User Manual for NetworkDistances 1.0: Calculating Network
Contents
1. 660000 662000 664000 666000 668000 UTM easting m Figure 5 Plot created by the function PlotNetworkPatches showing the eight habitat patches and two networks on the fourth iteration of the redside dace study area Note that patches Pop 4 Pop 6 and Pop 8 are all connected and are on network 2HC12 C5 these patches are not connected to the patches on network 2HC11_C5 e g Pop 1 Note also that patch names are shown in black for printing purposes but would normally be shown in green i e they have all been snapped to network lines cType Cluster type if doSnow Use SOCK for Windows machines or either SOCK or MPI for non Windows machines Value character nCores Number of cores for parallel processing if doSnow For example in Windows this indicates the number of instances of Rscript exe that are initialized and used in CalcDistMatrix dat Note that nCores controls a trade off between the number of cores and the memory available to each core Value integer 11 coreName Processor name if doSnow Value character e g localhost nZone UTM zone required to align patches and network lines Value integer doSpatPlots Set to TRUE to call PlotNetworkPatches and generate figures showing patches and networks for each iteration set to FALSE to skip this step Value logical networks Shapefile network name s not including extension s If there are mul tiple sh2. 739 HHAHHHHHHHHHMMHAHAMMMAHAAMHHAHAMMHAAAAMHAHAHH End of file NetworkDistances R TAL HHAHHMHHHHHMMHAHAMMHAHHAMHHAHAMMHHAHAHHAHAHH 28 INDEX calc_network_dist 10 CalcDistMatrix dat 8 CombineDistances dat 9 coreName 12 CreateUniqueID dat 7 cType 11 doSnow 10 doSpatPlots 12 EnsureUniqueSites dat 8 FillPairDists mat 9 ftM2graphNEL ft edgemode W 8 GetToFromDist dat 7 GridToUTM ptc asc 6 maxD 10 nCores 11 networks 12 NetworkShapefiles 12 nZone 12 PlotNetworkPatches 10 RDataOutDist 12 RDataOutTemp 12 RemoveDupPatches mat 9 SavedNetworkObjects 12 SnapToNodes pops 8 29
3. 437 End if there are rows in iNodes If there are no nodes dist is NA and print a warning 439 if dim iNodes 1 0 dVec lt NA Return the distance between the population point and the node 441 return min dVec End SnapToNodes function 443 Add patche to network 23 445 447 449 451 453 455 457 459 461 463 465 467 469 471 473 475 477 479 481 483 485 487 489 491 493 495 497 499 501 503 505 507 509 m i g i 8 C inDists lt apply X patches MARGIN 1 FUN SnapToNodes Append minDists to minDistMat This will allow the identification of patches that occur in multiple networks i e when maxD is too large and assign the patch to the network that is closest If it s the first iteration f i 1 Set up the empty matrix minDistMat lt matrix NA nrow nrow patches ncol length networks Name columns as networks colnames minDistMat lt networks Name rows as patches rownames minDistMat lt patches Site Add minDists to the ist column minDistMat 1 lt minDists End if the 1st iteration else Add minDists to the ith column minDistMat i lt minDists End if iteration is 2nd or more Collect garbage c Make the graph object Take in the toFromDist data frame and output the graph object indic
4. lt cbind mat colMat Set up a matrix for rows rowMat lt matrix NA nrow length noPatch ncol ncol mat Give it names rownames rowMat lt noPatch Append rows Zh 705 mat lt rbind mat rowMat Return the new table 707 return mat End FillPairDists function 709 Check if all the sites are in pairDists 711 if all patches Site Zin colnames pairDists If not run the function 713 pairDists lt FillPairDists mat pairDists End if there are missing sites 715 Order pairDists so that patches are in the original order 717 pairDists lt pairDists mixedsort colnames pairDists mixedsort colnames pairDists 719 Convert distances from m to km to conform with GRIP2 and RAMAS it is 721 crucial that users verify that distances are in the correct units pairDists lt pairDists 1000 723 Set the diagonal i e from the patch to itself from 0 0 to NA to 725 conform with GRIP2 and RAMAS diag pairDists lt NA 727 Save the habitat patches 729 save patches patchesUIM file paste RDataOutDist patches y RData sep 731 Save the pairwise distances with index y in newNreps 733 save pairDists file paste RDataQutDist pairDists y RData sep 735 Save the matrices indicating patches networks and distances snapped save minDistMat patchNetwork 737 file paste RDataOutDist patchNetworkDist y RData sep
5. toY lt datSID k 1 Y Get the UniqueID i e the river node numbers mat count frID lt datSID k UniqueID mat count toID lt datSID k 1 UniquelD Calculate the distance mat count dist lt sqrt datSID k X datSID k 1 X 2 datSID k Y datSID k 1 Y 2 End loop over rows within SID within PID End loop over SID within PID End loop over PID Remove rows that are NA these are due to repeated points return na omit mat End GetToFromDist function toFromDist lt GetToFromDist dat netVect Collect garbage gc Change the class of the toFromDist to a data frame to allow factors for node names population sampling points tfTable lt data frame friD toFromDist frID tolD toFromDist toID frxX toFromDist frx frY toFromDist frY toX toFromDist tox toY toFromDist toY dist toFromDist dist Remove toFromDist to save memory this can be a large object rm toFromDist Save the required objects for the next simulation save list c netVect tfTable file paste SavedNetworkObjects networks i RData sep J End if the saved object is not present in the working directory If the saved data object from a previous simulation IS available load the saved object to reduce computation time if desired if paste networks i RData sep in list files SavedNetworkObjects Load the
6. 41 43 45 47 49 3 Author Matthew H Grinnell Affiliation Pacific Biological Station Fisheries and Oceans Canada 5 Research group Conservation Biology Section Janelle M R Curtis Contact e mail matt grinnell dfo mpo gc ca tel 250 756 7326 7 e mail janelle curtis dfo mpo gc ca tel 250 756 7157 Project GRIP2 extension for movement between patches within networks 9 Code name NetworkDistances R Code version 1 0 11 Date started 2010 11 30 Date modified 2011 11 16 13 Goal Convert spatial lines i e networks and points i e patches to a 15 graph object and calculate network wise distances between each pair of habitat patches Output a matrix of pairwise distances pairDists which 17 is also saved as a RData object in the folder RDataOutDist These objects are indexed by iteration number y in newNreps e g pairDists 1 RData 19 Requirements This code is designed for use with GRIP 1 and RAMAS GIS 21 5 0 2 however the code could be modified for stand alone use Regardless of whether NetworkDistances is used alone or with GRIP2 read the 23 NetworkDistances user manual 3 for additional details 25 Notes Please contact the authors if you have suggestions comments or concerns Additionally we are attempting to keep track of this code s use 27 please contact the authors if the code was useful for research We recommend that users ve
7. only if there are elements to iNodes if dim iNodes 1 gt 1 Loop over nodes and calculate Euclidian distance for i in 1 nrow iNodes dVec i lt sqrt pt 1 iNodes X i 2 pt 2 iNodes y i 2 22 J End loop over rows in nodes 381 Ensure that the minimum distance is lt maxD note that this might not be true because dVec s are for points within the box but we need to 383 ensure that the radius is lt maxD if min dVec lt maxD 385 Determine the position of the closest select only one if a tie iRow lt which min dVec dVec 1 387 Get its unique ID iID lt iNodes UniqueID iRow 389 Determine whether the node is already a site This can occur if two sampling locations are close together and snap to the same node 391 Note that iID is a single number but may reference multiple nodes for example the node is a junction i e location at which two 393 streams merge If the node is not already a site 395 if is na netVect SiteName netVect UniqueID iID 1 Update the node to reflect that it s a sampling location from 397 tfTable frID tfTable frID iID lt lt pops Site Update the node to reflect that it s a sampling location to 399 tfTable toID tfTable toID iID lt lt pops Site Also update netVect to indicate population site and distance to 401 node netVect SiteName netVect UniqueID iID lt lt pops Site 403 ne
8. only ones that should be in distMat pnPatches lt rownames patchNetwork iRows Check that distMat doesn t have patches that aren t supposed to be in a different i e closer network if all colnames distMat in pnPatches FALSE Determine which patches should be included inclPatch lt which colnames distMat in pnPatches Subset distMat to include only patches that should be in the network distMat lt distMat inclPatch inclPatch If distMat is now empty i e there is only one patch ensure that it s a matrix with 1 row and 1 column with correct names and distance 0 if all distMat O 26 641 643 645 647 649 651 653 655 657 659 661 663 665 667 669 671 673 675 677 679 681 683 685 687 689 691 693 695 697 699 701 703 Make the matrix distMat lt matrix 0 nrow 1 ncol 1 Give it column and row names rownames distMat lt pnPatches colnames distMat lt pnPatches End if distMat is zero End if there are extra patches in distMat If there is data in distMat append the distances and names if is null dim distMat Get the number of rows nr lt nrow distMat If there are rows get data if nr gt 1 Append the names to the vector ptNames iRC iRC nr 1 lt rownames distMat Append distMat to the big matrix mat iRC iRC nr 1 iRC iRC nr 1 lt
9. 3 REFERENCES Ak akaya H R 2005 RAMAS GIS Linking spatial data with population viability analysis Applied Biomathematics URL www ramas com ramas htm gis User manual for version 5 Baddeley A and Turner R 2005 Spatstat An R package for analyzing spatial point patterns Journal of Statistical Software 12 6 1 42 URL www jstatsoft org R package version 1 21 6 Bivand R S Pebesma E J and G mez Rubio V 2008 Applied spatial data analysis with R Springer NY URL http www asdar book org R package version 0 9 80 Calenge C 2006 The package adehabitat for the R software A tool for the analysis of space and habitat use by animals Ecological Modelling 197 516 519 doi 10 1016 j ecolmodel 2006 03 017 R package version 1 8 4 Carey V Long L and Gentleman R 2010 RBGL An interface to the BOOST graph library URL http CRAN R project org package RBGL R package version 1 26 0 COSEWIC Committee on the Status of Endangered Wildlife in Canada 2007 COSEWIC assessment and update status report on the redside dace Clinosomus elongatus in Canada Technical Report Canadian Wildlife Service and Environment Canada URL www sararegistry gc ca status Csardi G and Nepusz T 2006 The igraph software package for complex network research InterJournal Complex Systems 1695 URL http igraph sf net R package version 0 5 5 2 Curtis J M R and Naujokaitis Lewis I R 2008a Sensitivity of population vi
10. A simple simulation model of dispersal of animals among units of discrete habitats Oecologia 7 2 95 116 doi 10 1007 BF00346353 Lewin Koh N J and Bivand R 2011 maptools Tools for reading and handling spatial objects URL http CRAN R project org package maptools With con tributions from E J Pebesma E Archer A Baddeley H J Bibiko S Dray D Forrest M Friendly P Giraudoux D Golicher V G Rubio P Hausmann K O Hufthammer T Jagger S P Luque D MacQueen A Niccolai T Short B Stabler and R Turner R package version 0 8 6 NRC Natural Resources Canada 2011 GeoGratis Geospatial data available online at no cost and without restrictions URL http geogratis gc ca Retrieved 5 January 2011 Pebesma E J and Bivand R S 2005 Classes and methods for spatial data in R R News 5 2 9 13 URL http cran r project org doc Rnews R package version 0 9 80 Peng R D 2010 gpclib General polygon clipping library for R URL http CRAN R project org package gpclib With contributions from D Murdoch and B Rowlingson GPC library by A Murta R package version 1 5 1 Poos M S and Jackson D A in press Incorporating species specific data into patch occupancy models Impact of dispersal on estimates of viability of stream metapopulations Landscape Ecology doi 10 1007 s10980 011 9683 2 RDCT R Development Core Team 2011 R A language and environment for statisti cal computing URL www R proj
11. NetworkDistances is sourced via GRIP2 there may be duplicate patch IDs if NetworkDistances is run independently This function can use parallel processing to decrease processing time if doSnow is TRUE Section 5 Note that the distance from the patch to the network minDists is not included in the pairwise distance calculation because the patch is technically on the network even if the patch s center is shifted slightly The argument dat is the graph object and the function returns distMat a matrix of pairwise dis tances with row and column names corresponding to patch names The distMat object is saved as a distMat netVect RData object in the folder RDataOutTemp so that distances between points in independent sub networks can be brought together as one large distance matrix using CombineDistances dat in Step 3 3 Combine the pairwise distance matrices from each independent sub network into one large matrix RemoveDupPatches mat Ensure that each patch is only in one network and ignore networks that do not contain any patches This function ensures that each patch is snapped to the network with the single closest node For example large maxD values can cause patches to be inadvertently snapped to two networks if patches are located within maxD of nodes on both networks The argument mat is the matrix of minDists named minDistMat which has a column for each network and a row for each patch The function returns patchNetwork wi
12. POS X Y Get the original river points patches lt patchesUTM If the saved data object from a previous simulation is NOT available in the working directory run the entire analysis this may take some time and save the required object for the next simulation if paste networks i RData sep Zin list files SavedNetworkObjects Create a column to indicate the unique ID for each unique node Note that some nodes are repeated i e the bottom coordinates of two streams that merge Gi e become one large stream will be the same as the top coordinates of the stream that they merge into These nodes need to have the same ID numbers for the graph object to consider them the same which they are CreateUniqueID lt function dat Select the columns of XY data from the data frame and load as a matrix mat lt matrix cbind dat X dat Y nrow nrow dat ncol 2 Initialize a vector to hold unique IDs vec lt 0 Fill vec with consecutive numbers for non duplicated rows vec duplicated mat lt 1 nrow mat duplicated mat Get unique duplicated rows dups lt unique mat duplicated mat Loop over unique duplicated rows for i in 1 nrow dups Determine the indices in mat that match the ith duplicated row iInd lt mat 1 dups i 1 amp mat 2 dups i 2 Set duplicate rows to the first number the ID vec iInd lt vec iInd 1 End loop over unique d
13. RSD do not migrate between watersheds we split the large river network in our study area into two small independent networks by watershed bound aries Figure 3 More generally consider a hypothetical scenario with three patches on one network e g patches a b c and three patches on a second independent network e g d e f Treated as one large network there are 15 pairwise distances to calculate for the upper triangle of the required 6 x 6 matrix a b c d e f 0 1 2 NA NA NA 1 0 3 NA NA NA 2 3 0 NA NANA 1 NA NA NA 0 4 5 NA NA NA 4 0 6 NA NA NA 5 6 0 o ana og where NA indicates that the distance cannot be calculated because the two patches are unconnected i e due to migration barriers between patches Note that the lower triangle is the transpose of the upper triangle because dispersal is assumed to be independent of direction Alternately treating the two sub networks independently reduces the number of pairwise distance calculations from 15 to 6 all of which can be calculated a b c d e f a 0 1 2 d 045 ee eee ae 2 2 3 0 f 56 0 To further reduce network sizes we then removed sections outside the study area bound ary 3The algorithm requires more time and memory to attempt to calculate distances between uncon nected patches than connected patches and eventually sets these distances to NA Second as a sensitivity analysis programme GRIP2 typically runs multiple itera tions and netwo
14. SD and refer to features of our RSD model in this manual to illustrate concepts limitations and opportunities where appropriate Most code within NetworkDistances is generic and could be applied to any spatially constrained species to calculate pairwise distances We attempt to highlight sections of code that may require some customization for application with other species The NetworkDistances code NetworkDistances R has extensive comments and should be referenced when reading this document Please contact the authors if you have questions comments suggestions or concerns regarding the manual or the code We are attempting to keep track of this code s use please cite this manual and contact the authors if you use NetworkDistances Note that NetworkDistances comes with absolutely no warranty 3 RSD HABITAT AND NETWORK DATA River data were acquired from Natural Resources Canada as a vector line shapefile scale 1 50000 NRC 2011 Georeferenced shapefiles for RSD habitat patches and rivers were projected in Universal Transverse Mercator UTM zone 17 in metres m using the North American 1983 datum Data preparation for RAMAS input files e g habitat mask habitat suitability grid was done using the geographic information sys tem programme ArcMap 9 2 ESRI 2006 Although spatial files for RAMAS input 2 Start set user specified inputs and source GRIP2 script Inputs RAMAS output files ptc and asc and NetworkDistances
15. User Manual for NetworkDistances 1 0 Calculating Network wise Distances Between Habitat Patches for Spatially Restricted Species M H Grinnell and J M R Curtis Fisheries and Oceans Canada Science Branch Pacific Region Pacific Biological Station 3190 Hammond Bay Road Nanaimo BC VOT 6N7 2011 Canadian Technical Report of Fisheries and Aquatic Sciences 2960 Fisheries and Oceans P ches et Oc ans il il H Canada Canada Canad Canadian Technical Report of Fisheries and Aquatic Sciences Technical reports contain scientific and technical information that contributes to existing knowledge but which is not normally appropriate for primary literature Technical reports are directed primarily toward a worldwide audience and have an international distribution No restriction is placed on subject matter and the series reflects the broad interests and policies of Fisheries and Oceans Canada namely fisheries and aquatic sciences Technical reports may be cited as full publications The correct citation appears above the abstract of each report Each report is abstracted in the data base Aquatic Sciences and Fisheries Abstracts Technical reports are produced regionally but are numbered nationally Requests for individual reports will be filled by the issuing establishment listed on the front cover and title page Out of stock reports will be supplied for a fee by commercial agents Numbers 1 456 in this series were issued as Technical Re
16. X Y to ensure the graph object is continuous By default shape files have a different ID for each node which can cause problems for nodes that are common to two lines that merge into a single stem e g river confluence These two nodes which have identical X Y loca tion must have identical IDs for the graph object to consider them attached The argument dat is the network object and the function returns the updated network object netVect with new columns espe cially UniqueID GetToFromDist dat Create a matrix indicating the unique ID for each segment s start e g from and end e g to nodes as well as the Eu clidean distance along each edge For these short edges the Euclidean distance sufficiently approximates reality if maps have a fine spatial res olution Nodes correspond to network vertices and edges correspond to lines between vertices Note that the words to and from simply indi cate endpoints because the graph object is undirected meaning that the Pairwise distances among patches can be calculated from one edge to the other from the edge of one patch to the center of the other or from center to center The center to center distance may be very different from the edge to edge distance when patches are large i e patch edges extend away from the patch center along network lines For simplicity we assume that the distance between patch centers best describes pairwise distances Thus network wise dist
17. ability analysis to spatial and nonspatial parameters using GRIP Ecological Applications 18 4 1002 1013 doi 10 1111 j 1523 1739 2008 01066 x Curtis J M R and Naujokaitis Lewis I R 2008b Source code for the program GRIP 1 0 Generation of Random Input Parameters URL http esapubs org archive app1 A018 033 supp1 1 htm Ecological Archives A018 033 S1 Supple ment Dijkstra E W 1959 A note on two problems in connexion with graphs Numerische Mathematik 1 1 269 271 doi 10 1007 BF01386390 Dray S and Dufour A B 2007 The ade4 package Implementing the duality diagram for ecologists Journal of Statistical Software 22 4 1 20 URL http CRAN R project org package ade4 R package version 1 4 17 14 ESRI Environmental Systems Research Institute 2006 ArcMap for ArcGIS Desktop URL http www esri com Version 9 2 Build 1324 ArcView License Gentleman R Whalen E Huber W and Falcon S 2010 graph A package to handle graph data structures URL http CRAN R project org package graph R package version 1 28 0 Johst K Brandl R and Eber S 2002 Metapopulation persistence in dynamic landscapes The role of dispersal distance Oikos 98 2 263 270 doi 10 1034 j 1600 0706 2002 980208 x Keitt T H Bivand R Pebesma E and Rowlingson B 2010 rgdal Bindings for the geospatial data abstraction library URL http CRAN R project org package rgdal R package version 0 6 33 Kitching R 1971
18. ally inversely related to dispersal distance Wolfenbarger 1946 Kitching 1971 The exchange of organisms between patches can affect patch dynamics and metapopulation persistence via patch recolonization and extinction rates Johst et al 2002 Dispersal rates among patches are typically mod eled as a function of distance and cost s associated with moving through suboptimal habitat within a landscape or seascape For some species the Euclidean i e straight line distance may be appropriate for modeling the migration distance between patches However landscape features may prevent other species from moving in a straight line be tween patches Figure 1 For these spatially restricted species the Euclidean distance may under estimate the effective distance between patches as well as over estimate migration rates and dispersal success leading to biases in predicted patch extinction and recolonization rates network line habitat patch Figure 1 Hypothetical landscape for a lotic species that is restricted to moving along network lines e g rivers that connect patches of suitable habitat e g riffles Note that patch size is proportional to circle size 2 BACKGROUND We assume that readers contemplating use of the NetworkDistances code are famil iar with the suite of RAMAS software specifically RAMAS GIS and Metapop Ak akaya 2005 as well as GRIP Curtis and Naujokaitis Lewis 2008a b Briefly the GRIP2 script written i
19. ances are calculated from center to center set distance lt Default Center to center in GRIP2 prior to running iterations to ensure that the ptfile file refers to patch centers 7 distance from Pop 1 to Pop 2 is equal to the distance from Pop 2 to Pop 1 Species that require a directed graph i e dispersal depends on direction will require the user to modify this function The argument dat is the network object and the function returns toFromDist later renamed tfTable a matrix of node IDs node locations and distances between nodes i e edge weights Save the output e g network object netVect and to from matrix tfTable as a netVect RData object to be used in subsequent iterations b Load the saved netVect RData object then EnsureUniqueSites dat Ensure that each patch has a unique ID so that pairwise distances are calculated for each patch Duplicate names are made unique by appending letters e g a to the second duplicate and so on The argument dat is the patches and the function updates the column Site with new IDs if duplicates exist SnapToNodes pops Snap each patch to the nearest network node Basi cally identify the closest node to the patch center and change the node ID to the patch ID Figure 4 Thus patch locations are shifted but are likely within tolerance considering that RAMAS uses a grid to define patches The search radius is controlled by the parameter maxD whic
20. apefiles i e the network is broken up into independent sub networks networks is a concatenation of each sub network name if there is only one net work networks is the network name Input shapefiles in UTM m must be in the folder NetworkShapefiles Value character vector e g c 2HC09 9HC10 for multiple sub networks character e g 2A11 for one net work The NetworkDistances code should be in the same folder as GRIP2 the work ing directory Create two folders in the working directory NetworkShapefiles and SavedNetworkObjects The folder NetworkShapefiles contains the shapefiles for the network s The folder SavedNetworkObjects may contain saved netVect RData objects from previous iterations to speed up computations if they are available Sub section 4 2 Step 2a Two additional folders are created during the simulation RDataOutTemp and RDataOutDist The folder RDataQutTemp holds temporary R output each itera tion The folder RDataOutDist contains pairwise distance matrices for each iteration and network Pairwise distance objects are named pairDists y RData in order to be retrieved later by GRIP2 to calculate various statistics Two other objects are saved in the folder RDataOutDist under the names patchNetworkDist y RData con tains minDistMat and patchNetwork and patches y RData contains patches and patchesUTM This folder may also contain the figure of patches and network
21. ating paths between vertices some of which are population sampling points and distances calculated as weights in the graph object First check for and remove edges that are specified multiple times To save time only do this if the network has patches any patches Site in tfTable frID any patches Site Zin tfTable toID Make a graph will all the nodes netGraphAll lt graph data frame tfTable 1 2 directed FALSE Remove nodes that are duplicated tfTable lt tfTable is multiple graph netGraphAll Make a graph with unique nodes netGraph lt ftM2graphNEL ft cbind tfTable toID tfTable frID edgemode undirected W tfTable dist End if the network has patches Collect garbage c Calculate distance matrix between pairs of sampling points If a pair of points are not connected i e not joined by lines the distance is NA The diagonal is zero i e distance between and point and itself and the distance to equals the distance from i e direction is irrelevant alcDistMatrix lt function dat Get character vector of unique site names from the graph object This is important because the distance function will work hard to calculate distances for unconnected patches which takes a very long time So only include patches that are actually on the graph patchSites lt patches Site which patches Site in nodes netGraph patchSites lt as character patchSites Set up the emp
22. distMat Update index for rows and columns iRC lt iRC nr J End if thre are rows End if distMat had data End loop over subsets Remove empty rows mat lt matrix mat 1 length ptNames 1 length ptNames nrow length ptNames If there are rows and columns if is null dim mat Add row and column names rownames mat lt ptNames colnames mat lt ptNames End if there are rows and columns Return the distance matrix return mat J End CombineDistances function Run this function if there is at least one row in patchNetwork i e there is at least one point in the area This only needs to be done for networks that have patches i e columns in the object patchNetwork if dim patchNetwork 1 gt 1 pairDists lt CombineDistances dat colnames patchNetwork End if there are points If there are zero points the pairDists matrix is 0x0 if dim patchNetwork 1 O pairDists lt matrix NA nrow 0 ncol 0 Collect garbage gc Fill in the pairDists matrix with NA if any patches were omitted FillPairDists lt function mat Get indices for the missing sites indMissing lt which patches Site Zin colnames mat Get missing site names noPatch lt patches Site indMissing Set up a matrix for columns colMat lt matrix NA nrow nrow mat ncol length noPatch Give it names colnames colMat lt noPatch Append cols mat
23. ect org R Foundation for Statistical Computing Vienna Austria R version 2 13 0 15 Schnute J T Boers N Haigh R and Couture Beil A 2010 PBSmapping Map ping fisheries data and spatial analysis tools URL http CRAN R project org package PBSmapping R package version 2 61 9 Strahler A N 1957 Quantitative analysis of watershed geomorphology Transactions of the American Geophysical Union 8 6 913 920 Tierney L Rossini A J Li N and Sevcikova H 2008 snow Simple network of workstations URL http CRAN R project org package snow R package version 0 3 3 Urban D L Minor E S Treml E A and Schick R S 2009 Graph models of habitat mosaics Ecology Letters 12 3 260 273 doi 10 1111 j 1461 0248 2008 01271 x Venables W N and Ripley B D 2002 Modern applied statistics with S Springer New York fourth ed URL http www stats ox ac uk pub MASS4 ISBN 0 387 95457 0 R package version 7 3 3 Warnes G R 2010 gtools Various R programming tools URL http CRAN R project org package gtools Includes R source code and or documentation contributed by B Bolker and T Lumley R package version 2 6 2 Wolfenbarger D O 1946 Dispersion of small organisms Distance dispersion rates of bacteria spores seeds pollen and insects Incidence rates of diseases and injuries American Midland Naturalist 35 1 1 152 WPD Wine Project Developers 2010 WineHQ Wine is not an emulator URL www wine
24. h restricts candidate nodes to those within maxD units of the patch It is important to note that patches that are more than maxD from all nodes are omitted from the analysis Although a habitat mask will ensure that patches are located near network lines distances between patch centers and network nodes can be large when network lines are straight i e fewer nodes or when patches are large An iterative search reduces processing time first search for nodes within max units of the patch if there are no nodes search again within maxD units The argument pops is set to the patch The function returns minDists which indicates the distance from each patch to the nearest node or NA if there are no nodes and the function updates the node ID in tfTable for both to and from nodes ftM2graphNEL ft edgemode W This function is from the graph pack age and creates an object of class graph to represent the network Prior to calling this function duplicate rows must be omitted from the tfTable object The argument ft is the to from table tfTable edgemode indicates that the graph is not directed and W indicates the edge weights The function returns the graph object netGraph CalcDistMatrix dat Calculate the shortest e g least cost network wise distances m between each pair of patches in the network using Di jkstra s 1959 algorithm implemented by the function sp between Although patches will have unique IDs if
25. h is the network that had the nearest node This is to ensure that there are no duplicates in pairDists output from CombineDistances below RemoveDupPatches lt function mat Determine which rows are ALL NA i e patches that were not snapped to a node in any networks these patches are omitted from the analysis naRows lt apply X mat MARGIN 1 FUN function x all is na x Take the inverse 25 575 577 579 581 583 585 587 589 591 593 595 597 599 601 603 605 607 609 611 613 615 617 619 621 623 625 627 629 631 633 635 637 639 naRows2 lt naRows FALSE Select the rows with patches that were snapped to node s mat2 lt subset mat subset naRows2 Loop over rows in mat and make sure that each patch only belongs to one node network if there are two set the further one to NA to ensure that the patch is only in one network for k in 1 nrow mat2 Get the elements in row k that are not NA dat lt mat2 k is na mat2 k FALSE If there are more than one pick the smallest one Otherwise ignore if length dat gt 2 Get the min minDat lt min dat Set the other s in the row to NA mat2 k which mat2 k minDat lt NA End if more than 2 networks End loop over k rows in mat Determine which columns are ALL NA Gi e networks with no patches naCols lt a
26. hq org Version 1 2 2 Yu H 2010 Rmpi Interface wrapper to MPI Message Passing Interface URL http CRAN R project org package Rmpi R package version 0 5 9 16 APPENDIX Electronic copies of the modified GRIP2 script for use with NetworkDistances the NetworkDistances R code Listing 1 and the RSD study area data e g river networks RSD habitat map are available free from the authors Listing 1 The NetworkDistances code NetworkDistances R version 1 0 is written in the programming language R RDCT 2011 L AHHHAHHAHMHAHAMMHHAAAMMMHHAAAMMHHAAAMMAHAMMMMAAAMAMMAHAMMAHAAAMMHHAAAMMHHAAAHHAHAE 35 1 Curtis J M R and Naujokaitis Lewis I R 2008 Source code for the program GRIP 1 0 Generation of Random Input Parameters URL http esapubs org archive appl A018 033 suppl 1 htm Ecological Archives A018 033 S1 Supplement 2 Akcakaya H R 2005 RAMAS GIS Linking spatial data with population viability analysis Applied Biomathematics URL www ramas com User manual for version 5 3 Grinnell M H and Curtis J M R 2011 User manual for NetworkDistances 1 0 Calculating network wise distances between habitat patches for spatially restricted species Can Tech Rep Fish Aquat Sci 2960 iv 29 p 4 RDCT R Development Core Team 2011 R A language and environment for statistical computing URL www R project org R foundation for Statistical Computing Vienna Austria R version 2 13 0 37 39
27. ifferent machines Of the total required time between 2 8 and 5 2 was used to run the NetworkDistances code Our analysis required fine spatial resolution because RSD are typically distributed in headwater streams that are closely spaced but networks for other species may not require such fine spatial resolution 4 2 OUTLINE OF THE NetworkDistances CODE Our analysis relies on well developed methods from graph theory to measure distances between patches along networks Although graph theory has been around for many years using graphs to model node e g patch connectivity is relatively new to the field of conservation biology Urban et al 2009 We developed the NetworkDistances code in the programming language R to facilitate implementation with GRIP2 and to cope with changing patch locations each iteration The NetworkDistances code is typically sourced via the GRIP2 script for spa tially restricted species and we assume that the user is familiar with GRIP2 Al ternately NetworkDistances can be run independently if all the required inputs are specified appropriately e g arguments for the function GridToUTM ptc asc and Section 5 The following algorithm outlines the NetworkDistances procedure and explains the code s major functions we recommend that users follow along in the NetworkDistances R code Listing 1 Appendix This algorithm is run for each y replicate iteration in newNreps as follows 1 Convert RAMAS spatial outp
28. in the folder RDataDutDist named plot pdf with one page for each iteration Figure 5 Patch names in green have been snapped to network lines patch names in red have been omitted from the analysis i e patches more than maxD units from all network nodes 5 INCORPORATING NetworkDistances INTO GRIP2 In addition to the usual controls and parameters required for GRIP2 and RAMAS NetworkDistances requires several additional user specified inputs which must be specified in GRIP2 or at the start of the NetworkDistances code calc_network_dist Set to TRUE to calculate distances along networks set to FALSE to calculate Euclidean distances Value logical maxD Maximum distance m from each patch to search for candidate network nodes in SnapToNodes pops Value number doSnow Set to TRUE to use parallel processing in CalcDistMatrix dat set to FALSE for no parallel processing Value logical habitat habitat patch w moved to D max search nearest node LA 7 radius Figure 4 Hypothetical network and habitat patch a The network is composed of nodes connected by segments Three nodes are within maxD units of the patch s center the SnapToNodes pops function shifts the patch s location to the nearest node b 10 newNreps 4 a cO ro oO D 8 Cc LO oo 2 cO LO LO
29. input parameters maxD doSnow cType nCores coreName nZone Create replicate habitat map doSpatPlots and networks Run RAMAS GIS Patch Convert patch maps to UTM Source NetworkDistances code Convert network s to graph object s V lati ary metapopulation parameters Locate patches on graph object s Run RAMAS GIS Metapop Dre Calculate network wise distances among connected patches last iteration yes Combine distances as pairDists Gather results from each iteration Output matrix of network wise distances pairDists brought into GRIP2 as Create NetworkDistances plots Pairwise_Distance End of file GRIP2 Figure 2 Simplified flow diagram of the GRIP2 script a and the optional Net workDistances code b The NetworkDistances algorithm is expanded in Subsec tion 4 2 and inputs are described in Section 5 e g asc must have inter alia consistent precision and spatial extent Ak akaya 2005 networks may extend beyond the grid s perimeter However larger networks may increase memory and processing time as discussed in Subsection 4 1 In our case study we modeled the metapopulation dynamics of RSD within a small study area which contains two watersheds Figure 3 Two RSD characteristics enabled us to simplify our analysis and thus our code First genetic analyses indicate that RSD do not move between watersheds M Poos unpublished data which allowed us to divide the study area into two independent wate
30. kip FALSE Get line info for the habitat patch data linePatchPTC lt grep pattern paste Npops populations sep x firstItemPTC perl TRUE 1 Print a warning warning Increase nmax in firstItemPTC to avoid scanning whole file J End if linePatchPTC is NA If linePatchPTC is still NA error if is na linePatchPTC Error message stop Check file ptc unable to find patch info End if linePatchPTC is still NA Scan to get patch info into a list Site X and Y in km referenced via the grid patchData lt scan file ptc skip linePatchPTC nlines Npops sep what list Site X 0 Y 0 quiet TRUE flush TRUE Get the first item from the first nmax lines in the sometimes large asc file This should contain the required lines since they are usually at the top of the asc file as a header firstItemASC lt scan file asc skip 0 sep t what character quiet TRUE flush TRUE blank lines skip FALSE nmax 10 Get the line info for the X location lineXASC lt grep pattern xllcorner x firstItemASC perl TRUE 1 If lineXASC is NA possibly due to not enough lines search again 18 21 123 25 127 29 31 133 35 137 39 141 43 145 147 49 51 53 57 159 161 63 65 67 71 173 75 77 179 81 183 if is na lineXASC Get the first item from all lines in the asc file thi
31. lines plot pdf 5 1 DISTANCE UNITS AND CONVERSIONS Distance units may vary between the RAMAS programme the GRIP2 script and the NetworkDistances code For consistency the NetworkDistances code uses me tres converting kilometres to metres when necessary For the RSD analysis network shapefiles are in metres and RAMAS output files are in metres e g Patchmap and kilometres e g ptcfile NetworkDistances calculations and inputs e g maxD are in metres However because RAMAS input files require distances in kilome tres pairDists is converted from metres to kilometres just prior to being returned to GRIP2 as a matrix of pairwise distances Pairwise Distance It is critical that users ensure that distances have expected units in RAMAS GRIP2 and NetworkDis tances input and output files 12 6 VERIFYING NetworkDistances AND EXTENSIONS Distances calculated using the NetworkDistances code should sufficiently approximate reality if network shapefiles are accurate and of sufficient spatial resolution However we recommend that users confirm the accuracy of the NetworkDistances output by checking various statistics the distance matrix pairDists and the figure generated by the function PlotNetworkPatches Additionally ensure that RAMAS output files i e spp asc line up with networks by plotting patches and network lines as well as verifying the patch map grid location Subsection 4 2 Step 1 Ensure that maxD is sufficientl
32. n the programming language R RDCT 2011 is designed for use with RAMAS GIS 5 0 software to perform systematic global sensitivity analysis of habitat and population parameters for spatially explicit population viability analy ses The RAMAS GIS programme links spatial data e g habitat suitability maps to stochastic metapopulation models and allows users to evaluate the influence of land scape structure on metapopulation dynamics by manually varying habitat parameters The GRIP2 script automates this time consuming process by generating a specified number of random sets of spatial and non spatial parameters and running these it erations by submitting batch files to RAMAS By default GRIP2 and RAMAS software calculate the Euclidean distance between patches We developed NetworkDistances version 1 0 an optional GRIP2 extension to be used when organism movement and dispersal is restricted to defined spatial networks Figure 2 For example the movement of lotic fish is restricted to river networks while other species may be restricted to moving along hedgerows coastlines trails or corridors Specifically we developed NetworkDistances to automate the calculation of distances between pairs of patches for redside dace RSD Clinostomus elongatus an Endangered stream dwelling minnow found inter alia in four watersheds in the Greater Toronto Area that discharge into Lake Ontario Canada COSEWIC 2007 We provide some background information on R
33. nced data graph Gentleman et al 2010 RBGL Carey et al 2010 and igraph Cs rdi and Nepusz 2006 to handle graph objects as well as gtools Warnes 2010 to sort strings with embedded numbers One or two other packages are optional snow Tierney et al 2008 to use multiple processors and also optionally Rmpi Yu 2010 to use MPI type clusters on non Windows machines Non Windows machines require additional code to ensure that files are compatible with both dos and unix as well as the WineHQ programme WPD 2010 to run RAMAS if NetworkDistances is used along with GRIP2 4 1 CHALLENGES AND SOLUTIONS TO MEMORY AND TIME REQUIREMENTS The main challenge to NetworkDistances is that large complex networks with many patches and high resolution maps may be costly in terms of required memory and pro cessing time However memory and time requirements can be reduced significantly us ing four strategies 1 splitting large networks into independent sub networks 2 load ing saved RData objects from the first iteration 3 parallel processing and 4 reducing map resolution First large networks will require less memory and processing time if they can be split into independent sub networks in a biologically meaningful way Splitting a large net work within which some patches are not connected into multiple sub networks within which all patches are connected reduces the number of pairwise distance calculations For example because
34. network wise distances between habitat patches for spatially restricted species Can Tech Rep Fish Aquat Sci 2960 iv 29 p il CONTENTS ABSTRACT RESUME 1 2 6 7 MOTIVATION BACKGROUND RSD HABITAT AND NETWORK DATA METHODOLOGY USING R 4 1 CHALLENGES AND SOLUTIONS TO MEMORY AND TIME RE QUIREMENTS at ee ol Mel SA Re DR ot 42 OUTLINE OF THE NetworkDistances CODE INCORPORATING NetworkDistances INTO GRIP2 5 1 DISTANCE UNITS AND CONVERSIONS VERIFYING NetworkDistances AND EXTENSIONS ACKNOWLEDGEMENTS REFERENCES APPENDIX INDEX ill iv iv 10 12 13 13 14 17 29 ABSTRACT Grinnell M H and Curtis J M R 2011 User manual for NetworkDistances 1 0 Calcu lating network wise distances between habitat patches for spatially restricted species Can Tech Rep Fish Aquat Sci 2960 iv 29 p We develop an approach to calculate distances along network lines between habitat patches using NetworkDistances version 1 0 The NetworkDistances code is an optional extension to the GRIP 2 script for species that are restricted to moving along defined networks e g rivers For these species the Euclidean distance may under estimate the actual distance between patches which may influence patch dynamics To more accurately reflect reality we calculate the shortest along the network distance between connected patches using NetworkDistance
35. object load file paste SavedNetworkObjects networks i RData sep Ensure that site names and distances from the last iteration are NA netVect SiteName lt NA netVect DistToSite lt NA End if using saved object Ensure that all sampling points have unique IDs EnsureUniqueSites lt function dat Letter index for first site 21 315 317 319 321 323 325 327 329 331 333 335 337 339 341 343 345 347 349 351 353 355 357 359 361 363 365 367 369 371 373 375 377 379 g S iLet lt 0 Get the original site names sites lt as character dat Site Print a warning that site s have been renamed warning Duplicate site name s were renamed networks i Iterative rename function RenameRename lt function siteNames Index the duplicated sites ind lt duplicated siteNames Rename the sites siteNames ind lt paste siteNames ind letters iLet sep return siteNames End RenameRename function Send the site names to the RenameRename function while there are duplicates while TRUE in duplicated sites Update the counter for new letters iLet lt iLet 1 Rename sites sites lt RenameRename siteNames sites End while loop Return the new site names as factors return as factor sites End CreateUniqueID functi
36. on If there are duplicate site names rename them TRUE Zin duplicated patches Site patches Site lt EnsureUniqueSites dat patches End if duplicate rows Collect garbage c Add the sampling points to the to from matrix at the nearest node within maxD units Outputs the minimum distances for each population and updates the nodes that are now population points If no nodes are within maxD units of the point the output is NA and the point is ignored napToNodes lt function pops Coordinates pt lt c as numeric pops X as numeric pops Y Function to get the set of nodes within some proportion of maxD units from pt Returns a subset of netVect that is within the specified distance up to a maximum of maxD GetPoints lt function srchD Get outer range in X xs lt c pt 1 srchD pt 1 srchD Get outer range in Y ys lt c pt 2 srchD pt 2 srchD Select the river nodes within the outer range to limit the search subRiv lt netVect netVect X gt xs 1 amp netVect X lt xs 2 amp netVect Y gt ys 1 amp netVect Y lt ys 2 Return the subset of netVect return subRiv End GetPoints function Run the GetPoints function with maxD 4 iNodes lt GetPoints srchD maxD 4 If there are no nodes run GetPoints again with maxD if dim iNodes 1 0 iNodes lt GetPoints srchD maxD Set up a temporary vector to hold distances dVec lt 0 Continue
37. one core If using multiple cores and idx has some data if doSnow amp dim idx 1 gt 0 Apply the indices to the function and output distances dists lt parApply cl snowClust X idx MARGIN 1 FUN GetDistance patchSites patchSites netGraph netGraph End if using more than one core If idx does not have any data if dim idx 1 O dists lt NA Place distances into the upper triangle dMat upper tri dMat diag FALSE lt dists And the lower triangle dMat lower tri dMat lt t dMat lower tri dMat Update the diagonal diag dMat lt 0 Return the matrix return dMat End CalcDistMatrix function To save time calculate distances only if the network has habitat patches if any patches Site Zin tfTable frID any patches Site in tfTable toID distMat lt CalcDistMatrix dat netGraph End if there are patches If there aren t any patches distMat is empty if any patches Site Zin tfTable frID amp lany patches Site Zin tfTable toID distMat lt matrix NA nrow 0 ncol 0 End if there are no patches Collect garbage gc Save the distance matrix as an RData object save distMat file paste RDataDutTemp distMat networks i RData sep End i loop over the number of networks Subset minDistMat to only have patches that are in a network and to only have networks that have patches Also each patch should only be in one network whic
38. ports of the Fisheries Research Board of Canada Numbers 457 714 were issued as Department of the Environment Fisheries and Marine Service Research and Development Directorate Technical Reports Numbers 715 924 were issued as Department of Fisheries and Environment Fisheries and Marine Service Technical Reports The current series name was changed with report number 925 Rapport technique canadien des sciences halieutiques et aquatiques Les rapports techniques contiennent des renseignements scientifiques et techniques qui constituent une contribution aux connaissances actuelles mais qui ne sont pas normalement appropri s pour la publication dans un journal scientifique Les rapports techniques sont destin s essentiellement a un public international et ils sont distribu s cet chelon II n y a aucune restriction quant au sujet de fait la s rie refl te la vaste gamme des int r ts et des politiques de P ches et Oc ans Canada c est dire les sciences halieutiques et aquatiques Les rapports techniques peuvent tre cit s comme des publications part enti re Le titre exact figure au dessus du r sum de chaque rapport Les rapports techniques sont r sum s dans la base de donn es R sum s des sciences aquatiques et halieutiques Les rapports techniques sont produits l chelon r gional mais num rot s l chelon national Les demandes de rapports seront satisfaites par l tablissement auteur dont le nom figure su
39. pply X mat2 MARGIN 2 FUN function x all is na x Select the cols networks that contain patches mat3 lt subset mat2 select which naCols FALSE Return mat all patches are in one and only one network and all networks have at least one node return mat3 End RemoveDupPatches function If minDistMat is not all NA if all is na minDistMat Get the subset of patches and networks with patches patchNetwork lt RemoveDupPatches mat minDistMat End if is not all NA If minDistMat is all NA set patchNetwork to a 0x0 matrix if all is na minDistMat patchNetwork lt matrix NA nrow 0 ncol 0 Finally combine the distance matrices from each subset CombineDistances lt function dat Initialize the big matrix to hold all the pairwise distances mat lt matrix NA nrow nrow patchesUTM ncol nrow patchesUTM Set up row and columns indices for the top left corner of the big matrix iRC lt 1 Initialize a vector to hold point names ptNames lt vector Loop over data subsets for i in i length dat Load the distance matrix load file paste RDataOutTemp distMat dat i RData sep Get the right column network from patchNetwork iCol lt which colnames patchNetwork dat i Get the rows that indicate the network s patches iRows lt which is na patchNetwork iCol FALSE Get the names of patches from patchNetwork these are the
40. r inputs Create a temporary directory to hold output each iteration if RDataOutTemp in list files w He RH Delete the old directory unlink x RDataDutTemp recursive TRUE Create a new directory dir create path RDataOutTemp End if directory exists otherwise else Make a new directory dir create path RDataOutTemp End if the directory does not exist Get habitat patch locations referenced via the grid from the ptc file and grid georeference info from the asc file to georeference the patches Convert to UTM and return habitat patches patchesUTM Note that users must verify that this function specifies distance units correctly as is this function expects distances in m asc and km ptc and converts to m GridToUTM lt function ptc asc Get the first item from the first nmax lines in the ptc file firstItemPTC lt scan file ptc skip 0 sep what character quiet TRUE flush TRUE blank lines skip FALSE nmax 200 Get line info for the habitat patch data usually line 58 linePatchPTC lt grep pattern paste Npops populations sep x firstItemPTC perl TRUE 1 If linePatchPTC is NA possibly due to not enough lines search again if is na linePatchPTC Get the first item from all the lines in the ptc file this can take a long time firstItemPTC lt scan file ptc skip 0 sep what character quiet TRUE flush TRUE blank lines s
41. r la couverture et la page du titre Les rapports puis s seront fournis contre r tribution par les agents commerciaux Les num ros 1 456 de cette s rie ont t publi s titre de Rapports techniques de l Office des recherches sur les p cheries du Canada Les num ros 457 714 sont parus titre de Rapports techniques de la Direction g n rale de la recherche et du d veloppement Service des p ches et de la mer minist re de l Environnement Les num ros 715 924 ont t publi s titre de Rapports techniques du Service des p ches et de la mer minist re des P ches et de Environnement Le nom actuel de la s rie a t tabli lors de la parution du num ro 925 Canadian Technical Report of Fisheries and Aquatic Sciences 2960 2011 USER MANUAL FOR NetworkDistances 1 0 CALCULATING NETWORK WISE DISTANCES BETWEEN HABITAT PATCHES FOR SPATIALLY RESTRICTED SPECIES by M H Grinnell and J M R Curtis Fisheries and Oceans Canada Science Branch Pacific Region Pacific Biological Station 3190 Hammond Bay Road Nanaimo BC VOT 6N7 E mail matt grinnell dfo mpo gc ca tel 250 756 7326 2E mail janelle curtis dfo mpo gc ca tel 250 756 7157 Her Majesty the Queen in Right of Canada 2011 Cat No Fs97 6 2960E ISSN 0706 6457 Cat No Fs97 6 2960E PDF ISSN 1488 5379 Correct citation for this publication Grinnell M H and Curtis J M R 2011 User manual for NetworkDistances 1 0 Calcu lating
42. rify their output by checking various statistics and graphs We 29 assume that the user has a working ability with R 4 and is familiar with spatial data It is crucial that users verify that distances are in the 31 correct units throughout this script This code comes with absolutely no warranty 33 References HHHEHHHHHHRHEHRRHEHREHREHREHRRHHAEHHRHRRERREHREHAREHRREHRRHHRE HHA HRA HEHEHE 51 CE EEEE EEEE EEEE EEEE EEEE EEEE EEEE EEE EEEE EEEE E E d 53 Start file NetworkDistances R LE EEEE EEEE EEEE EEEE EEE EEEE EEEE EEEE EEEE EEEE E E d 17 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 03 05 107 09 111 13 115 17 119 FB t HR HR Ensure that all the required user specified inputs are present Note if NetworkDistances is not called from GRIP2 these parameter values need to be initialized prior to here Also ensure the proper file structure has been created the required habitat patch information is available i e the ptc and asc arguments to the function GridToUIM and define y f all exists x c maxD doSnow cType nCores coreName nZone doSpatPlots networks Stop everything stop Missing required user specified inputs for NetworkDistances R End ensure use
43. rk lines remain constant from one iteration to another Thus networks can be saved to disk as RData objects on the first iteration and loaded from disk on subsequent iterations This strategy reduces processing time considerably for large net works However due to changing patch locations associated with random changes in landscape structure each iteration pairwise distances must be calculated iteratively Third calculating pairwise distances can be computationally demanding and takes considerable time when networks are large or when there are many patches In these cases calculating pairwise distances requires more processing time than creating net works and multiple processors can be used to reduce processing time In this case the NetworkDistances code starts multiple instances of R and divides pairwise dis tance calculations among processors on the cluster With sufficient memory parallel processing may even reduce processing time on computers with only one processor Finally time and memory requirements increase in proportion to increasing network size branching complexity number of pairwise distance calculations and size of input maps Processing time and memory requirements were considerable because the RSD study area was modeled at a fine spatial resolution our input maps have approximately 443 000 15m x 15 m grid cells For example between 1 0 and 1 5 hours were required to run 50 GRIP2 iterations of the RSD study area on two d
44. rsheds which we refer to as networks We defined individual networks by their Strahler stream order number a measure of branching complexity Strahler 1957 Second mark recapture studies indicate that RSD dispersal is independent of stream direction Poos and Jackson in press which allowed us to create undirected graph objects The benefits of these two simplifications are explained in later sections 4875 487 870 x 2 Z 4865 Z 4860 4855 Study area 4850 gt Lake Ontario 630 640 650 660 UTM easting km Figure 3 Two of the four watersheds e g 2HC11 run through the redside dace study area and discharge into Lake Ontario NRC 2011 Geographic coordinates are projected in Universal Transverse Mercator UTM zone 17 in kilometres km Note that networks are different colours to aid with differentiation 4 METHODOLOGY USING R We assume the user has at least a working ability with the R statistical and graphing programme RDCT 2011 and is familiar with spatial data In addition to the R pack ages required for GRIP2 sp Pebesma and Bivand 2005 Bivand et al 2008 rgdal Keitt et al 2010 spatial Venables and Ripley 2002 spatstat Baddeley and Turner 2005 adehabitat Calenge 2006 maptools Lewin Koh and Bivand 2011 ade4 Dray and Dufour 2007 and gpclib Peng 2010 NetworkDistances requires at least five additional packages PBSmapping Schnute et al 2010 to handle georef ere
45. rstItemASC perl TRUE 1 Get the number of rows ASCgridRows lt as numeric scan file asc skip lineRowsASC 1 sep t what list NULL numeric quiet TRUE flush TRUE nlines 1 2 Get the line info for the number of columns lineColsASC lt grep pattern ncols x firstItemASC perl TRUE 1 Get the number of columns grid X dimension ASCgridCols lt as numeric scan file asc skip lineColsASC 1 sep t what list NULL numeric quiet TRUE flush TRUE nlines 1 2 If any of lineYASC lineCellASC lineRowsASC or lineColsASC is NA error if is na lineYASC is na lineCellASC is na lineRowsASC is na lineColsASC Error message stop Check file asc unable to georeference the grid 2 J End if any of lineYASC lineCellASC lineRowsASC or lineRowsASC is NA Put scanned data into a dataframe with columns EID X convert km to m Y convert km to m and Site Note that users must verify that this function specifies distance units correctly patchDF lt data frame EID 1 Npops X patchData X 1000 Y patchData Y 1000 Site patchData Site Find the top of the grid UIM m gridTop lt ASCgridLLY ASCgridRows ASCgridSize Find the right side of the grid UIM m gridRight lt ASCgridLLX ASCgridCols ASCgridSize Convert patch X Y locations from grid to UTM m currently X Y indicates the number of grid cells from the upper left corner of the grid pa
46. s and apply our analysis to a stream dwelling minnow the redside dace Clinostomus elongatus RESUME Grinnell M H and Curtis J M R 2011 User manual for NetworkDistances 1 0 Calcu lating network wise distances between habitat patches for spatially restricted species Can Tech Rep Fish Aquat Sci 2960 iv 29 p Nous avons labor une m thode de calcul des distances le long des lignes de r seaux entre les parcelles d habitat au moyen de la version 1 0 de NetworkDistances Le code de NetworkDistances est une extension optionnelle du script GRIP2 utilis pour les esp ces dont les d placements sont limit s le long de r seaux d finis p ex des rivi res Pour ces esp ces la distance euclidienne peut sous estimer la distance r elle entre les parcelles ce qui peut influer sur la dynamique des parcelles Pour refl ter la r alit avec plus de justesse nous calculons la distance la plus courte lt le long du r seau gt entre les parcelles reli es au moyen de NetworkDistances puis nous appliquons notre analyse un m n fr quentant les cours d eau du r seau soit le m n long Clinostomus elongatus 1 MOTIVATION A metapopulation consists of multiple spatially discrete populations that occasionally exchange organisms even though each population is in a discrete habitat patch Or ganisms may move between patches when distances are less than the maximum dis persal distance and dispersal success is typic
47. s can take much longer firstItemASC lt scan file asc skip 0 sep Nt what character quiet TRUE flush TRUE blank lines skip FALSE Get the line info for the X location lineXASC lt grep pattern xllcorner x firstltemASC perl TRUE 1 Print a warning warning Increase nmax in firstItemASC to avoid scanning whole file End if lineXASC is NA If lineXASC is still NA error if is na lineXASC Error message stop Check file asc unable to georeference the grid End if lineXASC is still NA Georeference the grid s location get the left side X location UTM m ASCgridLLX lt as numeric scan file asc skip lineXASC 1 sep t what list NULL numeric quiet TRUE flush TRUE nlines 1 2 Get the line info for the Y location lineYASC lt grep pattern yllcorner x firstItemASC perl TRUE 1 Georeference the grid s location get the lower Y location UTM m ASCgridLLY lt as numeric scan file asc skip lineYASC 1 sep t what list NULL numeric quiet TRUE flush TRUE nlines 1 2 Get the line info for the cell size lineCellASC lt grep pattern cellsize x firstItemASC perl TRUE 1 Get the grid cell size m ASCgridSize lt as numeric scan file asc skip lineCellASC 1 sep t what list NULL numeric quiet TRUE flush TRUE nlines 1 2 Get the line info for the number of rows lineRowsASC lt grep pattern nrows x fi
48. tVect DistToSite netVect UniqueID iID lt lt min dVec J End if the node is not already a site 405 If the node is already a site else 407 Get the old site name oldName lt netVect SiteName netVect UniqueID iID 1 409 oldXY lt c netVect X netVect UniqueID iID 1 netVect Y netVect UniqueID iID 1 411 Make a new row to add to the dataframe with the distance between the new and old sites equal to zero i e same node location 413 newRow lt tfTablel 1 newRow frID lt pops Site 415 newRow toID lt oldName newRow frxX lt oldXY 1 417 newRow frY lt oldXY 2 newRow toxX lt oldxXyY 1 419 newRow toY lt oldXY 2 newRow dist lt 0 421 Finally append the new rows to the to from matrix tfTable lt lt rbind tfTable newRow 423 Also update netVect to indicate that the node has two population sites and the max of the distances 425 netVect SiteName netVect UniqueID iID lt lt paste netVect SiteName netVect UniqueID iID 1 pops Site 427 sep netVect DistToSite netVect UniqueID iID lt lt 429 max min dVec netVect DistToSite netVect UniqueID iID 1 Print a warning to indicate the node is already a site 431 warning Sites pops Site and oldName are on the same node networks i 433 End if the node is already a site End if min dVec lt maxD 435 Otherwise min dVec is gt maxD else dVec lt NA
49. tchDF X lt ASCgridLLX patchDF X patchDF Y lt gridTop patchDF Y Convert to EventData georeferenced in UIM m for PBSmapping patchEvent lt as EventData x patchDF projection UTM zone nZone Set up a list to return res lt list patchEvent patchEvent extent list top gridTop bottom ASCgridLLY left ASCgridLLXx right gridRight Return the list habitat patches as EventData and grid extent return res 19 87 89 191 93 195 97 201 203 205 207 209 211 213 215 217 219 221 223 225 227 229 231 233 235 237 239 241 243 245 247 249 End GridtoUTM function Run the GridToUTM function to get the patches and grid extent getGridToUTM lt GridToUTM ptc ptcfile asc OrigPatchmap Get the patches patchesUTM lt getGridToUTM patchEvent Get the grid extent for the plot below gridExtent lt getGridToUTM extent Loop over the number of networks for i in i length networks Get the river network via watershed name Note that users must verify that this function specifies distance units correctly as is this function expects distances in m netVect lt importShapefile readDBF TRUE projection UTM zone nZone fn paste NetworkShapefiles networks i shp sep Select only the required columns to reduce object size netVect lt subset netVect select c PID SID
50. th a column for each network that contains patches and a row for each patch that has been snapped to a network patches are assumed to belong in the network with the nearest node CombineDistances dat Combine distance matrices from each sub network into one large pairwise distance matrix The argument dat is the set of network name s that contain patches and the function returns the ma trix of pairwise distances for the entire group of networks pairDists The distance between points in different independent sub networks i e uncon nected patches is NA FillPairDists mat Ensure that pairDists has one column and one row for each patch even if the patch was omitted from the analysis The argument mat is pairDists and the function returns an updated pairDists The pairDists matrix is ordered by row and column names for compatibility with GRIP2 requirements The matrix is saved as pairDists y RData in the folder RDataOutDist to be retrieved by GRIP2 for further analysis 4 Step 4 is done after GRIP2 has run to completion and generates figures of networks and patches These plots can take considerable time to create when there are many large networks and many iterations skip this step to speed up the analysis Section 5 PlotNetworkPatches Plot georeferenced network s and patches in UTM m There are no arguments and the function does not return anything instead the function creates a portable document format PDF file
51. ty distance matrix with site names for rows and cols dMat lt matrix NA nrow length patchSites ncol length patchSites colnames dMat lt patchSites rownames dMat lt patchSites First generate a table of indices for the upper triangle of dMat num lt length patchSites idx lt expand grid i 1 num j 1 num upper tri diag num diag FALSE Function to get the distance apply over rows of idx to fill in the upper triangle of the distance matrix GetDistance lt function dat patchSites patchSites netGraph netGraph 24 511 513 515 517 519 521 523 525 527 529 531 533 535 537 539 541 543 545 547 549 551 553 555 557 559 561 563 565 567 569 571 573 wy He RR Load the required library require RBGL Get the pair of point names ptPair lt c patchSites dat 1 patchSites dat 2 Determine the shortest route and distance between the pair of points pairDist lt sp between g netGraph start ptPair 1i finish ptPair 2 detail FALSE Pull out the distance between the pair return pairDist 1 length End GetDistance function If using only one core and idx has some data if doSnow amp dim idx 1 gt 0 Apply the indices to the function and output distances dists lt apply X idx MARGIN 1 FUN GetDistance patchSites patchSites netGraph netGraph End if only
52. ups Add the data to dat and initialize columns for site name and distance dat UniqueID lt vec dat SiteName lt NA dat dist lt NA Return the site locations return dat End CreateUniqueID function netVect lt CreateUniqueID dat netVect Collect garbage gc Get locations to and from as well as distances between location pairs 20 251 253 255 257 259 261 263 265 267 269 271 273 275 277 279 281 283 285 287 289 291 293 295 297 299 301 303 305 307 309 311 313 GetToFromDist lt function dat mat lt matrix NA nrow nrow dat ncol 7 colnames mat lt c frID toID frX frY toX toy dist count lt 0 Initialize counter for rows Pull required columns into a matrix dat lt as matrix dat 1 6 ncol 6 byrow TRUE Loop over PIDs for i in 1 length unique dat PID datPID lt subset dat dat PID unique dat PID i Loop over SIDs within PIDs for j in 1 length unique datPID SID datSID lt subset datPID datPID SID unique datPID SID j Loop over rows within SIDs within PIDs for k in 1 nrow datSID 1 Update the counter for new row count lt count 1 Get coordinates mat count frxX lt datSID k X mat count frY lt datSID k Y mat count toX lt datSID k 1 X mat count
53. ut for patches from grid locations to UTM m GridToUTM ptc asc Retrieve spatial data for each patch from RA MAS output files ptcfile ie ptc_y ptc and OrigPatchmap ie spp PA asc where spp is typically the species name The ptcfile file indicates patch centers relative to the upper left corner of the grid in km while OrigPatchmap georeferences the lower left corner of the grid m Patch locations are converted to UTM m using the geographic information in the OrigPatchmap file header The arguments ptc and asc reference the ptcfile and OrigPatchmap files respectively The function returns a list with two elements the location of patches in UTM m patchesUTM as an EventData object and the grid outer extent in UTM m gridExtent 2 Step 2 is done once if there is only one network or iteratively if there are multiple sub networks First import the network shapefiles in UTM m as a PolySet object netVect which indicates node locations X Y and node connectivity Set patchesUTM to patches this is required because patches will be subset during the following calculations to include only the patches within the current network Each time the loop is iterated patchesUTM is re set to patches which ensures that all of the patches are considered a If available load the saved netVect RData object and skip to Step 2b Otherwise proceed as follows CreateUniqueID dat Create a unique ID number for each unique node
54. y large to locate candidate nodes in SnapToNodes pops Investigate the matrices in patchNetworkDist y RData to ensure that patches are assigned to the correct network These matrices will also indicate whether maxD is too small e g patches are omitted or too large e g snapped distances are much shorter than maxD Also ensure that RAMAS files grids and network lines have identical projections and correct units As previously mentioned one extension is to use directed graphs for example mi gration distance may depend on direction for fish that inhabit fast flowing rivers Step 2a A second use of directed graphs is to model the effects of patch size e g area and population on migration for example large patches may have more immigrants while large populations may have more emigrants Another extension is to incorporate a changing spatial network over time For example a previously continuous river net work could become fragmented by dams This type of temporal change would increase processing time because year specific network objects would have to be calculated each year 7 ACKNOWLEDGEMENTS The authors thank K Kinnersley for facilitating our use of the high performance com puting facility at the Institute of Ocean Sciences I Naujokaitis Lewis for technical support and M Poos for comments which improved the document Funding support was provided by Fisheries and Oceans Canada s National Species at Risk Programme 1
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