Population Viability Boyce

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Annu Rev Ecol. Syst. 1993:481-506Coprigh 199 b Annua Reviews Inc. A rhs eserved

POPULATION VABLY

ANALYSS

Mrk S. B*

Cete fo Eclogical Scieces ad Ceter o Theoretical Studes Idi Ittute oScic Baalo 62 Ida

INRODUCION

opaton vabty anayss (VA) s a process It entas evaaton o ataand modes or a popaton to antcpate the ehoo tht popton wlpersst for some arbtrary chosen tme nto the ftre (25, 12) cosey

d op is miimm i popaio (MV) ysis MV isan estmate of the mnmm nmber of oransms of a partcar speces thatconstttes a vabe popaton eference s aso mae to popaton vnerabty anayss whch s a neatve appeaton or VA VA embraces MV,bt wthot eekn to estmate the absote mnmm popaton necessaryto keep a speces vabe (13)

I the Ui ttes, the U os i has a mada o ps vbepopios o is ds d h aio os Mm 5iis h U ish d Widif i ad h io Mi ishis

ervce have been evaatn VAs or many speces or popts prpsefor stn erthe nanere peces Act 52) stabshn crtera orwhat constttes a vabe popaton s no oner strcty an academc prst

VAs have been attempte for a east 35 speces; perhaps the mostceebrate are those for the rzzy bear (Uru arco horribii (12, 129,44 an the northe spotte ow Sr idna aurna ( 79 99a) Most YAs are smaton stes that reman npbshe, or whenpbshed, they may ony nce otnes of moe strctre (9, 12, 13)hs iok aayi mhods o s of hm, aays dd ih

s ssmpios 5 VAs y aoi o h ecooy of thespeces the epertse o the moeers an the etent of avaabe ata

*Cuent addres: Depament of Zoology and Physioogy, Laamie, Wyoming

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2

Thee ae o uideis o ha osiues a aid PY ad eause eahase is uiue I am oahe o deise a aemp i uaiied ha ioesa popao simaio o aasis wi e ie o poei e

popaios o esimaig some exiio o pesisee paamee eg imeo exiio poaii o exiio, poaii o pesisig o 00 ease eiiio a eia o iiiy pesisee a exiio aeaiay esui a 95% poaiiy o suii o a eas 100 yesDisussio o suh ieia a e ou i Mae ade ) ad Thompso(

Coeig siie daa o deie eiae esimaes o a e paameeseessa o deemie MVP is simp o paia i mos ases. I is ueuesioae ow we eoloiss a pei he uue (, paiua oe

ime oizos eessay o poje exiios. he ohe ad ou 3)suess a maaes hae he ih o expe popuaio iooiss o poehe ume o aimas eessay o esue he ogem iaiiy o apopuaio Bu o o so has poe o e daeous oud (8 hi issdamagig he ediii o oseaio ioogiss

My puose i is eie is a aemp o pae PV a MVP o moeomoae goud y ideiyig a eaisi domai I maiai a PVouh o e a iea pa o a speies maaeme pa u ahe haeig so pesumpuous as o aim h we a aua use moeig o deie

a MVP o o esimae he poaiiy o exiio I use i as a oum oampio e aapie maageme appoa o oig 7) a Waes2) o hose aooee ases ha ao wai o a ow PYI eie empiia eidee suesi ha use o esohum o MVPsma o e eaisi.

MODEING EXNCION

udamea o MVP is he a ha sma popaios ae moe ie o oexi a ae oes de o ieedi depessio ad eei di osimpy e hea o hae i o deah ees demogapi sohasiiyUde ig eiomea aiae o aasopes howee maiaiigMVP ma o e as eeie a osaio age as od e maagig ospaia oiuaio ad oaio o aias 8, 85, 10 2) Iespeieo he ae he ojeie o PV is o poide isi io ho esouemaaem a hae paamees iuei he poaiiy o exiioThis hae ma eai ehei he expeed ime o exiio oedig e poaii o exiio wii some ime ame

e mos appopae mode se o a PV depeds o e aaiaiio daa ad he esseia eaes o e eoog o e ogaism. I is seio

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AN VATY 8

I eview sl ees o PY exiio moeli I ei wi isssio o sosi viio eess eleme i osieioo exiio poesses e eview ppoes osi o eeis

emop eolo ole wi e me ll o eseelemes o o o oee i e sme moel Bese o eomplexi o s moel, mos Ps will ee e elm o ompesimlio moeli

Sochsc

Rom eves e exemel impo i exiio espeill o smllpoplios, e e o mos PY 11 I sese e isiio eweeeemiisi sosi poesses i eolo is iiil ese lleoloil poesses e sosi M mi (97) pois o ese o eemiisi e sosi moels ol e siie mhemil oveiee" Fo heisi pposes se o eemiisimoels is ppopie Fo exmple, o esi o simple moel oompeiio o peio wol ol e ose e omplex mhemis o sosi vesio Bese e ae moe le eemiisimoels m iel os esls sosi moels e oe oo omplex oe solve lill s eie se o simlio meos

Usll olsios om sosi moels i eolo e sikil

iee om deemiisi oes (6 Tis is eell e ese o ile vies, ii olie io iii il skewe o oewiseoomll isie viles. Te siiie o i ve is eso es i e oex o exiio 8 ess spe is e vill ll eoloil poesses e olie (1 122 We essem ois olieiies is evio m ie mkel e o esesieli wi ses o ove io


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and morphoogica variation (but s 6 And it is possib or many o thsmasurs to vay amost indpndnty o on anothr (80 16 Gnticvariation within popuations on is masurd by man htoygosity or th

propotion o as that ar htroygous t, i pradaptation to utunsuts om othr spcis (disas, parasits, comptitors, prdators is thrason to prsrv gntic variaton, it may b important to ocus on prsrvngrar as (4 rhaps th numbr o as pr ocus is a mor importantmasu o gntic vaiation (a

Bcaus quantitativ traits ar most rqunty th targt o naturasction, Land Barrowcough (81 argu that hitabity shoud bmonitord as a asur o ntic variation or consrvation t rom apragmatic prspctiv w know that stimats o hritabity ar otn dicut

to intrprt caus th rspons to sction can b graty compicatd bymata cts (. Rativy ow vs o gntic variation may conrsubstantia hritabiity to som quantitativ trats (0 hr is aso thdiicuty o dcdng which quantitatv traits should b masurd oowingLand Barowcoughs (81 rationa, th most important traits ought to bthos that ar most rqunty th targt o natura sction t, ths aracty th taits pctd to bar th wst hritabiity s consqunc osction (6 40

How gntic variation is structurd withn popuations can aso bar on

conrvaton stratgis (1 Many popuation gnticsts bliv that spatiahtrognity is on o th most important mchanisms aintang gntcvariation in natura populations (6 hthr or not this prtains to thimotanc o inbrding in natura ouations has bcom th urc o aascinating dbat (11, 10, but irrspctiv o this, thr is no qustionthat spatia variation in gntic composition o popuations can b substantia ar just bginning to undrstand th ro o popuation subdivision ongntic structur and hritabiity (161 How signiicant is oca adaptation?How important is coadaptation o gn comps (4 Athough spatiastructuring o gntic variation is com and ntrsting, it is not car thatour undrstanding is suicint to us it as a basis or manipuating popuationsor consrvation Attmpts to manag th spcs by transpanting individuasbtwn subpopuations is an ctv too to maintain or incras gnticvaration withn popuations ( but may dstroy varanc amon popuations

h soution to this dimma may utimaty ntai orsing th sorts othrats a spcis is iky to ncountr I oca subpopuations ar iky to

b thratnd by habitat dstruction or poitica unrst, it may b xtrmyimpotant to maintain gographic varants to nsur that th spcs cancontinu to surviv n othr ocaitis (s 14, 14 owvr, i utur

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6 OYCE

thrats du to disass and parasits ar xpctd thr may a prmiumon nsurin th maximum ai divrsity throuhout th popuation (notnssariy a in on pa6

Is thr an optimum amount o mxin amon subpopuations that maximis tota gntic varianc in th popuation? caus irnt gns orgn compxs ar found in withinvsamong subpopuation componnts onti vaation a nra answr to this qustion proay dos not xistuthrmor th nti varianc within popuations is a convx unction odisprs (migration with mximum varian at th hihst possib disprsaiwis vaianc among popuations is a convx unction o disprsa butwith maximum vaian at zro dispsa 5 h sum of ths two functionsis simiar convx and no intrmdiat maxima xist hus w nd to

minimi disprsa amon sits to prsrv goraphic variation whinsuring nouh numrs in subpopuations to avoid inrdin oss ofgntic vnc

An appoach ommony usd in trying to dtrmin a gntic asis forMV is to xamin ftiv popuaton siz Ne ( Ne givs insight intoth potntia consquncs o ntic drit to oss o gntic divrsity but asis th cs or masurs o ntic variation w hav numrous masurs octiv ppuation si dpnding upon th mchanisms actin dit orxamp wns ( rviws th cacuation oNei rativ to inbrding Nev

or th varanc in gn rquncis among supopuations Nee tarting thrat o os o ntic variation and Nm or mutation ctiv popuationsi Sti mor masurs may drvd or xamp Nmta) dfins thctiv popuation siz in a mtapopuation xprincing rpatd xtinctionronition vnts ( ach o ths si masurs o N is thnsubt to adustmnt or unqu sx ratio a stctur (6 66 nd variabpopution si hr is no soun basis or scting on o ths asicmasurs ofN ovr anothr t as wns shows th an ad to muchdirnt cncusions aout MV

I concd y arin with Shar (28 and Land that modinntics is not iy to b as imprtant as modin dmoraphi andcoogica procsss in th formuation o a VA his dos not impy thatgntic cosidrations ar not portat rathr in any ca w o not ytundrstan th ntis w nough to us it as th asis for manamnt.h is an urnt nd fo sach on th in twn ntis anddmoraphy c 1 his conusion aso dos not impy that modso gntic variabiity shoud not orm t asis or YAs. Indd I thin thiswoud a nov approach for spcis in which rosion o gntic variabiityis i t an imporant onsidation in th fut managmn of spcis such as th Arican wid dog (Lycaon picu) which has a highysubdividd popuation (5 ut as Land has mphasid 8 dmography




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UA VAY 8

d oid ooy iky o of mor i iifi h mo PVA.

Bh-Dh nd Dogphy

BIRTH AND DEAH PROCESSES Poby h m roh o modextinction is a stochastic bih-death ro 3 11) mgdd Poodrbd brh d dh. Dmorh dr mo iky i m oo d o mi ff i. myb dvd do o rvv for h m gh of m d dvdvry h mbr of org hy r h roh h b d oov forn fio of oio iz N iv dyddr brth d dh r d:

E) 2 1/jd) b/d)] =

o mmm oib oio iz Nm.

A o mh h m ff r rmy iiv ooio iz 53 1) d h ff b iord if hoo rr h bo 30 dvd dd o rr).h o whr oo dvdd o r mbr ofboo h o m h f rk of h dmogrh

xo rooio i ow r b iif rik of oh ir oio by dmorhi ohiiy o 103).Evirom ohy mh mor f h m or

dmorhi ohiiy for vy m oo 54 55 4 85129). Recallin the assumption of Poisson distribution for birhs b) anddeaths d the variance in per capita growth rate at population size N r =b d) my

Vr) b + )/ .

Roz Lh (85 d Goodm (4 55 rwro h brthdhro mod Eq. 1) o mk E fo of h vr Vr)

jE) [/jjVr[rE[r [Vrr)+Er)[Vr)Er)

= = =i3.

Hr Vr) omhow bom vrom vr (52, albeit still afo of h md ofbd . h imor oom of h modfidbrdh ro mod h n r wh populaion morowy wh vrom vr h ( Goodm (

vidd rdiio of h modifid bihdh ro mod by imi mor om oo h dd dy dd d urd h ry fod ood oord bw mo r d

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OLATIO VAILITY 48

v re Px Fx) for Lee/Leovh mr be oved yy(.edrdPx or drdFx)24 79 99). Uderdg he repoe of growh reo perrbo vro po he fe be my yed gh o how

oe hod rge mgeme 79) For ogved pee, h he poedow, d rvv very eve demogrph prmeer, where pee wh horer geero me, fedy be mh more mpor83 99)

re, he eeme of projeo mr re rdom vrbe 14153) or fo of he evrome 34 60). Foreed rjeore ofpopo ze deped o oy o he hede of v re, b o o hevre hee re 156) mpor o oe h vro v

re ree deqbrm ge rre h frher ompe hedym. he vre popo growh re h rbbe o bohhe vro v re d he vre popo rre. Fordemogrphy of hm he Ued Se 960 ppromey wo hrdof he vre growh re be rbed o vare v re,where bo oe hrd de o fo ge rre 54).

Projeo mre her mpe form re mode of epoepopo growh. A h, here re eey wo pobe oome ofhee mode hey ree epoey o fy, or deree o eo

f he dom egeve for he verge projeo mr e h oe,eo red. B eve whe he verge projeo mr mghpred reg popo, eo my o or whe v revry 4 74 56) f ore, epoe growh mode re rye o me e eery o epore eo probbe

FORECASTIG METHODS Deveopme of heoy d ppo of foreg moy hve orred eoom, b he oppory e o ppymy of hee poedre o popo projeo Projeg oh

proe o he fre poe probem Fr, oe m me h hemehm geerg he hor d rem d hged hefre Seod, oe m ee he orre r mode h drve hepopo proe or rk ero eror predo hrd, error pedo re mgfed progrevey o he fre h h y oy few me erv be preded wh y ofdee or reby 3)

A me ere mode ommoy ed for foreg he ARMA(o-regreve egred movg verge) mode 0 15 9 31 154)Leqre regreo ed o e he depedee of N o g

of he ere me ere, N), Nt-2) . . N- Dereg empoyedo remove red, d movg verge be ed o mooh ohghfreqey oe he reg eqo he erpoed o hefre begg from he oberved d po he popo' rjeory

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4 OYCE

deermnes he orecas hs, he raecory does no show a poplaondecrease, he orecas may conne o ncrease who bond ondencenerals arond he orecased ale wll, neerheless, nclde 0 a some

re me, b hs wll nclde samplng error and wll be mch shorer han Many sascal soware packages nclde programs ha perormAMA orecasng

A smplsc approach o orecasng can be dered rom a dson modelwho age srcre 3 64). calcls s sed o sole a sochascderenal eqaon model o eponenal poplaon growh he probablydsrbon ncon o encon s he nerse assan dsrbon smlaro he lognormal), and oX) / lal, where s he log o he nalpoplaon sze, E s he pose poplaon sze dened o conseencon eg n seally reprodcng speces), anda s he aerage growhrae or he poplaon A mamm lkelhood esmaor MLE) or Innn)/(q ) whch only reqres knowledge o he nal, n and nalcensses, nq a mes and q respecely Or aleaely one may se alnear regresson approach 3). MLEs or2 are also easly calclaed 364)

Alhogh easy o se, one ms magne ha he poplaon rajecoryobsered hs ar wll also apply no he re Also, any srcral eares

o he poplaon process, e g densy dependence, whch are reeced n heme seres are oerlooked n he esmaor oa 54).Bldng on he resls o ljaprkar Orzack 56) and Heyde ohen

64) Lande Orzack 8 also modelled sochascy as a son processor eponenal age-srcred poplaons Smlaon rals were sed oaldae her esmaors or and 2 Alhogh ande Orzack 8emphasze ha only hree parameers are needed o se her model, one ohese parameers s nal oal reprodce ale whch reqres compleele hsory and agesrcre daa

A hrd approach o orecasng s o characerze he me seres o alraes wh AMA, and hen o nser hese models no a projecon mar84 54) Sch a meseres mar reans more o he dynamc conseqences o age srcre, and hereore poplaon lcaons ogh o bemore realsc I am naware o any applcaons o hs mehod n conseraonbology.

For each o hese orecasng models we assme a densyndependenpoplaon densy dependence acs n an age-specc manner whch sally does 43 44) he complcaons o he age srcre make dcl

o dere analycal resls or he dsrbon o encon mes en hadensy dependence ess n naral poplaons 33) een n densyage poplaons 43) I am skepcal abo sng densyndependenormlaons ecep n wo cases ) ery small poplaons where densy

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POPULAON VIABIITY 41

dependence may be nconseqental relate to demographc stochastcty55 or ) for short-term forecastng Frher research s needed to deelopforecastng models wth ecologcally realstc strctres eg wth densty

dependence Bt n the meantme Monte arlo smlaton procedres 60 can be sed to generate estmates and dstrbtons for etnctonparameters for models wth densty dependence

Senstty to ntal condtons ensres that long-term forecastng wll bensccessfl for chaotc poplatons () bt nonlnear forecastng methodsmay mproe shortterm forecasts for poplatons embedded n compleecosystems 45 Poplatons eperencng flctatons de to tme-laggedprocesses may be partclarly sted to one of seeral nonlnear methodsreewed by asdagl (3). Soware for generatng forecasts and calclatng

confdence nterals s descrbed by Schaffer dd (3). Unfortnatelythese methods work best for tme seres longer than are aalable for mostendangered speces

coogy

Althogh mch of the lteratre on PVA has focssed on sses of genetcsand stochastc demography t s clear that ltmate cases and threats ofetncton are prmarly ecologcal Loss or degradaton of habtat s the mostsgnfcant factor threatenng speces etnctons n the ftre l 07 64 Foraan taa crrently endangered by etncton % are assocated wth habtatloss 44% wth ecesse take 35% by ntrodctons and another % arethreatened by chemcal pollton or the conseqences of natral eents 4

Most PVAs hae gnored fndamentals of ecology sch as habtat focsngnstead on genetcs or stochastc demography Althogh ecologca factorsnflence demographc arables seldom s or nderstandng sffcent tosolate these eects A more approprate approach for many speces may beto model the habtat for the speces and aros strateges for managng ths

habtat For eample Fon Brenchley-Jackson4

modelled the salntytranspraton and sol mostre ofparina salt marshes n sothe alfoawhch s essental habtat for the endangered lght-footed clapper ral elabledemographc detals for the ral were naalable and the only connectonbetween the brd and the habtat was a lnear relatonshp between the bomassof Pacfc cordgrass parinafoioa and the nmber of rals

Most demographc PVAs performed ths far do not model ecologcalconseqences of other speces eg predators compettors parastes dseasen partclar eotc speces can be a maor threat n some systems 5 For

eample nasons of eotcs may be less lkely n commntes that possessa dersty of nate taa 4 n some speces dynamcs of dsease may bethe most sgnfcant consderaton n a PVA 35 6 Understandng schrelatonshps s necessary to predct poplaton ablty

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42 YCE

egrealy VA ofen do no eplcly nclde managemen 1.onder for eample applcaon of a forecang mehod o a poplaonrajecory for a pece whoe declne can e ared o haa lo. Imake no ene o eend ch a rajecory f all remanng haba for he

pece no proece. e h precely he nference ha one oldraw n applyng a forecang model cf Leavng managemen oof a PVA nfornae ecae one of he greae vale of PVA modelng he opporny o evalae he efcacy of varo managemen opon(67)

ndeed he aence of ecology and managemen fom mo aempa PVA a her bge weakne Thee procee ogh o be he nand bol of ch modelng eerce The power of ecologcal modelng ren or aly eenally o play wh nare o ancpae he coneqenceof varo managemen cenaro 39 147) Some apec of ecologych a deny dependence paal heerogeney and he Allee effec are ofpaclar gnfcance o PVA ecae hey have major coneqence o heproabl of enon

DENSITY EPENDEE The mple poble model of poplaon growh an eponnal poplaon growh model I ha no ecology. The mplepole eologcal model a denydependen mode ch a he logc.The eence of negave feedack n compenaory deny dependencedampen oplaon caon and can grealy redce he probably ofencon ( In moel elecon he prncple of Occam' azor commonly nvoked herey one reqre acal evdence for he eenceof deny dependence efore adopn he more comple denydependenmodel. m ha nead of eqrng acal demonaon of denydependence one hold e for devaon from a nll model of logc denydependence.

Th t a that etat aaete foa et eeetmoe

no who dffcle(9 4

n parclar lac of ndependencn a me ere of cen daa (0 0 One can avod ome o hepolem by eamnng deny dependence n vval o fecndy whconollng for key envronmenal parameer (3 lemen of a proeconmar ca e made fncon of deny yeldng dynamc qalavelymlar o he logc (4 60 Becae ffcen aa ae elom avalableo do je o characerng a deny dependen ncon one may need oreor o ng a form conen wh ha oerved for mlar aa (3 .Becae of he dfcle wh parameerzaon of deny dependence ha

een arged ha may e mo conervave o e deny-ndependenmodel cae hey were hogh o bear hgher probable of encon(4. B h no necearly re for eample encon ner deny




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POPAnON ABY 93

dependence s mmnen all haba or a speces has dsappeared. Frhermore do no accep hs raonale on he gronds ha reasonable behavoro he model shold be a hgh prory n model valdaon 6)

TESLD A low denses an Allee eec creaes a posve relaonshpbeween per capa poplaon growh rae and poplaon sze hs can becased by dcles n ndng maes 30) dcly n endng o predaorsor compeors I 8) socal or physologcal aclaon 80) or redcedpredaon ecency 8) Smlarly low densy conseqen o haba ragmenaon may resl n hgh jvenle moraly drng dspersal 78 7)

he conseqences o Allee eecs or PVA are eceedngy mporanbecase hese mechansms creae heshold or crcal poplaon szes below

whch enon s mch more probable or nevable As an eample Lande78) presen a model whcre lmaons o venl dspersal can creae anencon hreshold n erroral speces whch has been sed n Ys orhe spoed wl (79 5

owever he mechansms creang Allee eec are no well ndersoodecep n a ew speces ( 7) As a resl we do no know he generalyo he phenomenon. has however been poslaed o occ n a broadders o aa 7- c f empral edence s n par de ohe dc o sdng poplaons a ow denses. permenal wor schas ha b owell 9 shold help o deny he characerscs o specesos lely o eperence Allee eecs and aord a more objecve bass orncorporan relean sascal ncons no PYAs c 30)

nbreedn depreson can be modeled demographcally a an Allee eecbecase s eec becomes more severe as poplaon densy becomes lessHowever nbreedng s more comple becase nbreedng depresson sepeced o eode wh e as deleeros alleles are elmnaed by acombnaon o dr and selecon 80 81. Denns 30) revews models ha

can be sed o descrbe he Allee eec and her sascal properes

SPT STUC aba ragmenaon s he mos seros hrea obologcal dversy and s he prmary case o he presen encon crslco & Mrphy observe 6) wold seem hereore ha spaalsrcre shold be ncorporaed no mos PYAs e becase paronng apoplaon no spaal sbns can be comple o model and parameerze s oen gnored

Spaal heerogeney and dspersal can sablze poplaon caons 6

68) b can also have comple conseences dependng on nonlnearesn he sysem 7). Asynchrony can average o lcaon cased bydemographc or envronmenal sochascy and spaally removed asnchrony may ensre speces srvval n he ace o caasrophes ) O corse

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44

correlaed luuaons among subpopulaons can drascally redue ET(8)

ncorporaon of spaal srure no eologal models as nvolved a

dvery of approache nludng reaonduson equaons (86, dsreeineraing bouaion eniioned on a gi (7) and Maro raniionmarie l) Diffuson uually ha a ablzin efe on he dynami ofsnglesees modes endng o average populaon ucuaons n space.Bu when spaial sure obned w eologal neraons egompeo or predaon, hen nsaly and aial aes can emergeSpaal model n dsree me ao show he oenal for very complexynamcs, using inegrodifference equaions (76) or predaorrey differeneequaion wih disersal simulaed on a grd (1)

aia uure adds so mu omexiy o ecologial modes hageneralie can be dffcul o oban (7, ) or example epenng upone speces n queson orrdors among habia uns may be eer benefcalor dermenal. Corrors can reduce conseuence of nbreedng or emograpc sochasiy by faclang ispersal among sies; bu ey an alsoee a ranmion roue for deae, exo pees or redaors (12712a).

Reen onsderabe wor as fousse on meapopuaon models eree occupancy of dscree haba pahe or slands s a conequene of a

balane beween dsperal and exnon processes I 4 87). arg &Palohemo () sow how nerah ynams s fundamenal n eermnngpopulaion se n spaally srucured mode. As e isane beween habapache nreases ay as a onseuene of haba framenion iner-pahdspersal expeed o derease Te aly of dsperers o deec new abapaes can be an exceedngly mportan facor eermnng populaon epac occupan and probably of exncon ( 78). Ts a been eguidng rnie behn PYA for oe ow b ande (7 an Thomase a (}

The geomery of habia an be ca (17) and vtually mposible omoel anayal enues n a mulaon oel for e spoe owe landscape of suable aba a been mapped on a geogra nformaonyem (IS) and mpoed no a dspersal smulaon model (8a) Thsenolog has grea poenal for copng wi he complex roblem ofidenifying an aproriae spaial sruure for poaon modelng.

M-SS SSMS To onsr Y s fundamenal o developan underandng of he mehansms regulang polaon sze (13) Snglspeces models of populaon are probably unrealisc araeraon ofmo poplaon because populaon reguaon acually enas dynamcineraion among eie eg anerbivore redaorrey, araieho




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OLATO VIABIIT 4

interctions. erein lies serios ilemm or YA. e o not nerstnmltispecies processes well enogh for most species to incoporte schcompleity into PVA.

Modeling ecologicl processes idelly shold nclde the nterfce wthdemogrphy. For emple the dynmics of dsese n poplton cnltmtely be etermne by emogrphc processes. Demogrphc dseqlbri sstine by stochstc pertrbtions n itl rtes cn reslt n sstneepiemiologicl flcttions 55. nee sch interctions between imeelys cret by ge strctre n by ecologicl interctions my be eyto nderstning ynmic behior in generl ) Bt of corse to modelsch processes reqires detile informtion on the ge specifcity of theecologcl pocess.

cologicl processes re inherently nonliner. his ct long with thedestbilizing efects of enironmentl sesonlity n trophicleel interctions men tht comple ynmics incling chos re to be epecte inmny biologicl popltions. t hs been rge tht chos selom occrs inecologcl systems becse species wol be epecte to go etinct whenchotc cttions redce popltions to low leels 9 19) hs s notnecessrily tre becse riety of mechnisms cn ensre persistence. nprticlr refgi n sptil heterogeneity (2 1) cn ber locl popltions ginst etinction. And een if chotc flcttions were to cse locl

etinction ares my be repoplted in the sense of metpopltion 19).

f nything howeer recent nces n nonlner ynmics he me tcler tht een smple ecologcl systems cn possess remrbly compledynmics he impliction is tht sch comple dynmics my frstrte orbility to preict long-term trjectories necessry to estimte etinction timesf we re to consder PYAs for chotclly flcttng popltions the onlyhope my be to focs ttention on the mechnisms tht bon systemsynmics e.g. refgi sptil heterogeneity switching to ltetie prey.

hese remrs only gie glimpse into the te compleity o ecologiclsystems. n erforming PYAs we o not yet now how mch compleity inecessry to cptre the essence of the system. Deciding how mchcomplety s necessry shol be bsed on ice from feld bologsts ndmngers who he the best sense nd nrbly on the lblty of dt.

Ircos Ao Mchss

Becse seerl mechnisms cn contribte to etinction n becse ech

s comple in ts own rght the sl pproch hs been to onsider themechnisms only piecewise one or two t time n this pproc one mghtle which mechnsm ppers to be most senste nd whch reqres thelrgest MVP.

Annu.R



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46 BOYCE

Unorunaely his approach is lawe because he ineracion amongcomonens may yiel criical insigh ino he probabiliy o exincion neei Gilpin & Soule's (50) iea o eincion vorices has any valiiy he

synergism among procssessuch as habia reucion inbreeing epressionemograpic sochasiciy an loss o geneic variabiliys exacly whawill be overooe by viewing only he pieces

is easible an sraighorwar o buil a simulaion moel conainingboh emographic an environmenal sochasiciy posulae consequenceso inbeeing epression llee ees habia rajecories an consequenramiicaions o carrying capaciy ec all in he same moel hen one canconuc a sensiiviy analysis o le whih parameers have he mossigniican consequences an one can simulae managemen aleaives o

view heir epece consequences Fuhemoe simulaion oers he powero eplo: propagaion o variances an he eecs o various ypes oranomnes or complex sysems whih canno be unersoo excep in hullblow moel (0 8) ll hese hings are possible bu in pracice ourabiliy o preic he behavior o comple ecological sysems has been leshan eemplary ()

WHAT MKE GOOD P ND WHO DECIDE?

Y ma be a more ominous proposiion han poplaion biologiss araccusome o given ha Ys have been challenge in cour (5 5) Somo he lesons leae rom previous cour challenges o populaion moelsmay be insrucive or example he saisical reliabiliy o populaioprojecios is liely o be scuinie an i is hereore impoan haparamee esimaion robusness o moels an conience limis or projecions be careully consiere How eensible i ime o exincion oexample i i carries conence inervals spanning wo orrs o magniue

resenaion o resuls can be a elicae maer ven hough he moel may

be compl i is essenial ha eplanaion be clear an nersanable ononscienss Subsanial esimony in one o he spoe owl hearings wasignore b hejuge in her uing because she i no unersan he moeinge o oersimpliy may rs misrepresenaion

here exiss a elicae raeo beween builing a moel ha realisicallycapues he essenial ecology o he oranisms an eeping he moel simpleenough ha he number o parameers or esmaon s reasonable ( no he beauies o some o he orecasing mehos is ha sraighorwarmehos exis or exrapolaing he conience inervals an isribuional

properie o orecass ( a 6) Bu use o such simple moels requirebol assumpions abou exponenia populaion growh an perpeuaion ofpopulaio rajecories For moels ha are more ecologically realisic




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UATN VABTY 47

o suc anc smatos o not s rurn us o smuatonmetos e. bootstrappn an jackknn (00 Tre are no rues but astratec mor use t smpes possb moe tat st retans te

essnta eaurs o t systems cooy.To antcpat extncton probabts t s ssenta to unerstan tstructur o aranc artcuary nronmenta arance (c 00 t obtann oo stmates o arances or enronmenta anemorapc parameters reures ast amounts o ata Most PVAs conucteus ar a bn unab to o justc to ranc stmaton. ar (6as unabe o stnus beteen sampn an enronmenta aranc oremorapc paramtrs o rzzy bars Lan (7 stmate ony tebnoma component sampn aranc surrounn emorapc param

etrs or t spote oFor tm srs o opuaton s ancs on ncras as samp

sze ncreases (08. At te y east t ou appea om ta pesnteby Pmm Rea (108 tat 8 yas o ata ar nee to stabze tarance n nsect cnsus ata an 00 years or brs an mammas (10To caractrze t autocoaton structure n a tme sers reure eenmore ata yt autocorreaton s knon to be mortant n rectn extnctonprobabts (0 0

A ar terature exsts on t posopy an metos or smuaton

mon n cooy (6 8 04 8 47 kse tre ar seerabooent treatss on estmaton o opuaton an cooca arameters(77 1 17 4 38 63 Some paramters suc as surva orcoecents or mutspeces nteractons can prsent serous estmatonbms. An n many cass tr s tt op bcaus aa unaaabor nsucent In ese nstances one may use ata rom smar spcs orareas use a smper moe encumbere by unrastc assumptons on tstructure o t systm or xpor t beaor o te systm or a rano reasonabe aramtr aus

Dern sastcay reabe estmats or MVP s cary a cut notmossb ask But t can be an en touer task to xtrapoate rom teMVP nto stmatn t area o abtat necessay to suppot suc a popuatonc reurs a etae unerstann o a speces' abtat reuremnts (3Patcs o abtat must not ony b arr tan som crtca sz (80 tymust aso b n a sutab eometrc conuraton to nsure sprsa amonabtat unts Manamn or spot os ( ros a compx casestuy.

Grant (6 susts our mpotant comonnts or aatn any Amo Frst os t mo aress t probem Because te probem susuay a manaemnt ssue t may be useu to nterac te PVA t rskanayss (3 Secon os t moe possss reasonabe srctur an

Annu.R



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48 BOYC

ehaor? The hrd sep s o aep a quanae assessen o he accuracyand precson o he odels oupus and ehaor. And ourh s o conduc

a sensy analyss o he odel y changng seleced paraeers n heodel y an arrary aoun and hen sudyng syse response and ehaorGen careul consderaon o he audence e who decdes?) hese

aldaon approaches oer useul aselne crera or ealuang a VAodel Bu sll ndng he approprae alance eween coplexy andsascal relaly wll e arrary and dcul o ealuae ollowng hesealdaon crera soe approaches are undaenally nsucen as VAsor exaple sple calculaons o N > 0/00 or projecons o eslearces unl exncon. Exaples o VAs ha hae een partcularly

successul a sulang enlghened anageen nclude hose or grlyears 26) and spoed owls 98a 5).

GETTING EMPIRICAL

e canno expec ha sulaon VAs wll e conduced or os endangeredspeces Daa are oen nsucen e s crcal VAs can e cosly andhere are sply oo any speces needng aenon 36). or hese reasonshere connues o e grea neres n he orulaon o rules o hu" orMV and heN > 0/00 gudelnes or shorer ersus longer MVsare coonly ced 36 52)

The orgnal orulaon o hese rules o hu was genecally ased uno ased upon deensle crera (37 8) eerheless here s eprcaledence ha such rules o hu ay e o approprae agnude Sudeso exncon o gho sheep (Ovis cndeni)(7) and rds on oceanc orhaa slands (70 09 37) conssenly show ha N < 0 s clearlynsucen and he proaly o exncon was hgher or een ceran orsuch sall populaons. opulaons o 0 N < 200 were argnally secureand when N > 200 poplaons were apparenly secure oer he led eraes o hese sudes see 10) Clearly applcaons o such ledoseraons are resrced o parcular axa and we would expec uch largerpopulaon ses o e necessary or nsec populaons or exaple And hereare oous adanages o ananng hree or ore replcae populaons36).

There s opporuny o expand he epcal ass or VA and rules ohu 10). Ths should nclude exncon sudes ased upon eprcal

oseraons ro slands and experenal work wh replcaed sallpopulaons 29). e need o undersand wch acors conrue o exncon proales or arous axa or exaple socal ehaor has eenshown o e an poran conruor n praes 32) And s o greaneres o know wheher herores undergo greaer populaon lucuaons

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POPULAON AB 499

ta do predators 6) Wll smple sglespees models sffe for erboreswereas models orporatg tropleel dams are essetal for predators 9?

W demograp ompoets are most rta determg exttoprobabltes? Karr (7 fod tat forest dergrowt brd spees tat aegoe extt o Barro Coloado Islad BCI ae o aerage lower sralrates ad tat spees wt lower sral rates dsappeared earler ere wasttle edee tat N otrbted sgfatl to tese exttos o BCIter lfe stor trats ma also be mportat eg do saler spees dergomore olet popato fltatos tereb predsposg tem to a gerprobablt of extto l08 0?

If oserato boog s tl gog to be a setf dsple 10 tmst beome more atel oled expermetal resear Expermetalmaplato of abtats to deteme te oseqees to spees ressextto poplato toer ad dspersal are o target eg 89 10).ewse m old be gaed b performg PYAs for spees o dagerof extto were poplatos old be mapated expermetall torgorosl test te predtos of te model

CONCUSIONS: VIBIIY OF PV?

Costrtg models to lde ma of te omplextes of te eolog oforgasms presets o partlar dffltes bt we smpl do ot aesffet data to aldate s models for most edagered spees It ssedom f eer tat repatos exst 3 ts olsos aot be robst(8 A great dager exsts tat resore maagers ma led too mredee to a model we te ma ot fll derstad ts lmtatos

eerteless tere s too m to be gaed b deeopg a strogerderstadg of te sstem b modelg to sr modelg for fear of ts

beg msterpreted PYA as a proess s a dspesable tool oserato ad t oles m more ta feeble attempts to estmate MYP orprobabltes of extto PYA etals te proess of stesg fomato abot a spees or poplato ad deelopg te best possble model forte spees ge te formato aalable We doe properl ts olesworg losel wt atral resore maagers to deelop a og-termterate proess of modelg ad resear tat a reeal a great deal abotow best to maage a spees Doe properl PYA a be a arato oollg 67) ad Walters 16) oto of adapte maagemet w as

proe to be a powerfl tool ma areas of resore maagemetAdapte maagemet proposes applato of dferet maagemet tats

tme ad spae to deelop a better derstadg of te beaor of tesstem 16) or applato to edagered spees problems we possbe

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00 BOCE

memenaon o vaos managemn saeges shod be aeed nsatay saated sboatons. By so dong one an evaate the effayof vaos onsevaton stateges Ave manaton mst be a of sha ogam . habtat manaton edato o dsease ono manatonof otena ometos rovsonng tansanng ndvdas from ohersboatons to ssan genet viaton semntaon of oatonwh eeases of ave stok, et. onong of h gene and oaononseqees of sh manaons hen ovds daa o vadae and/oefne he VA mode

PVA ses a arge nmbe of etng eseah estons n oatoneoogy and genets ne omsng theoeta aea aeas o be eandngtheoy and aatons of enon oesses n agestted oatonse.g deveong aatons fom h genea hoy otnd by Ayheya &Kn (4) 8 101 0 154) Esene o te theshod oatons, ea defnv VP, deends on the estene of a denstydeendent mehansm sh as the Aee effet o beedng deesson (111) We havedstessngy t ema data on these oesses n nata oatons oovde a bass fo aamteaton of modes (30, 7) hs mst be one othe mos gent eseah needs fo VA

ost moant I am onfden tha PVA w ove o be a vaabe ooas we a! the etnton ss (14. me s not avaabe o efom PV A

fo a of he sees fo whh t s waanted ( 8 1) Indeed, sngesees aoahs to onsevaton ae too mted n soe fo mos aatonn to onsevaton ( onta 1, 1) We ms hoose sees foPVAs wsy bas rottng dvse ommnts and kystone ssmay afor dsoortonate benfs (17a)

KD

I thank Gadg, . Gaad, E eri, 1 y, U. a, . o. Shaffe and R. Skma fo omments Bown, K. Kevy R.

ambeson U ea, and me kndy ovded oes of nbshedeors o manss ro to baton I eeved sot fom AmeanInsttte f Indan Stdes S daona Fondaton n Inda Fbightogam aona Con fo A and Steam Imovment, and WyomngWae Reseah Cente

kcay, H. R. Ginzbu L. R 9 colgic rs sis fo sig

mltpe poios. I Speies Consevatio: A PoulatioBiologial Arch, d. . Si V. Lh 78 : h V

2. L J 13 ic

xinn n LV ciffio qio. Mh. Bs. 65

- of F W 16 c nd h vu yy Z B 8-0

3 c W R . w . .




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