population viability analysis of critically endangered ... of the likely time to extinction of the...

ENDANGERED SPECIES RESEARCHEndang Species Res

Vol. 21: 6576, 2013doi: 10.3354/esr00511

Published online July 3

INTRODUCTION

The worst vulture declines in recent history haveoccurred in southern Asia, where 95% of wild popu-lations of 3 Gyps species were extirpated before thedawn of the new millennium (Prakash 1999, Pain etal. 2003, 2008, Cuthbert et al. 2011). White-rumpedvultures Gyps bengalensis were classified as Criti-cally Endangered, the category for species facing anextremely high risk of extinction in the wild, in the

IUCNs Red Data Book following the Asian vulturecrisis (BirdLife International 2001). Until 1985, white-rumped vultures were described as possibly the mostabundant large bird of prey in the world (Houston1985), with an estimated global population of severalmillion birds. After precipitous declines throughoutthe Indian subcontinent, the estimated global popu-lation of white-rumped vultures falls within the bandof 3500 to 15 000 birds (BirdLife International 2012).The population decline has slowed due to the con-

Inter-Research 2013 www.int-res.com*Email: [email protected]

Population viability analysis of CriticallyEndangered white-rumped vultures

Gyps bengalensis

Nabin Baral1,*, Christopher Nagy2, Benjamin J. Crain3, Ramji Gautam4

1Department of Forest Resources and Environmental Conservation, Virginia Tech, Blacksburg, Virginia 24061, USA2Division of Vertebrate Zoology, American Museum of Natural History, Central Park West, New York, New York 10024, USA

3Department of Biology, University of Puerto Rico-Rio Piedras, San Juan, Puerto Rico 009364Department of Zoology, Prithvi Narayan Multiple Campus, Tribhuvan University, Pokhara, Nepal

ABSTRACT: More than a decade has passed since the catastrophic population decline in Gypsspecies was reported from South Asia, but much uncertainty remains about quantifying theirshort-term extinction risk. To estimate the future extinction risk of the white-rumped vulture Gypsbengalensis in Nepal, we conducted counts at 7 nesting colonies between 2002 and 2012. We com-pared 3 methods of estimating abundance based on count data and calculated mean populationgrowth rates and cumulative probabilities of extinction given the abundance estimates from eachmethod. The first 2 methods of abundance estimation were traditional indices: mean and maxi-mum values of all counts. The third method was a mixture modeling approach that corrected rawcounts by a detection parameter. The results of the traditional indices were characterized by highuncertainty levels as reflected in the wide confidence intervals, which limited their capacity tomake predictions about the fate of the populations with any confidence. The mixture modelingmethod provided more reliable results; there was a 51% probability of populations facing quasi-extinction (i.e. 20 vultures) in 13 yr and a 99% probability of quasi-extinction in 18 yr. Becausethe mixture modeling method provided more precise predictions while requiring minimal addi-tional effort, population biologists using count data are encouraged to employ such model-basedestimators. The white-rumped vulture populations in Rampur are in danger of disappearingwithin 2 decades, so conservation efforts should be expedited to prevent the loss of this species.

KEY WORDS: Asian vulture crisis Extinction probability Nepal Population ecology RampurValley Vulture conservation

Resale or republication not permitted without written consent of the publisher

Endang Species Res 21: 6576, 2013

certed efforts of stakeholders involved in vultureconservation, but there has been no strong evidenceof increasing or even stable vulture populations onthe Indian subcontinent (Pain et al. 2008, Cuthbert etal. 2011, Prakash et al. 2012).

A large number of factors have contributed to thedecline in vulture populations in southern Asia.Renal failure and visceral gout resulting from theconsumption of livestock carcasses contaminatedwith the veterinary drug diclofenac are believed tobe the main factors contributing to the large-scaleand rapid decline of Gyps vultures (Oaks et al.2004, Green et al. 2006). Simulations have shownthat just 1 in 760 livestock carcasses needs to con-tain diclofenac residues to cause the observedincrease in mortality rate and subsequent popula-tion declines in wild vulture populations (Green etal. 2004). In addition to diclofenac, other veterinarydrugs such as ketoprofen and aceclofenac areknown or suspected to be toxic to vultures (Naidooet al. 2010, Sharma 2012) and may play a role intheir population declines. Although diclofenac poi-soning took a heavy toll on wild populations in ashort period of time, white-rumped vultures displayseveral other characteristics (for example, a smallclutch size, slow breeding, and delayed maturity)that can reduce the ability of a population torebound even after negative influences have beenremoved (e.g. Meretsky et al. 2000, Antor et al.2007). Likewise, other factors such as habitatdestruction, food scarcity, and human persecutionhave also contributed to the slow decline in popula-tions over the long run (BirdLife International 2001,Ogada et al. 2012). Consequently, the future ofGyps species appears to be bleak.

The unprecedented population decline of Gypsvultures raises several questions: What is the chanceof recovery of white-rumped vultures? How long dowe have before they become extinct under currentconditions? What management interventions wouldimprove their population viability? Is captive breed-ing and re-introduction to natural habitat patches afeasible strategy for conserving white-rumped vul-tures? Answers to these questions are critical for theirsurvival, and population viability analysis (PVA) cansupply answers to questions like these.

PVA has emerged as an alternative to the magicnumber of 50 individuals suggested as the mini-mum number to prevent extinction (Gilpin 1996). Incontrast to the minimum viable population rule, aPVA is a stochastic quantitative process to evaluatethe extinction probability of a particular populationover time. PVA can serve 3 useful functions, partic-

ularly in the conservation and management of rareand endangered species. First, a PVA can deter-mine the urgency of recovery efforts based on theestimate of extinction probability within a specifiedlength of time (Dennis et al. 1991, Morris & Doak2002). Second, a PVA can assess recovery successby synthesizing monitoring data (Morris & Doak2002). Third, a PVA can identify key demographicprocesses or life cycle components suitable formanagement interventions (e.g. Crouse et al. 1987,Tremblay 1997, Beissinger & Westphal 1998). Be -cause of its useful functions, there have been num -erous case studies using PVA to address variousaspects of rare and endangered species manage-ment, including estimating extinction probability(Dennis et al. 1991, Morris & Doak 2002, Masatomiet al. 2007), testing the efficacy of recovery andreintroduction (Dennis et al. 1991, Kohlmann et al.2005, Zeoli et al. 2008, Schaub et al. 2009), assess-ing habitat requirements (Perkins et al. 2008,Coates & Duncan 2009), and analyzing the cost-effectiveness of conservation programs (Marshall etal. 2000, Bode & Brennan 2011).

Estimating abundance is a critical first step in PVA.Two widely used methods for estimating the abun-dance of white-rumped vultures in southern Asia arecounts of active nests and road transect surveys(Gilbert et al. 2002, Prakash et al. 2003, 2012, Chaud-hary et al. 2012). By counting the number of activenests, the first approach underestimates abundancebecause it ignores the subadults and juveniles pres-ent in a population. There are several major issueswith road transect surveys for white rumped vul-tures. First, data collected along roads are not repre-sentative of the population because nonrandomselection of survey locations (most often the case inroad transects) increases bias (Anderson 2001,Thompson 2002). Second, a large number of detec-tions is required to estimate a detectability function.This may not be feasible because of low populationdensities after the species declined by >95% (John-son 2008). Third, a transect survey is not useful whenthe area of interest is small or when the animals arespatially clumped, which is the case with white-rumped vultures that nest in relatively small, scat-tered colonies.

Consequently, when vultures are counted multipletimes over time and space in the breeding colonies,the simplest indices of abundance are the mean andmaximum values of all counts at each colony. Theseindex values are simple to calculate but invokestrong assumptions and at best are indices of relativeabundance (Thompson & Harwood 1990, Link &

66

Baral et al.: Future extinction risk of vultures

Sauer 1997, 1998, Severson & Plumb 1998). A majorcriticism of these index values is that they do not takeinto account detection probability, which makes itdifficult to make strong inductive inferences aboutpopulation growth or decline (Anderson 2001,Thompson 2002).

It is becoming increasingly apparent that biologistsneed to account for imperfect detection in their esti-mates of species presence and abundance (Royle2004, MacKenzie et al. 2006, Kry & Schmidt 2008).Even the maximum of a series of counts may besmaller than the actual abundance if animals aremissed (Thompson & Harwood 1990). Indeed, if oneassumes a stable abundance at a site within seasons,any deviation in counts at that site indicates imper-fect detection on the part of the observer and/or vary-ing availability of the animal to be detected even if itis present. While biologists have been aware of theseissues for many years, recent techniques have beendeveloped that can explicitly account for and modeldetection and availability rates (see MacKenzie et al.2006 for an in-depth discussion of similar issuesregarding presence/absence methods). Count dataare particularly important in avian ecology, and spe-cific techniques have been developed to handle suchdata (Royle 2004, Royle et al. 2004, Nichols et al.2009). Royle (2004) developed an N-mixture model-ing approach that estimates detection rate and popu-lation change from count data taken from multiplevisits to multiple sites. Dail & Madsen (2011)expanded this technique to allow for multiple sea-sons (i.e. primary periods) where abundance couldvary between seasons. Taking into account imperfectdetection is critical for a reliable estimate of abun-dance for PVA.

When it comes to conservation of critically endan-gered white-rumped vultures, developing robust andefficient PVA models will be useful for managementas these models provide critical information on theprobability of extinction in practical terms. McCarthyet al. (2003) concluded that at least 10 yr of data areneeded to obtain a PVA with good predictive power.In this study, we conducted a count-based PVA basedon 10 yr of count data from white-rumped vulturenesting colonies to quantify extinction risk for thisspecies in one of the Important Bird Areas of Nepal,the Rampur Valley.

The primary goal of this study was to obtain an esti-mate of the likely time to extinction of the RampurValleys white-rumped vultures. We were also inter-ested in comparing and examining the differences ofpredictions using 3 methods of abundance estimationfrom counts. These methods included the 2 tradi-

tional indices the mean and maximum values of allcounts and a more recent modeling approach toestimate and incorporate detection probability intoabundance estimates (Royle 2004, Dail & Madsen2011). To this end, we calculated abundances andgrowth rates from our count data and determined theprobability of quasi-extinction using count-basedPVA methods (Dennis et al. 1991, Morris & Doak2002). To our knowledge, this is the first attempt atusing a long-term data set to quantify extinction riskthrough empirical modeling for white-rumped vul-tures. As such, the findings should provide severalpieces of critical information on the populationdynamics of white-rumped vultures.

MATERIALS AND METHODS

Study site

The Rampur Valley (27 51 80 N, 83 54 24 E)lies in the Palpa District in the south-west part ofNepal (Fig. 1). The valley has the highest breedingden sity of white-rumped vultures Gyps bengalensis(Baral et al. 2005), and thus it has been included inBirdLife Internationals list of Important Bird Areasof Nepal (Baral & Inskipp 2005). Rampur has a sub-tropical climate, with an average (SD) yearly rain-fall of 1773 405 mm, an average minimum yearlytemperature of 16.5 0.9C, and an average maxi-mum yearly temperature of 29.0 0.8C for thedecade 2001 to 2010. The dominant vegetationcomprises hill sal Shorea robusta, kapok Bombaxceiba, khair Acacia catechu, karma Adina cordifo-lia, bel Aegle marmelos, and mango Mangiferaindica. Other resident vultures found in the valleyare the Critically Endangered slender-billed vul-ture Gyps tenuirostris, the Critically Endangeredred-headed vulture Sarcogyps calvus, and theEndangered Egyptian vulture Neophron perc-nopterus. Thus, the Rampur Valley provides criticalhabitat to a number of important species inaddition to the white-rumped vulture, making it apriority area for conservation efforts.

We found 7 breeding colonies of white-rumpedvultures in Rampur Valley: Islampur, Sadawarta,Jyagdi, Shera, Khairini, Shekham, and Keladi(Fig. 1). Except for Keladi, which was discovered in2006, we have been monitoring each of the colo -nies since 2002. After 2003, the Islampur colonywas deserted because local residents felled thenesting and roosting trees. Among the breedingcolonies, Khairini held the highest number of vul-

67


tures throughout the study period. The average distance between colonies was 4.1 2.1 km (mini-mum = 0.2 km between Islampur and Sadwarta,maximum = 7.1 km between Islampur and Shek -ham). Without marking or tagging vultures, it isalmost impossible to determine the movement ofindividual vultures between the colonies. Themovement of 5 satellite-tagged adult male white-rumped vultures ranged between 25 and 316 kmfrom their breeding or roosting sites in Pakistan in2003/2004 (Gilbert et al. 2007). This evidence sug-gests that vultures have the ability to move amongthe colonies within Rampur or from other colonieswithin the country. But, the degree of connectivityamong separate pop ulations and movements ofwhite-rumped vultures is still poorly known.

Field methods

In the past 10 yr, we spent a total of 225 d (at least5 h d1) in the field to count vultures at 7 nestingcolonies (1 was deserted in the second year, however,and therefore no data from this site were collected insubsequent years). On a yearly basis, average (SD)research effort was 22.5 5.7 d. Most often, field-work commenced in September and continued untilMay to coincide with the vultures breeding season.The breeding season commences with the congrega-tion of vultures and pair forming (or occupying a ter-ritory), which makes it easier to observe and countthem. At least 5 and at most 8 repeated counts weremade in each year, resulting in an average of 6.4 0.8 counts yr1.

68

Fig. 1. Network of Nepalese protected areas, Rampur, and vulture colonies. The active colonies are indicated by filled stars, and a deserted colony by an open star


Reliable counts of a population can be made atnests and roosts of raptor colonies, with increasingprecision in counts by standardizing the survey pro-cedure in terms of season, time of the day, andobserver experience (Glinski & Ohmart 1983).Accordingly, each year we attempted to count at thesame regular intervals and in the same months tocontrol for potential variability. Additionally, allcolonies were visited on the same days. We moni-tored all the roosting and nesting sites early in themorning (06:30 to 09:30 h) and late in the evening(17:30 to 19:30 h) and recorded all the vultures seenon nests and perched on roosts. In each survey, thecount represented the sum of adults, subadults, andjuveniles. Counting roosting as well as nesting vul-tures took into account non-breeders in addition tobreeding individuals. Because a single observerspearheaded all population counts, the variabilityamong observers was controlled by design.

Estimating abundance

True abundance is often unknown in wildlife stud-ies (e.g. Thompson & Harwood 1990), so it needs tobe estimated from data, i.e. counts of vultures atbreeding sites in this case. For the purpose of ourregional PVA, we summed site-specific abundances(i.e. abundances at each nesting colony) to get a totalabundance estimate for the Rampur Valley. We didnot model colonies separately because vultures areseemingly able to move between colonies given theinformation that is available on vulture movements(Gilbert et al. 2007) and because of the relativelysmall distances between our colonies (0.2 to 7.1 km).

Because we conducted population counts at least 5times in a year at multiple colonies, we had multiplecounts at each site in each season and could thus esti-mate abundance in a number of ways. We used boththe mean and maximum values of all counts as thefirst 2 estimators of annual breeding abundance. Themean value comprises all counts as comparable esti-mates of abundance, while the maximum value mayrepresent a more realistic approximation of abun-dance (Severson & Plumb 1998), since there were atleast as many animals at the site as the maximumcount. We used these indices to determine site-spe-cific abundances and then summed respective abun-dances to get annual total abundance for the entireRampur region.

To use Dail and Madsens method (hereafter DMmethod; Dail & Madsen 2011), we truncated our 5 to8 counts yr1 to include only October through Febru-

ary counts. We therefore had 39 counts in total for10 yr (3 counts for 3 yr, 4 counts for 5 yr, and 5 countsfor 2 yr). This period is the time of highest breedingdensity, and thus abundance is likely to be relativelystable during this stretch. Before October and afterFebruary, abundance could change substantially asvultures arrive and leave sporadically.

The DM method was implemented in the R pack-age unmarked using the pcountOpen function(Fiske & Chandler 2011) to estimate annual abun-dances at each site under a basic intercept-onlymodel (setting abundance as a Poisson variable anddetection as a binomial variable) with no site covari-ates. Site-specific abundance estimates based on thismodel were summed to obtain annual total abun-dances for the Rampur region. These 10 annual esti-mates were subsequently used to estimate popula-tion growth rates. We also estimated an overalldetection rate via the DM method, i.e. how likely wewere to count a vulture if it was at a particular siteduring a particular survey.

Estimating the parameters and 2

After obtaining annual abundances for the Rampurregion, we estimated the log geometric mean popula-tion growth () and the variance of the change in pop-ulation sizes (2) using linear regression (Morris &Doak 2002). Variance of log growth rate increases withincreasing time between counts; thus, to ensure equalvariances across time intervals, time intervals (i.e. ti+1 ti) are typically transformed via (ti+1 ti)1/2, and loggrowth rates are divided by (ti+1 ti)1/2; this transfor-mation standardizes the variance in log growth rateacross differing time scales. Since our surveys wereperformed at equal (annual) intervals, this transforma-tion kept all time intervals equal to 1. The slope of theresulting regression line was the estimated for ourdata using that abundance method, and the residualmean square (i.e. error mean square) was the estimateof 2. In our case, taking the arithmetic mean of theintrinsic rate of increase (r-values) and estimating thevariance would give the same results. This was done 3times, with each regression using the respective datafrom each abundance method (mean and maximumvalues of all counts and the DM method).

We also estimated confidence intervals for eachparameter. Following Dennis et al. (1991) and Morris& Doak (2002), a 95% confidence interval for wasestimated by the formula:

t, q1 SE () (1)

69


where t, q1 is the critical value of a 2-tailed t- distribution with = 0.05 and q = 9, the numberof seasonal transitions in our 10 annual surveys.Confidence limits for 2 were calculated using thechi-squared distribution with q 1 degrees offreedom

(q 1)2 / 20.025, q1, (q 1) 2 / 20.975, q1 (2)

Testing assumptions

Count-based PVA requires 4 major assumptions:(1) the mean and variance of the population growthrate remain constant, (2) growth rates and environ-mental effects are uncorrelated from one year to thenext, (3) there are no catastrophes or bonanzas, and(4) counts represent the population size, i.e. observa-tion error is insignificant (Morris & Doak 2002). Wetested these assumptions before embarking uponpopulation viability model simulation.

To test the first 2 assumptions, we explored densitydependence, demographic stochasticity, and tempo-ral environmental trends. First, we examined a plot ofthe r versus annual abundances (Nt) to see if growthrates changed with annual abundance (density de -pendence). No consensus exists regarding at whatpopulation size demographic stochasticity becomes amajor threat: Shaffer (1981) s uggests 50 individuals,Goodman (1987) and Lande (1993) suggest 20 indi-viduals, while MacArthur & Wilson (1967) suggest 10individuals to insulate a population from randomfluctuations in births and deaths. We followed themethods for other PVAs of large bird species (e.g.Engen & Sther 2000, Morris &Doak 2002) and set the quasi-extinc-tion threshold at 20 birds in total forall 6 colonies together in Rampur toaddress the demographic stochastic-ity issue. Fi nally, we performed a 2-tailed Durbin-Watson test to deter-mine whether successive annualgrowth rates were autocorrelatedand re gressed r-value and its vari-ance against time (yr) to look fortemporal environmental trends (i.e.correlation among growth rates ortheir variances).

Over the 10 yr of study there wasno evidence of extremely low orhigh growth rates. Our research pro-ject started after the catastrophicevent of mass mortality of Gyps vul-

ture populations on the Indian subcontinent, andthere were no outliers among the annual growth ratedata. We could not rule out the possibility of bonan-zas causing a larger number of changes in populationsizes in the future; however, failure to account forbonanzas would only lead to over-estimation of thetrue extinction risk.

To make sure counts best represent the true popu-lation size, we also estimated abundances account-ing for imperfect detection. Using the DM method,we explicitly estimated abundances from our countsbased on repeated counts adjusted by a detectionparameter (Royle 2004, Dail & Madsen 2011). Boththe mean-count and maximum-count indices ofabundance may not represent true population sizebecause some vultures might not be detected.

Determining extinction probabilities

The population sizes in the last survey year2011/2012 (58, 87, and 138 individuals, for the meanand maximum values of all counts and for DM meth-ods, respectively) served as a starting population sizefor projection (see Fig. 2 for the temporal trend of theabundance estimated by each of the methods).

After validating assumptions, we calculated theprobability of extinction at time t with the inverseGaussian distribution, given and 2 (see Lande &Orzack 1988, Morris & Doak 2002). Cumulative prob-abilities (or cumulative distribution functions) canthen be calculated by integrating these probabilitiesfrom t = 0 to t = tmax. We estimated the cumulative dis-tribution functions (CDFs) of the time to extinction for

70

Fig. 2. Gyps bengalensis. Temporal trend in abundance of white-rumpedvultures estimated by each of the 3 methods considered


the Rampur populations based on the respectiveabundances, values, and 2 values given by each ofthe 3 methods for up to 50 yr into the future. For esti-mating 95% confidence bands, 10 000 bootstrapresamples of and 2 and their respective standarderrors were used. Distribution functions and their95% confidence bands were calculated using MAT-LAB 7.1 (MathWorks 2005).

RESULTS

Diagnostics of assumptions

The assumptions of our count PVA appeared to bemet. Regression results showed that there has beenno substantial density dependence over the range ofpopulation sizes of Gyps bengalensis in the past 10 yrbecause the mean value and variance of the popula-tion growth rates remained constant: the mean-countmethod ( = 0.0038, t = 1.10, p = 0.309), the maxi-mum-count method ( = 0.0041, t = 1.45, p = 0.190),and the DM method ( = 0.0002, t = 0.31, p =0.765).

Similarly, there were no temporal trends in popula-tion growth rate in any of the 3 scenarios: the mean-count method ( = 0.0165, t = 0.48, p = 0.643), themaximum-count method ( = 0.0249, t = 0.86, p =0.420), and the DM method ( = 0.0008, t = 0.05, p =0.960). There were no temporal trends in the varia-tion of population growth rates either: the mean-count method ( = 0.0064, t = 0.96, p = 0.371), the

maximum-count method ( = 0.0047, t = 1.05, p =0.327), and the DM method ( = 0.0021, t = 1.01, p =0.344).

The first-order autocorrelation coefficients of thepopulation growth rates were not statistically signifi-cant in any of the 3 scenarios, although their signswere negative: the mean-count method (Pearsons r =0.38, p = 0.349), the maximum-count method (Pear-sons r = 0.38, p = 0.356), and the DM method (Pear-sons r = 0.21, p = 0.617). These results suggestedthat there was no substantial autocorrelation in thegrowth rates. Results of the Durbin-Watson testshowed a similar lack of autocorrelation because thevalue of the d statistic was close to 2 (mean-count: d =2.30, p = 0.624; maximum-count: d = 2.30, p = 0.620;and DM method: d = 1.40, p = 0.334).

Abundance estimation

Method-specific abundances varied substantially(Table 1), with the mean-count method providing thelowest abundances (range: 37 to 114 vultures) andthe DM method providing the largest (range: 107 to344 vultures). The substantially higher abundancesfrom the DM method were expected, since the countswere adjusted by detection rate (i.e. how likely is itthat a vulture will be counted if it is present at thetime of the survey); thus, an observer would tend tounderestimate the true population size proportion-ally by approximately 1 detection rate. The maxi-mum-likelihood estimate of the detection rate was

71

Survey Mean of replicate counts Maximum of replicate counts Dail and Madsens method year Abundance = r = Abundance = r = Abundance = r =

Nt+1/Nt log() Nt+1/Nt log() Nt+1/Nt log()

2002/2003 97 123 342 2003/2004 114 1.1753 0.1615 135 1.0976 0.0931 344 1.0063 0.00632004/2005 82 0.7193 0.3295 97 0.7185 0.3306 301 0.8747 0.13392005/2006 86 1.0488 0.0476 109 1.1237 0.1166 264 0.8751 0.13342006/2007 77 0.8953 0.1105 92 0.8440 0.1696 230 0.8714 0.13772007/2008 57 0.7403 0.3008 75 0.8152 0.2043 197 0.8567 0.15472008/2009 56 0.9825 0.0177 79 1.0533 0.0520 176 0.8951 0.11092009/2010 37 0.6607 0.4144 57 0.7215 0.3264 140 0.7934 0.23142010/2011 51 1.3784 0.3209 66 1.1579 0.1466 119 0.8507 0.16172011/2012 58 1.1373 0.1286 87 1.3182 0.2763 107 0.8962 0.1096

Mean () 0.0571 (0.2497 to 0.1354) 0.0385 (0.2094 to 0.1325) 0.1296 (0.1768 to 0.0825)Variance (2) 0.0627 (0.0286 to 0.2302) 0.0495 (0.0226 to 0.1816) 0.0039 (0.0018 to 0.0131)

Table 1. Gyps bengalensis. Abundance, the finite rate of population growth (), the intrinsic growth rate (r), and the estimationof parameters ( and 2) under the 3 different scenarios for assessing the extinction risk of white-rumped vultures in Rampur,Nepal, from 2002 to 2012. For method details see Royle (2004) and Dail & Madsen (2011). : the arithmetic mean of populationgrowth rate (r); 2: the variance of ; Nt and Nt+1: difference in abundance (N) between consecutive years (t and t+1); values in

parentheses: 95% confidence intervals


0.35 0.02 (mean and SE). Only the DM methodshowed a notable decline in population size overtime (Fig. 2).

According to the results of the DM method, theKhairini site had the highest number of vultures(range: 83 to 127) throughout the study period(Fig. 3). All other sites had disproportionately lowernumbers of vultures. At the Khairini site, the tempo-ral trend in vulture populations resembled a shallowcubic curve: a slight increase at the beginning, aslight decrease in the middle and then a slightincrease towards the end of the study period. But, atother sites, the numbers of vultures have shownsharp declines since 2008/2009.

Population trend

In all 3 scenarios, the mean values of the intrinsicrate of increase () were negative, but the confidenceintervals in the mean-count (0.2497 to 0.1345) andmaximum-count (0.2094 to 0.1325) methods werewider (and also included zero) than in the DMmethod. In both the mean- and maximum-count esti-mates, the upper confidence intervals of were posi-tive, and the confidence bands of the CDFs wereexceedingly wide (Fig. 4). Although the estimates of were negative, suggesting that the populationwould decline in these 2 scenarios, there may besome periods of population increase because thevariance of these estimates was relatively large. TheDM method provided more precise estimates of

and 2 because some of the variation in raw countswas accounted for in the estimate of the detectionrate, thus yielding a less variable pattern in fromyear to year.

Time to quasi-extinction

The results of the mean- and maximum-countmethods contained a great deal of uncertainty, asreflected by the wide confidence intervals, whichlimit their capacity to predict the fate of populationsaccurately. Using the DM method, predicted extinc-tion times were much less varied, due to higher reli-ability of the abundance estimate; there was a 51%probability of populations facing quasi-extinction in13 yr and a 99% probability of quasi-extinction in18 yr (Fig. 4). Although the quasi-extinction probabil-ity was higher for the mean- and maximum-countpredictions within the next 10 yr, the extinction riskincreased for the DM scenario after that time period.This switchover of extinction risk between the index-based methods and the model-based methods wasdue to the higher predicted starting abundance inthe DM method.

Sensitivity analysis

After examining the PVA results, we wanted todetermine what goals management would have toachieve in terms of improving population growth to

save the Rampur Valley population.We conducted a simple sensitivityanalysis where annual values fromthe DM estimates were in creasedby 5, 10, 15, and 20% to representhypothetical improvements in popu-lation growth as a result of success-ful conservation action. These en -hanced values were convertedinto values as before, and theextinction CDFs were re-calculated.It appears that an increase of 10 to15% in annual population growthwould dramatically improve the per-sistence probability of white-rumpedvultures in the Rampur Valley forthe next few decades (Fig. 5). Anincrease around 20% would likelyensure persistence for 50 yr, assum-ing other relevant factors remainsimilar.

72

Fig. 3. Gyps bengalensis. Estimate of abundance by the Dail and Madsenmethod across 7 sites for the time period between 2002/2003 and 2011/2012.The mean and mode of the estimates were fairly close, so we chose the mode torepresent abundance. The Islampur site was deserted during the second year,and the Keladi site was discovered in the fifth year. The first 4 yr for the Keladi

site were set to 0. (See Fig. 1 for site locations)


DISCUSSION

The comparative results suggest that the mixturemodeling approach (the DM method) gives more reli-able estimates of abundance and extinction probabil-

ity than traditional indices (mean and maximum val-ues of all counts), which yielded smaller annual abun-dances and much more variable growth rates. Theseresults are in accordance with other studies that docu-ment the shortcomings of using mean- or maximum-count data (Thompson & Harwood 1990, Anderson2001, Thompson 2002). Continual monitoring of pop-ulations on a regular basis and adjusting managementapproaches in light of new information would be use-ful for devising appropriate conservation strategies.We expect that some modifications in monitoring pro-tocols, for example, conducting more surveys betweenOctober and February, allocating more time for sur-veys in each colony, and deploying 2 observers to de-crease observation fatigue, can in crease detectionprobability in Rampur. Also, it is desirable to includeenvironmental covariates in the estimation of detec-tion probability. Count data ob tained from pointcounts or transects are generally biased because ofimperfect detection and, in some cases, because of thevariable probability of an animal present being ob-served (i.e. counted). Methods, such as those de-scribed by Royle (2004) and Dail & Madsen (2011), al-low the estimation of such observer-based parametersand thus provide more accurate abundance estimateswith minimal additional analysis. Most researchersacknowledge the need for multiple counts at theirsites; thus, upgrading to these new methods requiresfew adjustments and little additional field work. Weencourage biologists that use count data to explorethese concepts and adjust their study designs so theycan make use of these more powerful techniques.

73

Fig. 4. Gyps bengalensis. Cumulative distribution functionof quasi-extinction (


Since our sensitivity analysis indicates that a 10 to15% increase in population growth is necessary tomaintain the vulture population, several manage-ment options should be considered. Keeping inmind the ongoing decline in white-rumped vultures,strategies aimed at increasing population growthrates by removing the toxic chemicals from theenvironment are obviously needed. The declarationof an area of 39 122 km2 comprising 21 districts inNepal (including Rampur) as Vulture Safe Zones i.e. diclofenac-free areas could boost vulture pop-ulation growth (see Bowden 2013). Removing thetoxic chemicals would directly increase adult sur-vival and lead to significant population increasesbecause adult survival is the most elastic vital ratefor populations of long-lived, iteroparous animalssuch as vultures (Lebreton & Colbert 1991, Crookset al. 1998, Gaillard et al. 1998, Sandvik et al. 2005).Stopping the use of diclofenac, ketoprofen, ace-clofenac, and other harmful livestock medicines(Naidoo et al. 2010, Sharma 2012) would not onlysave adult vultures but also subadults and juvenilesthat are critical for population recruitment. Provisionof wholesome food through the establishment ofvulture feeding stations might prevent secondarypoisoning, which is the main cause of the Gyps vul-tures decline elsewhere (Muzinic 2007, Ogada &Keesing 2010). These management interventionsshould create a favorable environment for thewhite-rumped vulture population to grow (Sibly &Hone 2002).

A second strategy to stimulate population growthwould be protecting nesting sites. Many nestingtrees have been felled in the past to raise funds to runa school, compromising the vultures breeding suc-cess (Gautam & Baral 2009). Investigations on thepotential use of artificial nesting sites should there-fore be initiated. Thus, creating more suitable habi-tat, perhaps by creating artificial nesting sites, mayprove to be an effective management strategy forwhite-rumped vultures.

Another management strategy that may prove suc-cessful is captive breeding. Despite their limitations(see Snyder et al. 1996), captive breeding programshave helped to prevent the extinction of a number ofrare and endangered species. Captive breeding andrelease programs have proved to be effective for birdspecies such as griffon vultures Gyps fulvus, pere-grine falcons Falco peregrinus, and Puerto Rican par-rots Amazona vittata (Sarrazin et al. 1994, White etal. 2005). The Vulture Conservation and BreedingCenter was established in 2008 in Nepal with the aimof holding up to 25 pairs of white-rumped vultures,

and some promising results for long-term conserva-tion of vultures have resulted. A major demerit ofcaptive breeding is that the capture of wild vulturesis required, which may decrease growth rates evenfurther over a short-term period, which could be anoverly large risk if this could lead to stochastic extinc-tion. For example, when 17 chicks were capturedfrom the wild for the breeding center, vulturesdeserted all the nesting trees from which chicks werecollected (Gautam & Baral 2013). As with most con-servation strategies, however, each of these willrequire government, nongovernmental organiza-tions, and local communities working together.

A major limitation of a count-based model is thatit treats all individuals in the population as if theywere identical, and we summed all potentialbreeders (juveniles, subadults, and adults) in ourcurrent study. Reducing the dynamics of reproduc-tion and survival into a composite measure such as and r often obscures important age-specificdetails that can inform management (Allen et al.1992), e.g. adult survival and reproduction versusjuvenile survival and reproduction. An age-specificmodel based on data collected from marked vul-tures would provide more information about age-specific survival and reproductive rates, and directstrategies for conservation. Thus, future researchshould focus on banding a number of adult andjuvenile vultures and then building an age-specificPVA model.

CONCLUSIONS

Once numbering in the millions, white-rumpedvultures Gyps bengalensis are now estimated to havea global abundance of 15 000. If their precipitousdecline is not halted or reversed, many large breed-ing populations will disappear, possibly leading toglobal species extinction in a few decades. By provid-ing an estimate of the probability of quasi-extinction,the PVA presented here provides a realistic time-frame for conservation action and serves as a base-line for synthesizing monitoring data to assess therecovery of this species over time. Future researchshould focus on estimating age-specific survival andbreeding rates in addition to overall abundance andgrowth rates of white-rumped vultures in the wild.Based on the present models, managers and stake-holders have approximately 15 yr to reverse thedecline. If immediate actions are taken, there is suffi-cient time to intervene and establish viable vulturepopulations in Rampur, Nepal.

74


Acknowledgements. The Peregrine Fund (TPF), USA, TheRoyal Society for the Protection of Birds (RSPB), UK, andBird Conservation Nepal (BCN) provided research grants toconduct the field work. The funding organizations, however,had no involvement in the study design, in the collection,analysis and interpretation of the data, in the writing of thereport, or in the decision to submit the article for publication.We thank Prashant Bhattarai for his help in making Fig. 1and Carlos Milan for his assistance with the computer pro-gramming. The constructive comments from 3 reviewershelped to improve the quality of the paper.

LITERATURE CITED

Allen EJ, Harris JM, Allen LJS (1992) Persistence-time mod-els for use in viability analyses of vanishing species.J Theor Biol 155: 3353

Anderson DR (2001) The need to get the basics right inwildlife field studies. Wildl Soc Bull 29: 12941297

Antor R, Margalida A, Frey H, Heredia R, Lorente L, Ses J(2007) First breeding age in captive and wild beardedvultures Gypaetus barbatus. Acta Ornithologica 42: 114118

Baral HS, Inskipp C (2005) Important bird areas of Nepal.Bird Conservation Nepal, Kathmandu and BirdLife Inter-national, Cambridge

Baral N, Gautam R, Tamang B (2005) Population status andbreeding ecology of white-rumped vulture Gyps ben-galensis in Rampur Valley, Nepal. Forktail 21: 8791

Beissinger SR, Westphal MI (1998) On the use of demo-graphic models of population viability in endangeredspecies management. J Wildl Manag 62: 821841

BirdLife International (2001) Threatened birds of Asia: theBirdLife International Red Data Book. BirdLife Interna-tional, Cambridge

BirdLife International (2012) Species factsheet: Gyps ben-galensis. Available at: www.birdlife.org (accessed 13September 2012)

Bode M, Brennan KE (2011) Using population viabilityanalysis to guide research and conservation actions forAustralias threatened malleefowl Leipoa ocellata. Oryx45: 513521

Bowden C (ed) (2013) Report from the 2nd meeting of Sav-ing Asias Vultures from Extinction (SAVE). The RoyalSociety for the Protection of Birds (RSPB), Bedfordshire

Chaudhary A, Subedi TR, Giri JB, Baral HS and others (2012)Population trends of Critically Endangered Gyps vulturesin the lowlands of Nepal. Bird Conserv Int 22: 270278

Coates F, Duncan M (2009) Demographic variation betweenpopulations of Caledenia orientalis a fire-managedthreatened orchid. Aust J Bot 57: 326339

Crooks K, Sanjayan M, Doak D (1998) New insights on chee-tah conservation through demographic modeling. Con-serv Biol 12: 889895

Crouse DT, Crowder LB, Caswell H (1987) A stage-basedpopulation model for loggerhead sea turtles and implica-tions for conservation. Ecology 68: 14121423

Cuthbert R, Taggart MA, Prakash V, Saini M and others(2011) Effectiveness of action in India to reduce exposureof Gyps vultures to the toxic veterinary drug diclofenac.PLoS ONE 6: e19069

Dail D, Madsen L (2011) Models for estimating abundancefrom repeated counts of an open metapopulation. Bio-metrics 67: 577587

Dennis B, Munholland PL, Scott JM (1991) Estimation ofgrowth and extinction parameters for endangered spe-cies. Ecol Monogr 61: 115143

Engen S, Sther B (2000) Predicting the time to quasi-extinction for populations far below their carrying capac-ity. J Theor Biol 205: 649658

Fiske I, Chandler RB (2011) Unmarked: an R package for fitting hierarchical models of wildlife occurrence andabundance. J Stat Software 43: 123. Available at: www.jstatsoft.org/v43/i10/

Gaillard JM, Festa-Bianchet M, Yoccoz N (1998) Populationdynamics of large herbivores: variable recruitment withconstant adult survival. Trends Ecol Evol 13: 5863

Gautam R, Baral N (2009) Research on and monitoring ofwhite-rumped vultures (Gyps bengalensis) for sevenyears in Rampur, Nepal. Final report submitted to ThePeregrine Fund, USA; The Royal Society for the Protec-tion of Birds, UK; and Bird Conservation Nepal. ThePeregrine Fund, Boise, ID

Gautam R, Baral N (2013) Population trends and breedingsuccess of three endangered vulture species in PokharaValley, Kaski, Nepal. Ibisbill: J Himalayan Ornithol 2: 4654

Gilbert M, Virani MZ, Watson RT, Oaks JL and others (2002)Breeding and mortality of oriental white-backed vultureGyps bengalensis in Punjab Province, Pakistan. BirdConserv Int 12: 311326

Gilbert M, Watson RT, Ahmed S, Asim M, Johnson JA (2007)Vulture restaurants and their role in reducing diclofenacexposure in Asian vultures. Bird Conserv Int 17: 6377

Gilpin M (1996) Forty-eight parrots and the origins of popu-lation viability analysis. Conserv Biol 10: 14911493

Glinski RL, Ohmart RD (1983) Breeding ecology of the Mis-sissippi kite in Arizona. Condor 85: 200207

Goodman D (1987) The demography of chance extinction.In: Soule ME (ed) Viable populations for conservation.Cambridge University Press, Cambridge, p 1134

Green RE, Newton I, Shultz S, Cunningham AA, Gilbert M,Pain DJ, Prakash V (2004) Diclofenac poisoning as acause of vulture population declines across the Indiansubcontinent. J Appl Ecol 41: 793800

Green RE, Taggart MA, Das D, Pain DJ, Kumar S, Cunning-ham AA, Cuthbert R (2006) Collapse of Asian vulturepopulations: risk of mortality from residues of the veteri-nary drug diclofenac in carcasses of treated cattle. J ApplEcol 43: 949956

Houston DC (1985) Indian white-backed vulture (G. ben-galensis). In: Newton I, Chancellor RD (eds) Conserva-tion studies on raptors. International Council for BirdPreservation Technical Publication No. 5, ICBP, Cam-bridge, p 465466

Johnson DH (2008) In defense of indices: the case of birdsurveys. J Wildl Manag 72: 857868

Kry M, Schmidt BR (2008) Imperfect detection and its con-sequences for monitoring for conservation. CommunityEcol 9: 207216

Kohlmann S, Schmidt G, Garcelon D (2005) A populationviability analysis for the island fox on Santa CatalinaIsland, California. Ecol Model 183: 7794

Lande R (1993) Risks of population extinction from demo-graphic and environmental stochasticity and randomcatastrophes. Am Nat 142: 911927

Lande R, Orzack SH (1988) Extinction dynamics of age-structured populations in a fluctuating environment.Proc Natl Acad Sci USA 85: 74187421

75

http://dx.doi.org/10.1073/pnas.85.19.7418http://dx.doi.org/10.1086/285580http://dx.doi.org/10.1016/j.ecolmodel.2004.07.022http://dx.doi.org/10.1556/ComEc.9.2008.2.10http://dx.doi.org/10.1111/j.1365-2664.2006.01225.xhttp://dx.doi.org/10.1111/j.0021-8901.2004.00954.xhttp://dx.doi.org/10.2307/1367256http://dx.doi.org/10.1046/j.1523-1739.1996.10061491.xhttp://dx.doi.org/10.1017/S0959270906000621http://dx.doi.org/10.1017/S0959270902002198http://dx.doi.org/10.1016/S0169-5347(97)01237-8http://dx.doi.org/10.1006/jtbi.2000.2094http://dx.doi.org/10.2307/1943004http://dx.doi.org/10.1111/j.1541-0420.2010.01465.xhttp://dx.doi.org/10.1371/journal.pone.0019069http://dx.doi.org/10.2307/1939225http://dx.doi.org/10.1046/j.1523-1739.1998.97054.xhttp://dx.doi.org/10.1071/BT08144http://dx.doi.org/10.1017/S0959270911000426http://dx.doi.org/10.1017/S0030605311000688http://dx.doi.org/10.2307/3802534http://dx.doi.org/10.3161/068.042.0106http://dx.doi.org/10.1016/S0022-5193(05)80547-8


Lebreton JD, Colbert J (1991) Bird population dynamics,management, and conservation: the role of mathemati-cal modeling. In: Perrins CM, Lebreton JD, Hirons GJM(eds) Bird population studies: relevance to conservationand management. Oxford University Press, Oxford,p 105125

Link W, Sauer J (1997) Estimation of population trajectoriesfrom count data. Biometrics 53: 488497

Link W, Sauer J (1998) Estimating population change fromcount data: application to the North American breedingbird survey. Ecol Appl 8: 258268

MacArthur RM, Wilson EO (1967) The theory of island bio-geography. Princeton University Press, Princeton, NJ

MacKenzie DI, Nichols JD, Royle JA, Pollock KH, Bailey LL,Hines JE (2006) Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence.Academic Press, Burlington, MA

Marshall E, Homans F, Haight R (2000) Exploring strategiesfor improving cost effectiveness of endangered speciesmanagement: the kirtlands warbler as a case study.Land Econ 76: 462473

Masatomi Y, Higashi S, Masatomi H (2007) A simple popu-lation viability analysis of tancho (Grus japonesis) insoutheastern Hokkaido, Japan. Popul Ecol 49: 297304

MathWorks (2005) MATLAB, Ver. 7.1. The MathWorks Inc.,Natick, MA

McCarthy MA, Andelman SJ, Possingham HP (2003) Relia-bility of relative predictions in population viability analy-sis. Conserv Biol 17: 982989

Meretsky V, Snyder N, Beissinger S, Clendenen D, Wiley J(2000) Demography of the California condor: implica-tions for re-establishment. Conserv Biol 14: 957967

Morris WF, Doak DF (2002) Quantitative conservation biol-ogy: theory and practice of population viability analysis.Sinauer Associate Publishers, Sunderland, MA

Muzinic J (2007) Poisoning of seventeen Eurasian griffons(Gyps fulvus) in Croatia. J Raptor Res 41: 239242

Naidoo V, Wolter K, Cromarty D, Diekmann M and others(2010) Toxicity of non-steroidal anti-inflammatory drugsto Gyps vultures: a new threat from ketoprofen. Biol Lett6: 339341

Nichols JD, Thomas L, Conn PB (2009) Inferences aboutlandbird abundance from count data: recent advancesand future directions. Environ Ecol Stat 3: 201235

Oaks JL, Giltbert M, Virani MZ, Watson RT and others(2004) Diclofenac residues as the cause of populationdecline of vultures in Pakistan. Nature 427: 630633

Ogada DL, Keesing F (2010) Decline of raptors over a three-year period in Laikipia, Central Kenya. J Raptor Res 44: 129135

Ogada DL, Keesing F, Virani MZ (2012) Dropping dead: causes and consequences of vulture population declinesworldwide. Ann NY Acad Sci 1249: 5771

Pain DJ, Cunningham AA, Donald PF, Duckworth JW andothers (2003) Causes and effects of temporospatialdeclines of Gyps vultures in Asia. Conserv Biol 17: 661671

Pain DJ, Bowden CGR, Cunningham AA, Cuthbert R andothers (2008) The race to prevent the extinction of SouthAsian vultures. Bird Conserv Int 18: S30S48

Perkins DW, Vickery PD, Shriver WG (2008) Population

viability analysis of the Florida grasshopper sparrow(Ammodramus savannarum floridanus): testing recoverygoals and management options. Auk 125: 167177

Prakash V (1999) Status of vultures in Keoladeo NationalPark, Bharatpur, Rajasthan, with special reference topopulation crash in Gyps species. J Bombay Nat Hist Soc96: 365378

Prakash V, Pain DJ, Cunningham AA, Donald PF and others(2003) Catastrophic collapse of Indian white-backedGyps bengalensis and long-billed Gyps indicus vulturepopulations. Biol Conserv 109: 381390

Prakash V, Bishwakarma MC, Chaudhary A, Cuthbert Rand others (2012) The population decline of Gyps vul-tures in India and Nepal has slowed since veterinary useof diclofenac was banned. PLoS ONE 7: e49118

Royle JA (2004) N-mixture models for estimating populationsize from spatially replicated counts. Biometrics 60: 108115

Royle JA, Dawson DK, Bates S (2004) Modeling abundanceeffects in distance sampling. Ecology 85: 15911597

Sandvik H, Erikstad K, Barrett R, Yoccoz N (2005) The effectof climate on adult survival in five species of NorthAtlantic seabirds. J Anim Ecol 74: 817831

Sarrazin F, Bagnolini C, Pinna J, Danchin E, Clobert J (1994)High survival estimates of griffon vultures (Gyps fulvusfulvus) in a reintroduced population. Auk 111: 853862

Schaub M, Zink R, Beissmann H, Sarrazin F, Arlettaze R(2009) When to end releases in reintroduction pro-grammes: demographic rates and population viabilityanalysis of bearded vultures in the Alps. J Appl Ecol 46: 92100

Severson K, Plumb G (1998) Comparison of methods to esti-mate population densities of black-tailed prairie dogs.Wildl Soc Bull 26: 859866

Shaffer ML (1981) Minimum population sizes for speciesconservation. Bioscience 31: 131134

Sharma P (2012) Aceclofenac as a potential threat to criti-cally endangered vultures in India: a review. J RaptorRes 46: 314318

Sibly RM, Hone J (2002) Population growth rate and itsdeterminants: an overview. Philos Trans R Soc Lond BBiol Sci 357: 11531170

Snyder N, Derrickson S, Beissinger S, Wiley J, Smith T,Toone W, Miller B (1996) Limitations of captive breedingin endangered species recovery. Conserv Biol 10: 338348

Thompson WL (2002) Towards reliable bird surveys: ac -counting for individuals present but not detected. Auk119: 1825

Thompson P, Harwood J (1990) Methods for estimating thepopulation size of common seals, Phoca vitulina. J ApplEcol 27: 924938

Tremblay R (1997) Lepanthes caritensis, an endangeredorchid: no sex, no future. Selbyana 18: 160166

White T Jr, Collazo J, Vilella F (2005) Survival of captive-reared Puerto Rican parrots released in the CaribbeanNational Forest. Condor 107: 424432

Zeoli LF, Sayler RD, Wielgus R (2008) Population viabilityanalysis for captive breeding and reintroduction of theendangered Columbian basin pygmy rabbit. Anim Con-serv 11: 504512

76

Editorial responsibility: Michael Reed,Medford, Massachusetts, USA

Submitted: December 3, 2012; Accepted: April 16, 2013Proofs received from author(s): June 20, 2013

http://dx.doi.org/10.1111/j.1469-1795.2008.00208.xhttp://dx.doi.org/10.1650/7672http://dx.doi.org/10.2307/2404387http://dx.doi.org/10.1046/j.1523-1739.1996.10020338.xhttp://dx.doi.org/10.1098/rstb.2002.1117http://dx.doi.org/10.3356/JRR-11-66.1http://dx.doi.org/10.2307/1308256http://dx.doi.org/10.1111/j.1365-2664.2008.01585.xhttp://dx.doi.org/10.2307/4088817http://dx.doi.org/10.1111/j.1365-2656.2005.00981.xhttp://dx.doi.org/10.1890/03-3127http://dx.doi.org/10.1111/j.0006-341X.2004.00142.xhttp://dx.doi.org/10.1371/journal.pone.0049118http://dx.doi.org/10.1016/S0006-3207(02)00164-7http://dx.doi.org/10.1525/auk.2008.125.1.167http://dx.doi.org/10.1017/S0959270908000324http://dx.doi.org/10.1046/j.1523-1739.2003.01740.xhttp://dx.doi.org/10.1111/j.1749-6632.2011.06293.xhttp://dx.doi.org/10.3356/JRR-09-49.1http://dx.doi.org/10.1038/nature02317http://dx.doi.org/10.1098/rsbl.2009.0818http://dx.doi.org/10.3356/0892-1016(2007)41[239%3APOSEGG]2.0.CO%3B2http://dx.doi.org/10.1046/j.1523-1739.2000.99113.xhttp://dx.doi.org/10.1046/j.1523-1739.2003.01570.xhttp://dx.doi.org/10.1007/s10144-007-0048-2http://dx.doi.org/10.2307/3147041http://dx.doi.org/10.1890/1051-0761(1998)008[0258%3AEPCFCD]2.0.CO%3B2http://dx.doi.org/10.2307/2533952

cite43: cite5: cite56: cite14: cite3: cite27: cite55: cite13: cite41: cite26: cite54: cite40: cite25: cite53: cite38: cite11: cite24: cite52: cite8: cite23: cite51: cite36: cite6: cite49: cite22: cite35: cite4: cite63: cite21: cite34: cite2: cite47: cite62: cite33: cite18: cite46: cite61: cite59: cite32: cite60: cite45: cite31: cite16: cite9: cite29: cite44: cite7: cite30: cite57:

population viability analysis of critically endangered ... of the likely time to extinction of the...

Documents