population viability analysis of guadalupe fur seals ...mmru.ubc.ca/wp-content/pdfs/hernandez and...

ENDANGERED SPECIES RESEARCHEndang Species Res

Vol. 37: 255–267, 2018https://doi.org/10.3354/esr00925

Published December 13

© The authors 2018. Open Access under Creative Commons byAttribution Licence. Use, distribution and reproduction are un -restricted. Authors and original publication must be credited.

Publisher: Inter-Research · www.int-res.com

*Corresponding author: [email protected]

OPENPEN ACCESSCCESS

INTRODUCTION

The Guadalupe fur seal Arctocephalus townsendiis endemic to the Pacific Ocean and currently onlybreeds in Mexico (Aurioles-Gamboa et al. 2010). Itwas thought to have gone extinct by the end of the1800s because of the commercial fur trade. However,a small number of Guadalupe fur seals (

Endang Species Res 37: 255–267, 2018

In 2010, the minimum population size of Guada-lupe fur seals during the breeding season was esti-mated to be 2503 seals at the San Benito Islands and13 327 at Guadalupe Island (García-Capitanachi2011). At that time, the San Benito population wasex periencing a 30% annual growth rate (1997−2014),and the Guadalupe population was increasing 10.3%per year (1955−2015) (Sierra-Rodríguez 2015, Car-retta et al. 2017). All of these positive changes bodedwell for the recovery of Guadalupe fur seals. How-ever, unusual numbers of fur seals of different ageand sex classes stranded in recent years throughoutparts of their former distribution and beyond (i.e.central California, Pacific coast of Mexico, Gulf ofCalifornia, and Vancouver Island in British Colum-bia, Canada) (Villegas-Zurita et al. 2015, Elorriaga-Verplancken et al. 2016a, Aurioles-Gamboa et al.2017, Carretta et al. 2017). Equally troublesome arethe recent numbers of young seals that have strandedand died along the coasts of California and Baja Cal-ifornia, as well as the dead adult and subadult furseals that have washed ashore (Aurioles-Gamboa etal. 2017, Carretta et al. 2017).

The young stranded animals along the coast of Cali-fornia showed signs of malnutrition with bacterial andparasitic infections (https://www.fisheries. noaa. gov/national/marine-life-distress/2015-2018-guada lupe-fur-seal-unusual-mortality-event-california). This un-usual mortality event was associated with the large-scale warming of the Pacific Ocean caused by the2015 El Niño event (Elorriaga-Verplancken et al.2016b) and the ‘Blob’, which reached the waters of thewest coast of the Baja California peninsula in 2014and 2015 (Cavole et al. 2016). The Blob was a patch ofanomalously warm water formed in the northeastern

Pacific during the winter of 2013 to 2014. It ex tendedto the Baja California peninsula and affected organ-isms at all levels of the food web (Kintisch 2015). Theadult and subadult male fur seals that stranded on theBaja California peninsula during the post-breedingmigration were possibly using a new feeding groundin the Gulf of Ulloa (Aurioles- Gamboa et al. 2017).

The future of Guadalupe fur seals is uncertain inlight of the recent strandings and the increasing fre-quencies of extreme ocean climate events (Elorriaga-Verplancken et al. 2016b). One means of assessingthe probability that Guadalupe fur seals may goextinct is by conducting a population viability analy-sis (PVA) (Shaffer 1978, 1981). This quantitative tech-nique is commonly used in conservation biology toassess the probability of a population going extinctwithin a given number of years — and is one of theclassification criteria used by the IUCN and otherorganizations to assess whether wildlife populationsare endangered, threatened, vulnerable, or not atrisk (IUCN 2012). However, a PVA has never beenconducted to determine the viability of the Guada-lupe fur seal population.

We developed 3 count-based PVAs for the Guada-lupe fur seal occurring on (1) Guadalupe Island, (2)the San Benito Islands, and (3) the 2 colonies com-bined (Morris & Doak 2003). Count-based PVAs arebased on systematic counts and estimates of the totalnumber of individuals in the population to define theaverage growth trend and its variance (Dennis et al.1991). We used the models to determine the proba-bility of Guadalupe fur seals going extinct (IUCN2012) and estimated the average total population sizeof Guadalupe fur seals in 2017 using stochastic lamb -da values (λ).

MATERIALS AND METHODS

Model approach

We performed a count-based PVA using a simplestochastic diffusion approximation model. The diffu-sion approximation model uses linear regressionparameters to estimate λ. The model also providesmeasures of uncertainty, such as median time toextinction and the probability of the populationdeclining to threshold abundances (i.e. the cumula-tive probability of quasi-extinction) (Dennis et al.1991). We developed a PVA for each colony of furseals and for both colonies combined. For the latter,we combined data from the 2 sets of islands startingin 1997, when Guadalupe fur seals were first re -

256

Fig. 1. Location of Guadalupe Island and the San Benito Is-lands (Mexico), used by Guadalupe fur seals Arctocephalus

townsendi to breed and rest

Hernández-Camacho & Trites: PVA of Guadalupe fur seals 257

ported on the San Benito Islands. Considering thatpopulation counts were not made in the same yearsin both colonies, we fit a deterministic exponentialgrowth model on observed population counts to esti-mate missing counts for each colony.

We evaluated 3 scenarios of quasi-extinctionthresholds occurring when the populations fall below100, 500, and 1000 individuals. This parameter isgenerally difficult to define for any imperiled speciesbecause empirical data are limited. We chose those 3scenarios based on the historical reports of Guada-lupe fur seals during the first half of the 19th century.Although it is unknown how many animals survivedhunting, the first reports of Guadalupe fur seals atGuadalupe Island put numbers at


which both counts were available (Table 1). Thus, weused the corrected data for our PVA when both rawand corrected counts were available. When only rawcounts were available, we applied the estimatedmean correction factor. We call these values the min-imum corrected population. Studies reporting thesize of the San Benito Islands colony did not use anycorrection factor; thus, we applied the same meancorrection factor to those counts as well.

Applying the correction factors to animals countedonshore yields a minimum estimate of populationsize. However, they do not account for the numberof animals at sea during a survey. Another approachfor estimating total population size is to use the num-ber of newborn pups as an index of population size(multiplicative factor) because pups do not leave

the colony during their first few weeks of life (Berk-son & DeMaster 1985, Loughlin et al. 1994, Trites &Larkin 1996). The relationship between the numberof pups and the total population depends on a popu-lation’s age structure and vital rates (Berkson &DeMaster 1985).

The multipliers to estimate population size frompup counts vary depending on life history parame-ters (e.g. longevity, age-specific mortality rates) andpopulation tendency (Taylor et al. 1995). Thus, for theGuadalupe fur seal, we obtained a mean value (4.5)from the multipliers available for 2 fur seal specieswith increasing populations: the Australian fur sealArctocephalus pusillus doriferus (4.5; Kirkwood etal. 2010) and the New Zealand fur seal A. fosteri(4.2, 4.9; Taylor et al. 1995). These values fall

Date Abundance SourceYear Month Males Subadults Females Juveniles Pups Unknown To Tc Tp

Guadalupe1955 Jun 35 46 49 Hubbs (1956a)1956 Jun 92 120 130 Hubbs (1956a)1968 Jun 314 410 443 Brownell et al. (1974)1977 Jun−Jul 591 1073 1159 Fleischer (1978)1983 Jun 374 60 642 134 24 62 1296 1879 2029 Gallo-Reynoso (1994)1984 Aug 649 1597 1600 1728 Seagars (1984)1988 Jun−Jul 468 78 1134 472 998 109 3259 3531 3813 Torres (1991)1991 Jul 1349 198 1707 895 1197 78 5424 6361 6870 Gallo-Reynoso (1994)1992 Jul 1907 362 2036 419 894 134 5752 7348 7936 Gallo-Reynoso (1994)1993 Jul 1366 263 2594 347 1852 21 6443 7408 8001 Gallo-Reynoso (1994)1995 Aug 2381 7858 8487 Gallo-Reynoso et al. (2005)2000 Jun 5644 9346 10094 Gallo-Reynoso et al. (2005)2003 Jul 7648 12176 13150 Gallo-Reynoso et al. (2005)2006 Aug 7265 11625 12555 Hernández-Montoya (2009)2009 Jun−Jul 2763a 1567 300 2298 3104 10032 11046 11930 García-Capitanachi (2011)2010 Jun−Jul 3980a 3855 26 3183 2283 13327 17581 18987 García-Capitanachi (2011)

San Benito1997 Aug 0 0 0 0 9 247 256 334 Maravilla-Chavez & Lowry

(1999)2000 Jun 21 57 375 51 0 78 582 760 Aurioles-Gamboa et al. (2010)2007 Jul 17 96 540 292 7 614 1566 2045 Aurioles-Gamboa et al. (2010)2008 Jul 26 266 494 615 8 704 2113 2759 Aurioles-Gamboa et al. (2010)2009 Jun−Jul 438a 63 633 7 4130 5271 6883 García-Capitanachi (2011)2010 Jun−Jul 683a 538 296 8 978 2503 3268 García-Capitanachi (2011)2012 Jul 6 4572 5970 Sierra-Rodríguez (2015)2013 Jul 19 1969 2571 Sierra-Rodríguez (2015)2014 Jul 2 6 3674b 28 0 3710 4844 Sierra-Rodríguez (2015)2015 Jul 5 13 1460b 16 0 1494 1951 Elorriaga-Verplancken et al. (2016b)

aMales and subadultsbJuveniles and subadults

Table 1. Historical abundance of Guadalupe fur seals on Guadalupe Island and the San Benito Islands, Mexico, beginning with thefirst census in 1955 after being presumed extinct in 1928. Age and sex categories counted include males (breeding age adult males),subadults (young non-breeding adult males), females (breeding age females), juveniles (sexually immature individuals of both sexes>1 yr old), pups (nursing young of both sexes), and unknown or undetermined ages (Gallo-Reynoso 1994). Also shown are the totalnumber of fur seals observed (To) during the survey, the total corrected (Tc) for animals at the colony not seen during the survey,

and the total population (Tp) estimated by multiplying the number of pups by 4.5. Blanks: no data available


within the estimated range (3.5−4.5) for other polyg-ynous pinnipeds with increasing populations (Har-wood & Prime 1978). We multiplied the number ofpups (ob tained from the minimum corrected popula-tion) by 4.5 to estimate the total Guadalupe fur sealpopulation.

Guadalupe fur seal pups make up an estimated24 ± 3.4% of the total population (Gallo-Reynoso1994, Hernández-Montoya 2009). We therefore ap -plied this percentage to the minimum corrected pop-ulation estimates to obtain the number of pups bornwhen this value was not available (Table 1). Since theSan Benito Islands site is not a reproductive colony,we could not estimate the total population based onthe number of pups; thus, we only corrected the non-pup counts for this colony.

The population counts represent the period fromthe first year animals were reported to have recolo-nized the 2 islands to the most recent publishedcount (1955−2010 for Guadalupe Island and 1997−2015 on the San Benito Islands). However, countswere made at irregular intervals, and count data aremissing for both colonies for some years (Table 1).

Model assumptions

Our model assumed that (1) all individuals areidentical, and the count data represent the true num-ber of individuals in a population (i.e. observationerror is minimal); (2) the patterns of populationgrowth and fluctuations will be the same in the future(i.e. the mean and variance of the population growthremain constant); (3) environmental conditions areuncorrelated from one year to the next; and (4) thereare no catastrophes or bonanzas (Dennis et al. 1991,Morris & Doak 2003). The validity of this type ofmodel has been questioned by some because of thedifficulty of projecting the distant future when condi-tions are challenging to predict (Boyce 1992, Ludwig1999). However, such uncertainty does not mean thatPVA predictions are meaningless given that theycontribute to evaluating the potential outcomes ofdifferent scenarios — and biologists using their pre-dictions acknowledge the model limitations and areconservative when drawing conclusions and makinginterpretations (Gerber & González-Suárez 2010).

We evaluated whether these assumptions (exceptno occurrence of catastrophes and bonanzas) weremet to determine if our analysis was valid and, moreimportantly, to assess whether the violation of any ofthese assumptions was likely to render our estimatesof the probability of extinction optimistic or pes-

simistic. We did not have enough data to determinewhether catastrophes or bonanzas occurred and withwhat frequency. Thus, our estimates of the extinctionrisk would be underestimated if one or the othershould occur.

Assumption 1: Individuals are identical, and thecounts represent the true number of individuals in apopulation. Observation error results in the failure tocount the true number of animals during a surveyand will lead to pessimistic measures of viability(Morris & Doak 2003). We accounted for observationerror (undercounts) by applying 2 correction factorsto the minimum population size estimates, as de -tailed in the previous subsection. The Guadalupe furseal counts are not estimates of total population sizebut rather estimates of the minimum number of ani-mals at a colony. There are 2 main sources of uncer-tainty regarding the number of fur seals not countedduring a survey. The first is that the number of ani-mals counted may be affected by weather, tides, vis-ibility from the boat, observer experience, etc. Thesecond source of uncertainty is due to an unknownnumber of animals being at sea during any given sur-vey. In our study, we accounted for both sources ofuncertainty.

Several methods (models) have been used to ac -count for observation error under different samplingscenarios and for a variety of species (Morris & Doak2003). However, in our case, applying correction fac-tors previously used by other researchers workingwith the same or related species was a biologicallymore informed way to account for the major issue ofobservation error (undercounts) than trying to fit amodel that attempts to estimate these errors (D. F.Doak pers. comm.).

Assumption 2: Mean and variance of populationgrowth do not change over time. After eliminatingthe observation error from our estimates, it would bereasonable to assume that any variation in the esti-mated growth rates was due to environmental sto-chasticity. However, density dependence, demo-graphic stochasticity, and temporal environmentaltrends may cause growth rates to vary from year toyear, violating Assumption 2, and lead to inaccurateestimates of extinction risk.

We tested whether negative density dependence(decline in growth rate at high density) existed in ourpopulations (at each colony and at both colonies com-bined) by assessing the correlation between ln(Ni+1/Ni)versus Ni. Since the census interval was >1 yr in somecases, we accounted for the time interval as

(4)ln( )N Nxi i

i

+1


where i is year, Ni is population size at time i, Ni+1 ispopulation size at time i+1 and xi is Eq. (2). If the cor-relation is significant and positive slope values arepresent at low population sizes, or negative valuesare present at larger ones, then the populationgrowth rate is density dependent (Pollard et al. 1987,Morris & Doak 2003).

Demographic stochasticity is the random variationaround mean birth and death rates that will cause thegrowth rate of small populations to vary even in aconstant environment with no change at all in meanvital rates (Foley 1994, Mills 2012). The most conven-ient way to account for demographic stochasticity isto set the quasi-extinction threshold (lower limit pop-ulation size below which a population goes extinct) at>100 individuals or sufficiently high that demo-graphic stochasticity is minimized (Morris & Doak2003, Mills 2012). Thus, as we previously described,we assessed the quasi-extinction threshold scenariowherein the population was reduced to 100, 500, and1000 individuals.

Environmental stochasticity produces randomchanges in the mean (μ) and variance (σ2) of the popu-lation growth rate; the effect can be either positive ornegative and will violate the assumption of constantparameters. All populations are inevitably ex posed tosome degree to environmental stochasticity and willexperience good and bad years. There are 2 types ofchanges in μ and σ2. The first one is an abrupt changefollowing an unusual event, with μ and σ2 having onevalue before and another value after that event. Thesecond and most common type of change is an ongo-ing trend in μ and σ2 over a specific number of years,which represents a greater violation of the assumptionof constant parameters than the first type. Thus, weexplored whether there was a significant linearchange in μ by regressing ln(Ni+1/Ni) against year.Finding a significant positive or negative slope wouldindicate a temporal trend (Mills 2012).

Assumption 3: Environmental conditions are un-correlated from one year to the next. The count-basedPVA assumes all μ values at different time intervalsare independent. Where an autocorrelation exists be-tween μ values, the effect may be positive or negative.A positive autocorrelation means that a good year isfollowed by another good year or that a bad year is fol-lowed by another bad year. If μ is density independent,a positive correlation would mean a higher risk of ex-tinction because the events that cause a population todecrease occur in a series. On the other hand, a nega-tive autocorrelation would delay extinction becausebad years tend to be followed by good years, leadingto an increase in the population (Morris & Doak 2003).

We used the Durbin-Watson d statistic and theautocorrelation coefficient to test the strength of theautocorrelation in the regression residuals (Dennis etal. 1991). We compared the d (positive correlation)and 4 − d (negative correlation) with the lower andupper critical values dL and dU at a significance levelof α = 0.05. Finding d < dL or 4 − d < dL means theresiduals are significantly autocorrelated, whereasd > dU or 4 − d > dU means the residuals are not sig-nificantly correlated; otherwise, the test is inconclu-sive (Kutner et al. 2005).

RESULTS

Model assumptions

We accounted for observation error (undercounts)by applying 2 correction factors to the minimum pop-ulation size estimates. The μ indicates that no signifi-cant density dependence occurred on GuadalupeIsland (r = 0.4, p = 0.07) or at both colonies combined(r = 0.3, p = 0.14) over the range of population sizesfrom 1952 to 2015. However, there does appear to bea density-dependent response in numbers of sealsusing the San Benito Islands colony over all the yearsanalyzed (r = 0.75, p = 0.007).

Regarding temporal environmental variation, therewas no linear change in the rate of increase of theSan Benito Islands colony (r = 0.4, p = 0.12) or of bothcolonies combined (r = 0.4, p = 0.10). However, therewas a linear change in the population growth rate innumbers of seals breeding at Guadalupe Island (r =0.7, p < 0.001). This linear trend may be a function ofthe significant gaps in the time series count — partic-ularly during the first 4 census counts when the inter-val between counts was quite wide (e.g. 12, 9, and6 yr) relative to the rest of the data set (1−5 yr). Suchgaps in annual counts make it difficult to identifyseasonal tendencies. We confirmed this by carryingout the analysis using data starting in 1983, fromwhich point the time interval was similar betweenabundance data sets. It showed no evidence of a lin-ear tendency in rates of increase between censuscount (Guadalupe Island p = 0.61; San Benito Islandsp = 0.12; both colonies combined p = 0.87).

Finally, we found no autocorrelation in the popula-tion growth rates (μ values) at the San Benito Islandscolony (d = 3.0, 4 − d = 1, r = 0.2, p = 0.52, df = 10) orat the Guadalupe Island colony (d = 1.4, 4 − d = 2.6,r = 0.60, p = 0.01, df = 14). For both colonies com-bined, there was a negative autocorrelation (d = 2.6,4 − d = 1.4, r = 0.3, p = 0.09, df = 21), although the 4 −

260

Hernández-Camacho & Trites: PVA of Guadalupe fur seals

d value was nearly equal to the dU (1.5). Thus, the dvalue leads to a result falling between inconclusiveand no significant autocorrelation. Moreover, thefirst-order autocorrelation of the residuals has a non-significant p-value.

PVA

Guadalupe fur seals have increased at an annualgrowth rate of 11% on Guadalupe Island and 10% atthe San Benito Islands (Table 2, Fig. 2). Both coloniesappear to have similar growth rates. However, thelower bound of the 95% CI on these rates also encap-sulates a rate of decline at the San Benito Islands of2%. The higher range of the CI for the San Benitocolony is due to the high variability in the recentannual counts (Table 2, Fig. 2). Combining counts

from both islands indicates an overall annual growthrate of 11% and yields an average minimum totalpopulation size in 2017 of ~41 000 individuals (⎯x =40 614, 95% CI = 35 778−46 877). This represents anincrease of 55% over 7 yr from the last populationsize reported for the species in 2010.

The San Benito population is the less secure of the2 Guadalupe fur seal colonies and meets the IUCN’squantitative criteria for being Endangered if thequasi-extinction threshold is 100 or 500 seals andCritically Endangered if the threshold is set at 1000seals (Fig. 3, Table 2). In contrast, the larger popula-tion breeding on Guadalupe Island is secure andviable. Treating both colonies as a single populationalso leads to the same conclusion that the Guadalupefur seal is not close to the IUCN quantitative analysiscriteria for being considered Critically Endangered,Endangered, or Vulnerable (IUCN 2012) and is thus

261

Fig. 2. Corrected numbers of pups born (triangles) and estimated total population size (including newborns) (circles) for Guada-lupe fur seals on (a) Guadalupe Island, (b) the San Benito Islands, and (c) both colonies combined. Open circles and triangles

represent estimated values for the missing counts for each colony


of Least Concern. However, the probability of extinc-tion at the upper confidence limit meets the IUCN’squantitative criteria for being Vulnerable if thethreshold is 1000 seals.

DISCUSSION

A count-based PVA is a useful quantitative tech-nique for determining the probability of Guadalupefur seals going extinct. While it is impossible to makeprecise predictions about extinction times for a spe-cies, the technique provides insight into a range oflikely fates for the 2 colonies of Guadalupe fur sealsand the species as a whole.

In contrast to count-based PVAs, demographicPVAs offer more informative predictions for species(e.g. identifying the most vulnerable life history ageand sex class, estimating the probability of extinctionunder different management scenarios). However,better predictions are possible only if age- and sex-specific vital rates are available for the study species.When these data are lacking, it is common to para-meterize demographic PVA models with surrogatedata based on the assumption that the life historytraits and the ecological conditions experienced bythe target population are similar to the surrogatepopulation (Caro et al. 2005).

Although the life history parameters for organismsof similar species share general patterns, there arelikely major regional differences due to site-specificenvironmental and demographic conditions specificto each population as well as the anthropogenic dis-turbances unique to each region. Thus, it may beunrealistic to assume that the demography of onespecies can serve as a proxy for another species(Nilsen et al. 2009, Murphy et al. 2011). For example,using demographic data from one colony of Califor-nia sea lions Zalophus californianus in the Gulf ofCalifornia to make predictions for another colony ledto erroneous conclusions — which were particularlypronounced when colonies had different populationtrends (Hernández Camacho et al. 2015).

For the Guadalupe fur seal, we lacked nearly allparameters needed to undertake a demographicPVA. As an exercise, we tried running a model inVortex (Lacy & Pollack 2014) using surrogate datafrom northern fur seals. Northern fur seals inhabitthe North Pacific Ocean and share habitat in thenorthern limits of the Guadalupe fur seal populationrange. Unfortunately, we were unable to run themodel because of a lack of data on genetics (e.g.inbreeding depression), status variables (e.g. habitat

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characteristics), dispersion between colonies, andcatastrophes (e.g. survival frequency and survivaleffect).

Model assumptions

A count-based PVA model can provide reasonableassessments of extinction probabilities as long as theassumptions of the model are met (Boyce 1992).

Specifically, violating the density independence as -sumption can lead to inaccurate results (Morris &Doak 2003). In our study, the density independenceassumption was not met for the San Benito Islandscolony. However, PVA models can still provide anaccurate assessment of the extinction probability aslong as the population does not increase or decreasedrastically over the study time horizon (Sabo et al.2004). Meeting the model assumption of densityindependence was only met when San Benito was


Fig. 3. Unconditional cumulative probability of Guadalupe fur seal numbers falling below the quasi-extinction thresholds ofNe = 100, 500, and 1000 seals over time (from 2017 to 200 yr in the future) at the Guadalupe Island colony (top panels), the SanBenito Islands colony (middle panels), and both colonies combined (bottom panels). The solid line is the cumulative probabilityof quasi-extinction (based on the best estimates of mean, µ, and variance, σ2), and the dashed lines delineate an approximate95% CI determined by bootstrapping. Stars indicate when the probability of extinction in the wild is at least 50% (CriticallyEndangered when occurring within 10 yr or 3 generations, i.e. 30 yr), 20% (Endangered when within 20 yr or 5 generations,

i.e. 50 yr), and 10% (Vulnerable when within 100 yr or 5 generations) (IUCN quantitative analysis criteria)


combined with Guadalupe Island to treat bothcolonies as a single population.

The rate of increase in fur seal numbers betweencensus counts at Guadalupe Island was linear overtime but not at the San Benito Islands colony or atboth colonies combined. The linear increase ingrowth rates at Guadalupe Island violates the PVAmodel assumption that mean growth rates are con-stant. However, we suspect that the linear trend atGuadalupe Island is an artifact of the paucity of cen-sus counts at the beginning of the time series—andnot because the growth rate changed significantly.

Although there was a negative autocorrelation inthe growth rate (μ) values for both colonies combined,it was a very weak correlation (the d value of theDurbin-Watson test fell between inconclusive and nosignificant autocorrelation). A negative autocorrela-tion will cause viability results to be overly optimistic(delaying extinction) (Morris & Doak 2003). However,in our case, the effect was negligible.

We were unable to determine if catastrophes or bo-nanzas occurred over the years we analyzed. How-ever, we observed notable variability in counts in re-cent years, especially at the San Benito Islands, whichcoincided with the 2015 El Niño event (Elorriaga-Ver-plancken et al. 2016b) and the Blob, which reachedthe waters of the west coast of the Baja Californiapeninsula in 2014 and 2015 (Cavole et al. 2016). These2 events occurred simultaneously and affected organ-isms at all levels of the food web (Kintisch 2015).

In addition to the assumptions tested, genetic factorsmay also influence population viability. Very smallpopulations have certain genetic disadvantages (e.g.low genetic diversity) that increase the risk of extinctionbecause of environmental and demographic stochastic-ity (Mills & Smouse 1994, Armbruster & Reed 2005). Toevaluate such scenarios, the effective population size(i.e. the size of an ideal population that experiences ge-netic drift at the same rate as the population inquestion) can be used to estimate the rate of inbreedingand the genetic variation in wildlife (Frankham 1995,Charlesworth 2009, Husemann et al. 2016).

The Guadalupe fur seal population went through 2bottlenecks — and is now increasing. Although thisspecies has still not returned to its original populationsize (estimated at ca. 200 000 individuals) (Hubbs1956a), the population is considered genetically robust(Bernardi et al. 1998, Weber et al. 2004). The effectivepopulation size (Ne) for the Guadalupe fur seal duringthe 2015 breeding season was 13 627 individuals forboth colonies, and its harmonic mean (average Ne) was283 individuals (Frankham 1995). We calculated the effective population size as Ne = 4NefNem/Nef + Nem,

where Nef is the corrected number of breeding females,and Nem is the number of breeding males — with adultmales assumed to comprise 15% of the total populationand adult females 33% (data from Hernández-Montoya2009). The estimated effective population size for theGuadalupe fur seal is significantly higher than that re-ported for the South American fur seal Arctocephalusaustralis in Peru (Ne = 2153 individuals), which is indanger of extinction and has decreased significantly(de Oliveira et al. 2006). Genetic drift may thus have agreater impact on the South American fur seal popula-tion than on the Guadalupe fur seals.

The Guadalupe fur seal counts covered only a fewyears and were made at irregular intervals, withsome missing years for both colonies. Despite theseshortcomings, we met most of the model assump-tions, including that the growth rate be density inde-pendent (which could have led to inaccurate esti-mates of extinction risk). We also ruled out geneticfactors affecting the PVA.

Even if some assumptions of our PVA had been vio-lated, count-based models are still very useful (Morris& Doak 2003). They provide, for example, relativemeasurements of extinction risk, facilitating compa -rison of the extinction risks of different species or populations.

A greater concern than violating assumptions isthat limited count data sets can compromise the re -liability of viability measurements. The minimumnumber of counts recommended to obtain reliableestimates of extinction is 10 (Morris & Doak 2003). Inour case, we had 16 for Guadalupe Island and 10 forthe San Benito Islands.

Thus, both count-based as well as demographicPVA models are useful for estimating the probabilitythat a population will persist. Researchers must con-sider the available data and the specific goals of theirresearch when selecting the most appropriate modelfor a given study (Coulson et al. 2001, Gerber &González-Suárez 2010).

PVA

The San Benito Islands colony is a recolonization ofa former breeding site and appears to be well estab-lished after 2 decades of occupation (1997−2017;Fig. 2). However, variability in colony size from oneyear to the next has been extremely high during thepast decade (ranging from 6883 seals in 2009 to just1951 seals in 2015; Fig. 2). In addition, the San Benitocolony is not yet a distinct breeding populationbecause so few pups are currently born here (pups

Hernández-Camacho & Trites: PVA of Guadalupe fur seals

represent


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Editorial responsibility: Louise Chilvers, Palmerston North, New Zealand

Submitted: September 14, 2017; Accepted: October 1, 2018Proofs received from author(s): November 24, 2018

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