Vogt Et.al. Functional Connectivity (2009)

8/21/2019 Vogt Et.al. Functional Connectivity (2009)

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Ecological Indicators 9 (2009) 64-71, http://dx.doi.org/10.1016/.!colind.200".01.011

NOTE: For legal reasons we can only provide a reprint of theoriginal article in Ecological Indicators 9, (2009), pp. 64!".http#$$d%.doi.org$"0."0"6$&.ecolind.200'.0".0"".

MAPPING FUNCTIONAL CONNECTIVITY

eter *+", -oseph . FE/I2, odd . **1I+3I2, oert 5.+/E2, 17rt 5. IIE8, 1atar:yna *8/*;Ient and 87stainaility, and ?anage>ent and at7ral5a:ards @nit, ..26", ia E.Fer>i ", 2"020 Ispra (/), Italy.

2/ppalachian aoratory, @niversity of ?aryland ental 8cience, Frost7rg, ?aryland 2"A2, @8/

@8 Forest 8ervice, 8o7thern esearch 8tation, 04"


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Introductonented ecosyste>s is the 7nderstanding of how>ove>ent of organis>s is affected y landscape change.?aintaining connectivity, defined as the degree to which the

landscape facilitates or i>pedes >ove>ent a>ong reso7rcepatches (aylor, "99), is generally regarded as an essential goal ofenviron>ental conservation (For>an and +odron, "9'6D atic.

he connections in a landscape are typically 7antified y itsstr7ct7ral ele>ents s7ch as stepping stone patches or haitatcorridors. he i>portance of these ele>ents has een widelyadvocated in ecological theory, altho7gh e>pirical evidence thatcorridors i>prove >ove>ent across the landscape re>ainse7ivocal (5arris, "9'4D oss, "9'!D 8i>erloff and ayerand i%, "99D 3eier and oss, "99'). he effectiveness of potentialwildlife corridors depends, for e%a>ple, on the species, the 7alityof haitat within the corridor, the >atri% that s7rro7nds the corridor,and the width, length and red7ndancy of the corridor networB,a>ong other factors (ovethro7gh a landscape) wo7ld re>ove so>e of the a>ig7ityassociated with relying solely on the physical arrange>ent oflandscape ele>ents (str7ct7ral connectivity) to deter>ineconnectedness. ?eas7res of f7nctional connectivity recogni:e thatconnectivity is speciesspecific and e%plicitly consider the aility of aspecies to disperse etween patches (s to >ove a>ong the>. / species >aye capale of crossing haitat gaps, or the >atri% separating

patches, and th7s f7nctionally connect areas that are notstr7ct7rally connected. he >atri% etween two patches >ayconsist of co>ple% ense>les of >7ltiple land 7ses, so>e >orea>enale to organis> >ove>ent than others. referred >ove>entpathways thro7gh >atri% ele>ents are th7s f7nctional (7t notnecessarily str7ct7ral) corridors.

In practice, the identification of f7nctional connectors (i.e.,pathways for dispersal and i>>igration) re>ains an open iss7e d7eto at least two challenges# (") the asence of oservational datare7ired to >aBe speciesspecific assess>ents of >ove>ent

potential, and (2) the lacB of 7antitative and o&ective >ethods foranaly:ing the >ove>ent data in a spatial conte%t (a>ecB, "99!D

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os et al.D 200"D os et al.D 2002D inden>ayer et al., 2002).?athe>atical >odels are availale for estalishing potentialconnectivity a>ong patches (as defined y ethods generally provide a list of patches thatare connected rather than a description of the preferred pathways

7sed to s7ccessf7lly >ove etween patches. 5owever, it isprecisely this spatially e%plicit >apping of f7nctional corridors that isnecessary fro> a >anage>ent perspective in order to preserve,and, in so>e cases, restore connectivity.

he preferred approach for gathering data to >ap f7nctionalcorridors is direct oservation of >ove>ent, ideally in a designede%peri>ent (e.g., et al., 2004). 37t direct oservation of >ove>ent isi>practical over road e%tents or for a large n7>er of species.F7nctional connectivity analysis thro7gh >ove>ent si>7lations(e.g., +7stafson and +ardner, "996D +ardner and +7stafson, 2004D5argrove et al., 200A) provides an alternative, o&ective eval7ationof connectivity for >any species in real or artificial landscapes.

/tte>pts to analy:e >ove>ent data (whether fro> directoservation or si>7lation) incl7de calc7lating the fraction ofdispersers arriving at a Gdestination patchH fro> a Gso7rce patchH(e.g. 1ra>er8chadt et al., 2004). he approach is e7ivalent tocreating an ad&acency >atri% to define connectivity for graphanalysis (e.g., ?inor and @ran 200!). +raph representations arehighly 7sef7l for sensitivity analyses at the scale of networBconnectivity (e.g. @ran and 1eitt, 200")D however, speciesspecific

assess>ents of f7nctional connectivity often re7ire directBnowledge of interpatch dispersal pathways. 3y si>plifying thelandscape into an ad&acency >atri% for>at, graphs do not retain theinfor>ation necessary to identify the specific spatial pathways thatfacilitate >ove>ent within the >atri% environ>ent etweenpatches. his infor>ation >ay e re7ired for conservation>anage>ent.

he o&ective of this paper is to de>onstrate the 7se of>athe>atical >orphology as a concept7al idea for identifyingf7nctional corridors and other interesting feat7res of si>7lated oroserved >ove>ent data. he >ethod is ro7st and o&ective,

allowing connecting ele>ents to e identified y an 7ns7pervisedprocess (ogt et al., 200!a) and can e applied to any Bind of inaryinp7t >ap derived fro>, e.g., least cost s7rfaces (8ingleton et al.,2002)D dispersal or >ove>ent >aps fro> individ7alasedsi>7lation >odels, s7ch as -walB (+ardner and +7stafson, 2004) or/5 (5argrove et al., 200A)D synthesi:ed co>ple% >ove>entpatterns 7sing >ini>7> conve% h7ll or B>eans cl7stering (+raveset al., 200!)D or spatially e%plicit data of oserved species>ove>ents (evilla et al., 2004D 1ra>er8chadt et al., 2004). ;eprovide a short s7>>ary of the >ethodD adapt the na>ing sche>e

of the res7lting geo>etric classes to the f7nctional nat7re of theinp7t dataD and s7ggest ideas for their interpretation, which >ay e

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eneficial for the analysis of >ove>ent data and landscapeplanning in general.

Met!ods

Ma"s o# $o%e$ent o ill7strate the approach, we first needed to generate >ove>entdata. 3eca7se the o&ective of the analysis was to provide a realisticyet clear ill7stration of the proposed >ethods, we choose tosi>7late the >ove>ent of a hypothetical organis>. he >ove>entof an ani>al can e divided into daytoday >ove>ent within theani>als ho>e range and infre7ent, longrange dispersal eventsthat res7lt in the relocation of the ho>e range (For>an, "99A). ;einvestigated the si>7lated dispersal patterns of an organis> withattri7tes typical of a s>all, forestdwelling >a>>al. / portion ofthe el>arva enins7la, @8/, located to the east of the 7lation fro> the 200"ational and er et al., 2004). he >ap isrepresentative of a str7ct7rally co>ple%, >7ltihaitat landscape forwhich iss7es of connectivity >ay e a concern. It was sa>pled at"A> spatial resol7tion and condensed into si% land cover classes(Fig7re ", ale "). Forest was selected as the preferred haitat,and a >ini>7> forest patch si:e of "0 ha was designated asnecessary to s7pport stale pop7lation densities. ine forestpatches with an area e%ceeding "0 ha were identified (Fig7re ",right panel).

F&ure ': Le#t: () *and co%er c*asses o# t!e #oca* *andsca"e+ ,&!t: Grdce**s %sted durn& success#u* ds"ersa* e%ents -&ray. between t!e nne#orest "atc!es -brown.+ T!e &ray area re"resents t!e /0$a"+ T!e &rayarea co$bned wt! t!e brown area re"resents t!e 10$a"+

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ispersal of individ7als fro> these nine so7rce patches was thensi>7lated with -walB, a selfavoiding, rando> walB algorith>designed for si>7lating dispersal within >7ltihaitat, griddedlandscapes (see +ardner and +7stafson, 2004 for details regardingthe -walB >odel). ara>eters in the >odel, proaility of

>ove>ent (>ove) and >ortality (>ort), were assigned reasonaleval7es for each cover class for a forestdwelling s>all >a>>al(ale "). he p7rpose of the si>7lation was to generate a data seton species >ove>ent, while not getting >ired in iss7es of sparse orpoor 7ality data. hese are i>portant considerations and certainlyrelevant to the collection of >ove>ent data, 7t o7r goal is tode>onstrate the 7se of >athe>atical >orphology to analy:ef7nctional connectivity. he >ethod is general and can e appliede7ally to any >ove>ent data set for any species. /ltho7gh thesi>7lation o7tp7t is roadly representative of >ove>ent patterns(+ardner and +7stafson, 2004), the res7lts sho7ld not e viewed asrepresenting a specific species.

Land co%erc*ass

Probab*ty o# Mo%e$ent-P$o%e.

Morta*ty-P$ort.

;ater 0.00"0 0.2000877ran 0."000 0.0020@ran 0.0"00 0.00A0Forest 0.9000 0.000"/gric7lt7re 0.2000 0.00"0

;etlands 0.0"00 0.0"00

Tab*e ': 1abtat de"endent "robab*ty o# $o%e$ent and $orta*ty o# t!es) *and co%er c*asses used n t!e 20wa*3 ds"ersa* s$u*aton+

Individ7alased dispersal events were si>7lated with -walB ythe release of an individ7al at the edge of one of the nine so7rceforest patches. ?ove>ent was allowed 7ntil the ani>al either diedor reached a different forest patch. For each of the nine patches,"0,000 dispersers were si>7lated, and s7>>aries (incl7dingspatially e%plicit >ove>ent tracBs) were recorded for all s7ccessf7l

dispersers to the eight other patches./t present, o7r >orphological analysis can only e applied to a

inary inp7t >ap. o acco>>odate this re7ire>ent we foc7s onlyon the s7ccessf7l >ove>ent. ;e converted the -walB generated>ove>ent fre7ency >ap into a inary >ap y assigning a val7e ofone to any pi%el with at least one visitation y a s7ccessf7l disperserand assigning a val7e of :ero to all other pi%els. o investigate thei>pact of the haitat on the dispersal we selected two inary >aps.In the first inary >ove>ent >ap, we constrain the analysis only tothe dispersal area etween patches (ispersal >ap or G>apH). Inthe second inary >ove>ent >ap, we ass7>e that 7nli>ited>ove>ent can also occ7r within the nine forest patches (ispersalJ 5aitat >ap or G5>apH).

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Mat!e$atca* $or"!o*o&y he 7se of >athe>atical >orphology (?atheron, "96!D 8oille,

200) for classifying str7ct7ral patterns on a inary >ap of forestedland cover was ill7strated y ogt et al. (200!a,). he inary inp7t>ap is co>posed of a foregro7nd, showing o&ects or regions

delineating the areas of interest, and the co>ple>entaryacBgro7nd. he >ethod applies a se7ence of >orphologicaloperators Bnown as erosion, dilation, and anchored ho>otopicsBeletoni:ation. he erosion operator shrinBs the o&ects, thedilation operator grows the>, and the anchored ho>otopicsBeletoni:ation iteratively re>oves the o7ndary pi%els of an o&ect7ntil the o&ect is depicted y its line representation or sBeleton. /logical se7ence of these operations allows classifying the originalinary i>age into a pi%ellevel >ap of 7p to nine >7t7ally e%cl7sivethe>atic classes descriing geo>etric feat7res of the foregro7nd>asB. 5ere, we only provide this rief s7>>ary. For a detaileddescription of the >ethodology the interested reader is referred to ogtet al. (200!a,) and to the res7lts of a sensitivity st7dy 7sing ne7tral>odel data in iitters et al. (200!). he application, doc7>entation,and a sa>ple set of inp7t$o7tp7t data are availale online#http#$$forest.&rc.ec.e7ropa.e7$iodiversity$*nlineKrocessing.

F&ure 4: T!e$atc c*asses o# t!e s$u*ated $o%e$ent data+ Le#t:Ana*yss o# t!e /0$a" w!c! recorded success#u* ds"ersa*+ ,&!t:Ana*yss o# t!e 10$a" w!c! added $o%e$ent n t!e #orest "atc!es tot!e record o# success#u* ds"ersa*+ ,e&on ' !&!*&!ts a #unctona*brd&e between two core ds"ersa* areas+ ,e&on 4 !&!*&!ts a *oo"wt!n t!e sa$e core ds"ersa* area -see w!te *ne.+ ,e&ons 5 and 6s!ow d##erences n c*ass#caton t!at resu*t #ro$ t!e d##erent n"ut

$a"s+ 7!te bac3&round re"resents "orton o# *andsca"e not %sted byany o# t!e success#u* ds"ersers+

6

http://forest.jrc.ec.europa.eu/biodiversity/Online_Processinghttp://forest.jrc.ec.europa.eu/biodiversity/Online_Processing


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epending on the application and the inp7t data it >ay e>eaningf7l or even necessary to e less specific and co>ine twoor >ore of the >a%i>7> res7lting nine classes into a class with anew na>e that is appropriate for the specific application. heassign>ent of an appropriate na>ing convention and the

interpretation of these pattern classes depend on the nat7re of theinp7t >aps eing considered. For e%a>ple, for a inary inp7t >ap7sing rivers and laBes as the foregro7nd, the class core co7ld ena>ed GlaBeH and the area enclosed y the class perforation wo7lde Gisland.H /lternatively, the foregro7nd co7ld e a >ap ofsi>7lated >ove>ent data, or >eas7red tele>etry data, dispersaldata, or the liBe. For the present application, we ill7strate thegeneric applicaility of the proposed pattern analysis vicario7sly onthe >ap of s7ccessf7l >ove>ent etween forest haitats. henat7re of this inp7t differs consideraly fro> previo7s analyses ofstr7ct7ral landscape patterns, which 7sed inary forest cover >apsas inp7ts (ogt et al., 200!a,). In this conte%t, the class entitledpatch in ogt et al. (200!a) is not applicale here eca7se it wo7ldcorrespond to an isolated s>all area of >ove>ent witho7tconnection to a forest haitat which, according to o7r definition, isnot s7ccessf7l >ove>ent and therefore ine%istent. Fro> there>aining eight classes, we co>ine all ranch classes into oneclass Granch,H and a>end the class na>ing definition to reflect thenat7re of >ove>ent inp7t >aps, res7lting in o7tp7t >aps with thefollowing si% the>atic classes of f7nctional connectivity#

". ove>entD

2. Edge# >ove>ent in o7ter o7ndary of core areaD. erforation# >ove>ent in inner o7ndary ad&acent to holes incore areaD

4. oop# >ove>ent o7tside a core area that ret7rns to the sa>ecore areaD

A. 3ridge# >ove>ent o7tside a core area that connects to adifferent core area, andD

6. 3ranch# >ove>ent o7tside a core, loop, or ridge area thatter>inates.

In o7r >orphological analysis, the thicBness of the class edge

corresponds to the si:e of the Gstr7ct7ring ele>entH (see ogt et al.,200!), a predefined set of connected pi%els si>ilar to the Bernel ini>age convol7tion. For vis7al clarity of the res7lting classes in thisst7dy, we choose the si:e A which is e7ivalent to an edge thicBnessof five pi%els or !A >eters. 87ch an edge thicBness >ay econsidered typical for a wide range of species, 7t that is not criticalfor the p7rpose of this paper+

,esu*ts

87ccessf7l >ove>ents were recorded fro> each patch to at leastone other patch in the landscapeD therefore all nine haitat patches

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were connected as part of one large cl7ster. Fig7re 2 provides theo7tp7t of the >orphological analysis for the two inp7t >aps.ap of dispersal >ove>ent (Fig7re 2, left),the >a&ority of the grid cells are coded as core areas, which areconnected y ridges and loops. 5ere, core represents road

pathways for potential dispersal a>ong patches. he indicatedegion " (Fig7re 2) shows two ridge pathways etween differentcore areas. hese ridges are displayed with the correspondingland cover in Fig7re . he two core areas are separated y awetland which is a arrier to dispersal for the si>7lated organis>(ale "D see circles in Fig7re ).

F&ure 5: ,e&on ' n #&ure 4+ T!e #unctona* "attern c*ass brd&econnects d##erent core ds"ersa* areas -*e#t. across a wet*and ds"ersa*barrer -crc*ed.+ T!e corres"ondn& area o# *and co%er s "ro%ded ont!e r&!t+

For the ridge in the lower half of Fig7re , and >oving fro> theright to the left side of the >ap, the >ove>ent pathway follows theforested haitat 7ntil it reaches the less desirale wetland landcover type. ?ove>ent thro7gh this less desirale haitat was onlys7ccessf7l at locations that >ini>i:ed the distance traveled acrossthe wetland (circled). / si>ilar >ove>ent pattern is apparent forthe ridge in the 7pper part of Fig7re , where individ7al areas offorest f7nction as steppingstones etween forest patches which areapparent when co>paring the >ap with the land cover >ap. heridges provided a ro7te for s7ccessf7l dispersal acrosspredo>inantly forest and agric7lt7re areas, the organis>spreferred haitat types (ale "), and they identified the shortestpaths across the inhospitale wetland haitat when these ostaclesco7ld not e avoided.

eferring to the indicated egion 2 in Fig7re 2, Fig7re 4

ill7strates a narrow loop that connects the sa>e core area 7sing ase7ence of forested pi%els within a wetland >atri%. hat loop is

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red7ndant of the core >ove>ent area (i.e., the do7leended whitearrow in Fig7re 2 indicates that oth ends of this loop are connectedto the sa>e core area.), 7t it offers a potential shortc7t etweendifferent parts of the sa>e forest haitat patch.

F&ure 6: ,e&on 4 n #&ure 4+ T!e #unctona* "attern c*ass *oo"dent#es a "at!way connectn& two re&ons o# t!e sa$e core $o%e$entarea -*e#t.+ T!e corres"ondn& area o# *and co%er s "ro%ded on t!er&!t+

In general, the >ove>ent classes identified y >athe>atical>orphology reflect the intrinsic properties assigned to each landcover class within the -walB si>7lations. For e%a>ple, theperforations in the core dispersal areas indicate potential >ove>entostacles. / co>parison of these areas with the corresponding landcover >ap showed that the perforations are associated with s>all

wetlands. 8i>ilarly, the edge class indicates a transition etweenlocally road (core) dispersal regions and narrow (ridge, loop,ranch) dispersal regions. he ranch class indicates where narrowdispersal paths end (e.g., d7e to 7nfavorale >ove>ent conditions)and the disperser retraces its steps.

he 5>ap e%tends the area of >ove>ent analysis y adding allforest patches (Fig7re 2, right). he >orphological analysis of the5>ap reflects the changes in this e%tended inp7t >ap. /co>parison with the analy:ed >ap ill7strates the difference inclassification derived fro> the two >ove>ent >aps. For e%a>ple,the indicated egion in Fig7re 2 contains a feat7re that is laeled

as a ranch in the >ap that eco>es a ridge in the 5>ap. Inanother e%a>ple, the indicated egion 4 in Fig7re 2 contains

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feat7res that are laeled as edge in the >ap, 7t eco>eperforations in the 5>ap. he difference in classification is directlyrelated to the different inp7t >aps, and the res7lts ill7strate theinterpretation of spatial patterns of different types of >ove>ents7ch as dispersal events vers7s daytoday >ove>ents.

/scusson he concept7al asis of the >orphological analysis is of a genericnat7re eca7se it is a geo>etric analysis process. a dispersal si>7latorcalirated for a road class of forest >a>>als. he application ofthe very sa>e classification sche>e wo7ld e e7ally valid for inp7tdata derived for specific species, regardless of scale, species, andeven the the>atic application. For e%a>ple, the >ove>ent >apshown in Fig7re " co7ld as well e the >ove>ent >ap of an avianspecies at continental scale or a gro7p of ants at very local scale. he analysis of the inp7t data wo7ld e identical and only thena>ing convention of the res7lting classes and their interpretationwo7ld need to e adapted to the species 7nder st7dy.

Inter"retaton o# t!e "attern c*asses: *7r analysis provides classification of several feat7re classes of

>ove>ent data. he feat7re class perforation is a o7ndarys7rro7nding a arrier to >ove>ent. Edge represents the o7ter

o7ndary of a core area, eyond which no visitations occ7rred.3eyond the edge the landscape >ay contain landscape ele>entsfavorale to >ove>ent in general (i.e., low cost), 7t do notcontri7te to the traversal of organis>s a>ong patches in a corearea, or etween core areas. For e%a>ple, the white space etweenthe large core regions in the >ap (Fig7re 2) is pri>arily lowresistance agric7lt7re and forest. 5owever the river and wetlands inthe center of the landscape (Fig7re ", left) present a >ove>entarrier. h7s a portion of the landscape s7rro7nding these arriers>ay e 7sed (e.g. for feeding or for >ating p7rposes) 7t it is notpart of >ove>ent pathways etween patches.

E%tending o7tward fro> core areas are ranches, whichrepresent regions of the >atri% that are not specific pathwaysetween any two patches 7t are visited y organis>s d7ring interpatch >ove>ents. If portions of the landscape classified asranches are lost d7e to develop>ent or other land 7se change, thec7rrent interpatch connectivity wo7ld not e greatly affected. *nthe other hand, ranches >ay e the res7lt of corridor dissection,an event that co7ld e detected y analy:ing >ove>ent patterns attwo different points in ti>e, and noting the locations of corridorsthat eco>e ranches (i.e., the locations of LroBenL corridors). he

classification >aps wo7ld then provide the geographic locationswhere interpatch connectivity can e increased with >ini>7>

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effort y reestalishing physical connections or otherwise providingfavorale haitat at these dissection points.

he feat7re class loop represents a shortc7t connecting regionsof a core area to itself. 8hortc7ts >ay e of conse7ence inanalyses at the scale of the networB of connected patches. For

e%a>ple, if the loop (egion 2, Fig7re 2, left) were re>oved (i.e. d7eto 7rani:ation) organis>s wo7ld have to taBe a >ore circ7ito7sro7te to span the sa>e section of core (white line, Fig7re 2, left).87ch a change in networB properties >ay e indicative of anincreased graph dia>eter, which has i>plications with regards tothe spread of disease or the ease of traversing a cl7ster ofconnected patches (e.g. @ran and 1eitt, 200").

is7ally, ridges and loops appear si>ilar when looBing at theclassified >ove>ent data (Fig7re "), 7t >orphological analysisdifferentiates their f7nctional >eaning (Fig7re and 4) with regardto the dispersal of the focal species. atches e>edded in a corearea are connected y at least one pathway to at least one otherpatch within the sa>e core area. In o7r analysis of the 5>ap,there are two core regions (Fig7re 2). aintenance is critical to s7stain transfer ofindivid7als etween core areas. In essence, if these ridges weredisr7pted, the large cl7ster of nine connected patches wo7ld reaBinto two s>aller cl7sters of si% and three connected patches. hefact that there are two ridges connecting the core areas indicates alevel of red7ndancy in ter>s of how well the two cores are

connected.

I$"*catons on $ana&e$ent "o*ces: ?orphological analysis of >ove>ent data has direct application

to the decision >aBing process faced y conservation >anagers.For e%a>ple, if a li>ited a>o7nt of f7nding is availale to p7rchaseease>ents or to provide ta% incentives for landowners to >aintainopen space, s7ch f7nding co7ld e targeted at those regionsidentified as eing cr7cial for connectivity a>ong pop7lations. hese sites co7ld e identified thro7gh >athe>atical >orphology asthe region(s) in which the feat7re class ridge occ7rs. ?anagers

co7ld also target >aintaining the feat7re class core in Fig7re 2,which wo7ld >aintain road >ove>ent regions. hese roadpathways are predo>inantly thro7gh agric7lt7ral fields that co7lde c7ltivated as a >anage>ent prescription in a way that was >ostco>patile with the dispersal dyna>ics of the focal organis> (e.g.,seasonal rotation of crops that offer lower >ove>ent resistance)./lternatively, the classes loop and ridge can e targeted for>anage>ent prescriptions ai>ed at slowing or halting the spread ofinvasive species or disease vectors within or a>ong core areasrespectively.

he co>parison of the two >ove>ent >aps, >ap and 5>ap,shows the sensitivity of the >ethod to changes in the inp7t data.

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his feat7re can e 7sed to eval7ate and >eas7re potential i>pactsof landscape changes. For e%a>ple, the val7e of a specific ele>entof the inp7t >ap for the overall connectivity can e assessed yco>paring the classification of the inp7t >ap with and witho7t thisele>ent. / si>ilar logic applies to adding favorale ele>ents for

dispersal to the e%isting >ove>ent pattern. he infl7ence ofinserting s7ch an ele>ent, its e%tent and location, can e7antitatively assessed in ter>s of its contri7tion to f7nctionalconnectivity with this >orphological >ethod.

(enst%ty to sca*e: /ll analyses of str7ct7ral$f7nctional >ap attri7tes are 7tterly

scalecontingent. *7r analysis only seg>ents the i>ageco>ponents in >7t7ally e%cl7sive classes and therefore >aintainsall spatial details. /s a res7lt, the difference in spatial detail d7e tothe difference in data scale directly translates into the analysis. />7ltiscale sensitivity st7dy co7ld e an interesting topic which,when co>ined with e%pert species Bnowledge, co7ld reveal aspeciesspecific scale for which it is possile to set an appropriateedge width for that organis> via the si:e of the str7ct7ring ele>entwithin the >orphological analysis. Met, in this paper, the p7rpose isto ill7strate in a generic way that the concept worBs for detectingf7nctional corridors on >ove>ent >aps, and for this p7rpose it isacceptale to 7se an aritrary scale analysis. he principal effectsof changing the analysis scale have already een doc7>ented inFig7re 4 in ogt et al (200!a)D Fig7re A and Fig7re 6 inogt et al

(200!)D and a ne7tral >odel analysis in iitters et al (200!).

(enst%ty to $o%e$ent #re8uency: his approach co7ld e applied to oserved species >ove>ents

(i.e., tele>etry data) in a si>ilar fashion or alternatively to theaggregate s7> of visitations of all s7ccessf7l dispersers at the pi%ellevel. he res7ltant >ap wo7ld have large val7es for pi%els thatwere visited often and s>all val7es for pi%els less fre7ently visited. his type of >ove>ent >ap wo7ld e representative of a GflowH>ap, which is si>ilar to the inverse of a cost s7rface (high flowpi%els e7ivalent to low cost$resistance). 5owever, 7nliBe a cost

s7rface, the flow >ap wo7ld only contain val7es for pi%els act7ally7sed y s7ccessf7l dispersers. /ll the>atic classes identified inFig7re 2 co7ld then e classified 7sing >athe>atical >orphologyased on threshold val7es assigned for each class in the flow >ap.epending on the threshold chosen, all Gleast cost pathsH a>ongand etween patches wo7ld e vis7ali:ed si>7ltaneo7sly (not &7stthe single least cost path etween each pair of connected patches).

he p7rpose of this analysis was to ill7strate the 7tility of the>ethod for analy:ing >ove>ent data and to interpret the res7ltinggeo>etric classesD therefore the res7lts are for an G7nthresholdedH

flow >ap. hresholds of "0

, "0

2

, "0 or " disperser visitationfre7ency at the pi%el level co7ld e iteratively applied and its

12


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analysis can yield additional insights ao7t >ove>ent patternsincl7ding the identification of regions of GstrongH vers7s GweaBHconnectivity. /lternatively, threshold val7es co7ld e set ased onthe iology of the species 7nder consideration. Finally, in the case ofsparse or li>ited data, we can only analy:e what the inp7t data

provide. It is th7s cr7cial that the >ove>ent >ap is a reasonalerepresentation of the >ove>ent for the oserved species andhaitat. 5ere, Nreasonale is very species$haitat specific and >7ste eval7ated on a caseycase st7dy y the e%pert. In o7r paper,we foc7s on the feasiility of o7r approach which is ill7strated for ageneric e%a>ple on a Nreasonale >ove>ent >ap.

Generc9 syner&etc #ra$ewor3: +ood ecological indicators are those that can e applied to

different types of inp7t data witho7t having to invent so>ethingnew every ti>e. In the case of organis> >ove>ent and haitat,>aBing the leap fro> str7ct7ral to f7nctional assess>ents is 7s7allyapproached y inventing new indicators and$or 7sing new >ethods(ayi>pede a holistic analysis eca7se the relation etween theindicators of the two sets is 7s7ally not well defined or 7antifiale. he present paper shows that indicators ased on >athe>atical>orphology can e derived for >aps of f7nctional as well asstr7ct7ral connectivity. his feat7re re>oves a Ndegree of freedo>and provides the possiility to 7se the sa>e indicator not only to

descrie str7ct7ral and$or f7nctional connectivity, 7t also toco>pare the two and >aBe inferences ao7t the relation etweenstr7ct7re and f7nction.

Conc*uson*7r 7lti>ate interest centers on regional to continental scale

i>pacts of landscape change on pattern and connectivity for whichthe ill7strated >ethod provides two i>portant types of infor>ation.First, in addition to ta7lar s7>>aries of str7ct7ral and or f7nctionalpattern indicators, a >ap of patterns is a powerf7l co>>7nication

device to increase the awareness of spatial pattern in policyfor>7lation, i>ple>entation, and >onitoring. 8econd, eca7sepatterns are >apped at the pi%el level, their stat7s and trends cane interpreted relative to other geographically e%plicit infor>ations7ch as land develop>ent. /cc7rate and repeatale >apping andanalysis of f7nctional >ove>ent patterns over very large regionsand across >any oservation scales will allow ecologists to etteraddress the concept of connectivity in iological conservationst7dies and policies. he application of >athe>atical >orphologyprovides val7ale infor>ation for the interpretation of si>7lated or

oserved >ove>ent data.

1#


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Ac3now*ed&e$ents he research descried in this article was perfor>ed as a part of theent (o. 22'2200A06 808< I8) etweenthe -oint esearch ission, Instit7te for

Environ>ent and 87stainaility and the @nited 8tates epart>ent of/gric7lt7re, Forest 8ervice. /dditional s7pport was provided y acooperative agree>ent (o. FE40 0-""2422'00") etweenthe @niversity of ?aryland ental 8cience and the@nited 8tates epart>ent of /gric7lt7re, Forest 8ervice.

,e#erences3a7>, 1./., 5aynes, 1.-., ille>7th, F.., atri% enhances the effectiveness of corridors and steppingstones. Ecology 'A, 26!"26!6.

3eier, ., oss, .F., "99'. o haitat corridors provideconnectivityO ove>ent and patch si:e andisolation. Ecology '6, "02"0.

parisonshoppers g7ide toconnectivity >etrics. Frontiers in Ecology and the Environ>ent 2,A29A6.

entcharacteristics of rown ears on the 1enai enins7la, /lasBa.andscape Ecology 22, !6AP!!2.

+7stafson, E.-., +ardner, .5., "996. he effect of landscapeheterogeneity on the proaility of patch coloni:ation. Ecology!!, 94"0!.

5addad, .?., "999. ove>ents# a landscape e%peri>ent with 7tterflies. Ecological/pplications 9, 6"2P622.

5addad, .?., 3owne, .., , /., anielson, 3.-., evey,.-., 8argent, 8., 8pira, ., 200.


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Ecology '4, 6096"A.5argrove, ;.;., 5off>an, F.?., Efroy>son, ./., 200A. / practical

>apanalysis tool for detecting potential dispersal corridors.andscape Ecology 20, 6"!.

5arris, .., "9'4. he Frag>ented Forest. he @niversity of s. ares, F., Ferreras, ., elies, ?.,2004. Effects of >atri% heterogeneity on ani>al dispersal# fro>individ7al ehavior to >etapop7lationlevel para>eters. he/>erican at7ralist "64, "0"A.

iitters, 1.5., ogt, ., 8oille, ., 1o:aB, -., Estreg7il, odel analysis of landscape patterns fro> >athe>atical

>orphology. andscape Ecology 22, "0"04. http#$$d%.doi.org$"0."00!$s"09'000!90'9.

1$

http://dx.doi.org/10.1007/s10980-007-9089-3http://dx.doi.org/10.1007/s10980-007-9089-3


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8i>erloff, ., entcorridors# conservation argains or poor invest>entsOB7hl, -.F., 2002. andscapeper>eaility for large carnivores in ;ashington# a geographicinfor>ation syste> weighteddistance and leastcost corridorassess>ent. esearch aper A49, @nited 8tates epart>ent of/gric7lt7re Forest 8ervice, acific orthwest esearch 8tation.

8oille, ., 200. ?orphological i>age analysis# principles andapplications. 8pringererlag, 3erlin.

aylor, .., Fahrig, ., 5enein, 1., ?erria>, +., "99. ent of landscape str7ct7re. *iBos 6', A!"A!.

@ran, .., 1eitt, .5., 200". andscape connectivity# a graphtheoretic perspective. Ecology '2, "20A"2"'.

ogt, ., iitters, 1.5., IwanowsBi, ?., Estreg7il, ericanat7ralist "', 244".

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Documents

Vogt Et.al. Functional Connectivity (2009)