rate is then fixed as proportional to each light class density deficit defined as max 0 max density obs density The suggested default valuefor recruitment rate is half of the density deficit and expressed as a number of recruits per unit area In other words it is assumed that the plot density would asymptotically reach its target maximum density with a rapid initial increment as 9596 of maximum density would be reached in just 4 time steps using the default parameterisation if the light conditions would not change 49
73. se Crown Form Index CF Update Crown Position Index CP Update Y Crow Volume a amad us l arai i Height Increment 4 DEH increment Figure 52 Main of SExI simulator 5 1 2 DBH Increment and growth reducers DBH as a function of time t follows a Chapman Richards function dbh dbh max e 40 SExI FS User Guide And approximating DBH annual increment with the first derivative of DBH with respect to time t one can express dbh increment as a function of current dbh as follows 1 dbh ine ie e eg dbh_max One can note that maximum increment is then c l dbh inc max dbh_max k I C which is attained when C dbh dbh _max I Default initial diameter is one cm DSH Increment Giyadt m i DHH Fe idh Ci D d COUR OEH iyi y ose ooj me 138 Figure 53 DBH Increment Function Potential DBH increment as defined above is reduced by the effect of aboveground and belowground competition Thus the actual DBH increment is dbh inc act dbh_inc growth_reducer Growth reducers considered in this model are Light Stress Crown Position Index Crown Form Index Local fertility index Tree Production Effect competition for carbon allocation between growth and production of resin latex or fruit Belowground competition based on local crowding Other possible growth reducers could relate to other ec
74. sing data from other experimental plots where growth of seedling was measured starting from planting Why should maximum potential growth decrease faster in PSP even after increments have been corrected for CF CP and tapping than what is observed in low density plantation trials There are at least two possible explanations The first oneis that below ground competition which we have not corrected for is stronger in PSP mature agroforest than in young plantations whereit is minimal during the earlier stages A similar conclusion i e that below ground competition most probably limits early growth of rubber saplings grown in rubber agroforest was reached after careful comparison of growth of rubber plants under artificial shading and under live canopy Vincent et al in prep H owever such an explanation is not entirely satisfactory as high below ground competition should most likely translate into a sustained lower growth rate over the whole period of early growth and cannot be unequivocally related to a shift in maximum dbh growth rate Another possible explanation is that the difference observed betw een rubber agroforest and young plantation reflects the fact that dbh 11 SExI FS User Guide increment in young trees growing under strong light gradient may be reduced as a consequence of accelerated height growth which occurs under limited light and which correlatively limits diameter increment To test this hypothesis we can test
75. statistical packages but requires the development of a global optimization algorithm see Canham et al 2004 for such an example which we have not done yet 19 SExI FS User Guide References Akinnifesi F K RoweE C Livesley Kwesiga F R Van Lauwe B and Alegre C 2004 Tree root architecture In Van Noordwijk M Cadisch G and Ong C K eds Below ground interactions in tropical agroecosystems Concepts and models with multiple plant components CABI publishing p 61 82 Alder D Synnott T J 1992 Permanent sample plot techniques for mixed tropical forest Tropical Forestry Paper 25 Oxford Forestry Institute Department of Plant Science Oxford Brisson J 2001 Neighborhood competition and crown asymmetry in Acer saccharum Can J For Res Rev Can Rech For 31 2151 2159 Canham C D LePage P T Coates K D 2004 A neighborhood analysis of canopy tree competition effects of shading versus crowding Canadian Journal of Forest Research Revue Canadienne De Recherche Forestiere 34 4 778 787 Gilbert R Seavers G P Jarvis P G Smith H 1995 Photomorphogenesis and canopy dynamics Phytochrome mediated proximity perception accounts for the growth dynamics of canopies of populus trihocarpa x deltoides Beaupr Plant Cell and Environment 18 475 497 Grist P Menz K Thomas 1998 Modified BEAM Rubber Agroforestry Models RRYIELD and RRECON Canberra Australia ACIAR Hall F Oldeman R A A Tomlinson P B 1978 Tropical
76. te Cancel seed for controlling the random generator Click a Plant Tem plate Figure 31 Random planting dialog 2 SExI FS User Guide To add more trees repeat the above procedure Click the Apply Template Trees button below the template table Figure 28 to finish the plantation The template trees will be cleared and the real trees are added to the plot 3 5 3 Pattern Planting To plant the template trees using pattern press the Pattern button on the Tree Planting tab Figure 28 The pattern planting dialog will show up Figure 32 Select the Species and set the size of the pattern Click on the pattern plot to place the tree template as pattern The plot will show a preview of the current pattern Figure 33 3 Haltern Pari BJ Project1 species gii Species iam ec n smt Prec n Height POPP eee eee eee eee eee eee ee s Lonbosdasobrelsedsechiest CRRELENEZ GGG ERREUR DOOR Oe eee eee eee eee eee eee eee eee ee rrr errr verre ree eS ORR ee eee eee eee eee eee eee eee ee beobeodeccelocbeodoeceo esstosdesshes GGG tondeuses DOOR IO eee ee Cee eee eee eee eee eee eee ee ee eRe eee eee eee eee eee ere eee eee ee ee epee eee eee eee eee eee eee ere ee eee ee eee ee eee eee eee eee eee eee BOAR eee eee eee eee eee eee eee Maid leita Figure 32 Single species planting pattern Figure 33 Single species planting pattern preview You can create pattern with more than a single tre
77. th in diameter appears to be advantageous under specific conditions and disadvantageous under others If all soecies in the mixture share the same ability and the same sensitivity to light level then this potential competitive advantage turns out to be disadvantageous both for individual tree growth and for overall plot productivity But when trees with different sensitivity to light level or different ability to alter their allocation of growth between height and diameter occur ina mixture then this capacity proves to be an effective competitive advantage for individual species By accelerating the establishment of a multi strata structure It also increases the overall productivity of the plot through better allocation of spatial resources Similarly rather counter intuitively an increased growth rate for a given crown size appears to be an advantage for a species under certain circumstances but not all under very crowded conditions large crowns showing low efficiency in terms of light and space utilization can show competitive advantage by suffering less from crown encroachment and shading out competitor more efficiently These are but a few examples of the insight such generic models can bring More direct applications of the model include comparing alternative scenarios in terms of financial return for instance involving rotational versus permanent agroforests etc SExI FS User Guide 1 2 The SExI FS Software SExI FS software is avai
78. ti Description imulation Project Simulation Age 0 Number of Trees 0 Plot Size 100 0 x 100 0 Figure 12 Project properties SExI FS User Guide Highlight the root project section The main project property will show in the Properties windows Define the project name and description You can t run the simulation before you plant trees on the plot or add some pioneer species component You can use default setting and jump to Tree Plot section to start planting the trees Or define your preferred setting for this simulation project 3 2 1 Environment Setting Under the Environment tab values of some general parameters used in the Regeneration module and the Belowground competition module are set The random seed is for the user to contro the random generator used here Properties e E mar onmes Fes mcg 9 Liga Randorn Seed Regeneration Natural Mortatif Use Raion Seed whether use defined random seed or no gr Setting Figure 13 Environment Setting 3 2 1 1 Regeneration e Natural Mortality Set this setting to true for enabling natural mortality e Natural Recruitment Set this setting to true for enabling natural regeneration 11 SExI FS User Guide e Empty Cell Preference Controls the regularity of spacing of juveniles 0 completely random 1 most even e Max Density Maximum density trees per ha Recruitment ceases once max density is reached e Elaborate Light M ap Set this to true t
79. ties Component Speech Compani mW M Species 1 a Species A Species Pism Trees Figure 22 Species component properties 10 SExI FS User Guide Once you have added some species component to the list highlight one of the species item on the Projects window or double click the one on Properties window both will have the same list of species The properties window will show the parameters of the species selected Figure 23 You can directly modify the parameters according to your preferences Label and description are identification for the species And the color is used for visualization purposes only legend It is not meant to simulate the real color of the tree species Other parameters are grouped according to their function as explained right Figure 23 Species parameters 3 3 1 Basic Characteristics Here arethe general characteristics of a species e Initial DBH Properties Species 1 1 Label Species Description Species Description Legend Color HROG255B0 Basic Characteristics nit 3 D BH JU r n Zr mess Survival Probability Mortality Modifie 2nd Mortality Probability iit Size DBH gt DBH Function DBH Maximur BH i Height Allometry Height Height Max Absolute 9 Crown Allometry e wT T town Width E 9 Light Sensitivity Mininum Light Leye L ght L ave ensi Crow gt Regeneration Beta Shape 1 T r Seta Shane alatrya Abundance o Belowground F t
80. um 2 OnceVB have grown the crown surface is checked against the expected crown surface cf allometric relation between dbh and crown volume in reference open grown trees In case current crown surface is above reference crown surface additional selective branch shedding will occur until crown surface is reduced to the maximum possible crown surface V Bs are dropped one by one starting with the VB receiving the lowest light comparing lower most vb along all azimuths As an alternative crown volume may be used instead of crown surface as a measure of crown size The procedure is similar to using crown surface as a control First each VB is assigned a weight approximating its contribution to crown volume The elementary volume associated to a VB used to compute is weight is the volume of the 2 tetrahedra defined by the three vertices defined by the closest 3 neighbouring VBs left right and top neighbours and the target VB itself The weight of a VB is then computed as the sum of the elementary volume assigned to it to the sum of all such elementary volumes When a particular VB is dropped the total crown volume is reduced proportionally to the weight of the shed VB SExI FS User Guide N otes If systematic crown rise of reference tree occurs it should be specified through the graphic user interface can NO significant crown overlapping is tolerated in the model except for possible in growth of a treewithin alarger overhanging cro
81. ummary Step 5 Install complete Done you can start using the software Simi Et Install Complete Congratulations SEx FS nas been successfully installed 1 CP rograen F hes SExt FS Press Done 1n gull tie installer Figure 5 Install complete 50 9 te SExI FS User Guide 2 2 Running SExI FS Double click the SExI FS shortcut on your computer By default it will be under Start gt Programs gt SExI FS on Microsoft Windows The application will start with the main window as showed in Figure 6 It consists of Projects windows left Welcome windows center and Properties windows right pue CICE nip RAE ima GM afaa Typen Wak nn pain SExI FS paiay EDT Serial Sirili Create Maw Sleirilati r Prajord Figure 6 Main Window SExI FS User Guide 3 User Manual 3 1 Create New Simulation Project You can create new projects either via the File menu on the M enu Bar Figure 7a or directly by clicking the New project options in Welcome window GE TE IN File Project Tree Plot Help File Project Tree Piot Help I Load Project ud Save Ase 8 o VE TRE e neg dr Sae contiguration Exit Application gt Run Figure 7a File menu Trew Plot O Show 30 TE 3D Roots View T Tree kata tight Tatie AX Close Figure 7b Save Configuration If you select the N ew project menu trough the File menu bar it will show the same options Figure 8 You can create a new project either by usin
82. w 0 Some typical values for the two parameters are reported below and the corresponding function plotted in the graph below where X refers to canopy openness Shade tolerant shp1 2 shp2 10 eg duku RED Light demanding shp124 shp2 12 e g damar rubber BLUE Pioneer shp1 12 shp2 8 eg pulai GREEN 5 A Figure 63 Hypothetical density probability functions 0 bis of sapling presence as a function of canopy openness 0 0 0 2 0 4 0 6 0 8 1 0 SExI FS User Guide Therecruitment rate number of saplings recruited per unit area per unit time is a function of the level of saturation of the plot carrying capacity Carrying capacity is itself considered to increase linearly from 0 to maximum carrying capacity as canopy openness ranges from Oto 1 Contribution to the recruitment rate of the various species depend on the meta community composition relative abundance in regional floristic pool and local community composition relative abundance of adult trees per species in plot Let be the relative weight of meta community composition in recruitment It may be hypothesized that everything else being equal will decrease with increasing size of plot and with plot compactness area border Thealgorithm is based on a light map available at 1 m above ground level and a map of distribution of the existing trees and is outlined below Outline of recruitment algorithm Step 1 Light map segmentation Sort light map elementary cell
83. wever the VB growing from inside another crown will be halted if they cometo intersect with containing crown envelope Note that crown shyness is used hereto refer to the reaction of a tree crown colliding with another tree rather than in the more restricted meaning it usually refers to individual subcrowns and crowns which grow clearly separated from one another with intervening vegetation free borders most common in single specie and single cohort stands and in stands on windy sites Two primary hypotheses have been put forth to explain canopy shyness the first that wind blown branches abrade each other at tree boundaries and damage buds preventing leafing and the second that mutual shading at the boundaries of trees prevents growth Putz et al 1984 and see Rudnicki et al 2003 Stand structure governs the crown collisions of lodgepole pine Can J For Res 33 7 1238 1244 63 SExI FS User Guide 5 2 6 Triangulation algorithm A proprietary triangulation algorithm is used which takes advantage of the fact that VBs are regularly spread and notably that on a given azimuth there can be no missing VB between lower most VB and apex Let n be the number of azimuth and p the number of inclinations The total number of VBs including apex in a full crown no missing VB is then n p 1 1 and the associated number of triangles is n 2 p 2 1 2n 2p 3 Each time a non vertical VB is dropped so are two triangles as can b
84. wn At present a species with low flexibility and high shade tolerance will show higher crown boldness as it will retain its VBs longer and fail to reallocate growth preferentially to well lit V Bs Differential crown shyness could further be controlled by limiting the number of steps a V B may survive if prevented from extending laterally As a consequence species tolerant to low light may in fine be even more tolerant to crown collision as they may be halted only temporarily and resume growth oncethe other crown has shed its branches At each time step V Bs areresampled along a set of fixed directions and V B tips new position interpolated from previous V Bs positions If V Bs are missing the lower most remaining V B is always located along the vector immediately below larger angle with vertical the existing V B at the same distance from tree vertical axis If all V Bs along a particular azimuth have been dropped a new V B is regenerated with length equal to average length of all V Bs of same inclination 5 2 5 Collision detection Collision determines halt of growth of VB The collision between neighboring crowns is detected if there is intersection between the horizontal vector joining VB tip to tree crown vertical axis and any triangle defined as a result of triangulation of VB tips location in 3D of neighboring trees N ote that as a result of this implementation vertical growth rate of tree top apex is not affected by collision Ho

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