Comparing estimates of census and effective population size in an endangered amphibian

The field of conservation has seen a shift in focus from monitoring trends in census population size to trends in ‘effective’ population size. Numerous genetic methods exist for estimating effective population size, resulting in uncertainty among conservation practitioners as to which methods are most appropriate when conducting population assessments or evaluating recovery efforts. Demographic approaches offer a promising avenue to provide a link between census and effective population size using life‐history information, but rarely do studies have all three sources of data (genetic, demographic, life history) necessary to perform an explicit evaluation of their performance. Using data from a long‐term study of reticulated flatwoods salamanders (Ambystoma bishopi) in western Florida, USA, we assessed the magnitude of temporal variation in census population sizes N and the effective number of breeders Nb of two breeding populations to (1) document changes in the number of breeding adults over the 9‐year study duration, (2) determine whether N and Nb provide similar information about population size and trends and (3) compare alternative demographic and genetic approaches for estimating Nb . We found that genetic estimates of N̂b , particularly if averaged across multiple estimation methods, closely tracked spatiotemporal variation in N . Demographic estimates of Nb also closely tracked N but were sensitive to the assumed variance in reproductive success. In the absence of genetic information, detailed knowledge of mating systems and the environmental factors that skew reproductive contributions appear necessary for demographic Nb to reliably inform management decisions. In these populations, N̂b appears too small (<40 individuals) to confer long‐term genetic resilience, highlighting the importance of restoring landscape connectivity and indicating that caution must be taken when sourcing animals for reintroduction efforts. More generally, our study reveals insights into the utility of alternative Nb estimation methods in guiding recovery efforts of threatened and endangered species.


Introduction
Reliable estimates of population sizes are one of the most fundamental and salient metrics in applied ecology (Seber, 1982;Grimm, Gruber, & Henle, 2014;Stephens et al., 2014;López-Bao et al., 2018).They are used both to determine whether certain species warrant conservation listing status and to identify regions that contain substantial proportions of a species' global abundance (Moilanen et al., 2005;Arcos et al., 2012;Ashe et al., 2013;Corrigan et al., 2014;Camaclang et al., 2015).Estimates of population size frequently are used by managers when assessing the efficacy of conservation actions to determine whether recovery goals have been met (Campbell et al., 2002;Morris et al., 2002;López-Bao et al., 2018).Indeed, many recovery plans incorporate the concept of minimum viable populations, MVPs (Soulé, 1987), to provide achievable goals for management and to quantify the biggest sources of risk to populations stemming from the 'small population paradigm' (Caughley, 1994).Criteria that emanate from the MVP concept however, such as the '50/500 rule', are governed not by the total number of breeding adults in a population (hereafter census population size or N ) but rather by the effective population size (N e ; Wright, 1931).Reduction in the effective size of a population can lead to inbreeding depression and a loss of genetic diversity, increasing vulnerability to future environmental and pathogenic stressors (Crnokrak & Roff, 1999;Nieminen et al., 2001;Keller et al., 2002;Frankham, 2005;Wang et al., 2011).As a result, the field of conservation has shifted focus from recovery criteria based solely on census population size to include criteria based on effective population size (Soulé, 1980;Nunney & Elam, 1994;Frankham, 1995a;Luikart et al., 2010;Schlesselmann & Robertson, 2020).
Recovery goals related to effective population size rarely consider the subtle differences between N e per generation and the effective number of breeders (N b ) per cohort, making it difficult for non-geneticists to be able to evaluate the relative success or shortcomings of management efforts.For most agestructured wildlife species, population monitoring and genetic sampling programmes apply more naturally to annual cohorts than to multi-year generations, and thus N b might often make for a more natural conservation metric than N e (Waples & Antao, 2014;Luikart et al., 2021).A variety of methods exist for estimating N b .Among the 'single-sample' estimators, methods typically use either linkage-disequilibrium or sibshipfrequency methods in the computation (Waples, 2006;Wang, 2009, Gilbert & Whitlock, 2015;Wang, 2016).Performance of these various estimators depends strongly on the biology of the species and characteristics of the genetic markers at hand (Sánchez-Montes et al., 2017).As effective population size becomes increasingly favoured as the metric of choice for monitoring population health, it is important for conservationists to understand the limitations of each method and the inferences that can and cannot be made from a given approach (Pierson et al., 2018;Olah et al., 2021).Only with this knowledge is it possible to inform management activities to achieve recovery goals (Wang, 2005, Luikart et al., 2010, Olah et al., 2021).
One common application of genetic studies is to infer N from estimates of b N b or b N e (hereafter we follow the convention of using b N b or b N e when an estimate emanates from a genetic approach and N b or N e otherwise).Whereas estimating N requires relatively arduous sampling designs (e.g.mark-recapture studies), collecting the genetic samples necessary to estimate b N b may be less costly (Capellà-Marzo, Sánchez-Montes, & Martínez-Solano, 2020).Conversion of b N b estimates to estimates of N , however, requires that the b N b : N ratio is known for the species in question or can be accurately characterized (Kalinowski & Waples, 2002;Ferchaud et al., 2016;Sánchez-Montes et al., 2017).An b N b : N ratio <1 usually is expected in natural settings (Nunney, 1993, Palstra & Fraser, 2012), but a wide range of values have been reported for wild populations (Lande & Barrowclough, 1987;Frankham, 1995b;Vucetich, Waite, & Nunney, 1997;Waples, 2002;Ferchaud et al., 2016;Capellà-Marzo, Sánchez-Montes, & Martínez-Solano, 2020).Simply assuming the relationship between N and b N b , therefore, is fraught with uncertainty (Palstra & Fraser, 2012).Recent methodologies have been developed to derive expected N b : N ratios from life-history traits like lifespan and reproductive variance (Waples, Do, & Chopelet, 2011;Waples et al., 2013), but rarely do studies have all three sources of data (genetic, demographic and life history) necessary to perform an explicit comparison between estimates (Palstra & Fraser, 2012;Ferchaud et al., 2016;Sánchez-Montes et al., 2017).
Reticulated Flatwood Salamanders (Ambystoma bishopi, hereafter flatwoods salamanders) are endemic to longleaf pine ecosystems of the southeastern US (USFWS, 2009;USFWS, 2020a).Flatwoods salamanders are currently listed as endangered under the Endangered Species Act, with habitat loss and fragmentation cited as the primary reasons for their decline (USFWS, 2009;USFWS, 2020a).Translocations are being attempted for flatwoods salamanders, with the goal of re-establishing the species at sites where they historically occurred.However, translocation planning is hampered by limited knowledge of the current genetic or demographic viability of local breeding populations, potential benefits or risks of mixing source animals from multiple populations (Liddel, Sunnucks, & Cook, 2021), and the number of animals that can safely be removed from a source population without jeopardizing its long-term viability (Easton, Bishop, & Whigham, 2020).Accurate estimates of effective size will shed light on these issues and potentially help to identify candidate source sites.Genetic information also will be useful in measuring the success of translocation attempts and tracking recovery progress.
Like other recent recovery plans for amphibians, effective population size is included as a metric of progress towards recovery in the Recovery Implementation Strategy for flatwoods salamanders (USFWS, 2017, 2020b), though it is not specified whether N e or N b should be the recovery metric of choice.Here, we chose to focus on N b rather than N e because flatwoods salamanders are an iteroparous species with overlapping generations, complicating sampling of and inferences about individual generations (Lee, Engen, & Saether, 2011;Waples et al., 2013;Waples, Antao, & Luikart, 2014).The effective number of breeders N b ð Þ however, readily applies to single cohorts that may have been produced by parents from multiple generations (Beebee, 2009;Luikart et al., 2021).Moreover, although evolutionary considerations about effective size are typically framed in terms of N e (Frankham, Bradshaw, & Brook, 2014), with a few key available life-history parameters the N b : N e ratio can be inferred (Waples et al., 2013).
Here, we assessed the magnitude of spatial and temporal variation in census and effective sizes of two flatwoods salamander breeding populations on Eglin Air Force Base.Owing to long-term monitoring of flatwoods salamanders that has involved sampling all stages of the species life cycle and collecting tissue samples from multiple populations, there presents a novel opportunity to compare estimates of N , b N b and b N b : N ratios at these two sites.We developed multiple estimates of the genetically effective number of breeders b N b at each site in two separate breeding years (i.e.four cohorts total).In so doing, we leveraged the availability of (1) multiple single-sample genetic estimation approaches that focused on different signals in the data, (2) the availability of demographic information on survival, fecundity and variance in reproductive success, which facilitated estimation of the expected value of N b based on demography and (3) mark-recapture-based estimates of N, which enabled calculation of demographic N b : N and genetic b N b : N ratios.Our goals were then to (1) quantify spatial and temporal fluctuations in estimates of population size and how they corresponded with estimates of effective number of breeders, (2) contrast alternative approaches for estimating N b and (3) evaluate how the information generated from these estimates might influence management decisions for flatwoods salamanders and other similar species.

Field sampling
We selected two wetlands on Eglin Air Force Base for demographic and genetic study (Sites 4 and 5 in Wendt et al., 2021, which we refer to throughout as Sites 1 and 2 respectively).We completely encircled wetlands with drift fences and funnel traps (see Erwin et al., 2016 for details).The drift fences were constructed from 60-cm tall steel (to resist fire) flashing buried in the sediment c. 15-20 cm.We placed funnel traps with dimensions 85 cm by 20 cm flush with the fence and ground at c. 10-m intervals on both sides of the fence (Gibbons & Semlitsch, 1981;Palis, 1997).Traps were checked multiple times per night throughout the flatwoods salamander breeding season (typically October-March) from 2010 to 2020.
We checked every salamander encountered at the drift fences for an existing tag, and if untagged, was uniquely tagged using a passive integrated transponder (PIT) or visual implant elastomer (VIE) tag.Following processing (which included determining sex and measuring size), we released animals on the opposite side of the fence to which they were caught.Genetic sampling focused on Age-0 larvae and metamorphs, because (1) we felt confident assuming that these individuals hatched in the site where they were captured and (2) focusing on a single-age cohort of juveniles (vs. a mixed-age sample of adults) facilitated single-sample estimation of b N b (see below).During the 2013-14 and the 2015-16 breeding seasons, we collected tissue samples from all metamorphs captured at drift fences.Adults captured in drift fences were also sampled, for use in pedigree reconstruction (see below).In addition to drift fences, we sampled wetlands for aquatic larvae using dip-netting, as described in Bishop et al. (2006).We took tissue samples from the tail of each animal using surgical scissors that had been sterilized by wiping with alcohol and then burning.We then placed each sample in 95-100% ethanol until DNA extraction.Although larval sampling increases the risk of obtaining a biased sample of a cohort, for example, if certain families are sampled disproportionately to their true abundance (Waples and Anderson 2017), we presume that our samples were unbiased and representative because (1) sampling was spatially extensive across the entirety of breeding sites, and thus unlikely to underrepresent isolated groups of families, (2) samples were collected from free-swimming larvae or emerging metamorphs, which had time to randomly mix prior to sampling, (3) samples were collected across multiple points in time, further reducing the chance of missing early or late-breeding families and (4) these sites were drift-fenced, such that metamorphs (and their family lineages) had little chance to evade capture.

Laboratory methods
We extracted whole-genomic DNA from 632 tissue samples (see Table S1 for breakdown) using a DNeasy Blood and Tissue Kit (Qiagen, Hilden, Germany) following the manufacturer's protocols.We genotyped each individual at nine microsatellite loci that were found to be polymorphic in A. bishopi (Wendt, 2017), and we visualized amplified PCR products on an ABI 3500 Genetic Analyzer with a Genescan 500HD LIZ dye standard (Applied Biosystems).Two of the authors (AW and JR) then scored allele sizes independently in GeneMapper (GeneMapper v4.0; Applied Biosystems), and any discrepancies were discussed until consensus was reached or the genotype was discarded.All loci passed tests for Hardy-Weinberg and linkage equilibrium (Wendt, 2017), and were retained for further analysis.Based on genotype matching, only one case of individual double-sampling was observed; only one copy of this genotype was retained for analyses.

Census population size
We defined census population size (N) as the total number of adults in a local breeding population (site) per breeding season.To estimate N, we fit a hierarchical Bayesian model to mark-recapture data of adult flatwoods salamanders collected over 10 years of drift fencing.We define adults as individuals captured returning to breeding wetlands, such that they must be at least 1 year old but may or may not be reproductively mature.To prevent issues related to age-based emigration and survival, we excluded emerging metamorphs from the analysis.We adopted the superpopulation parameterization of Crosbie & Manly (1985) that uses conditional entry probabilities and an inclusion parameter to account for open populations and zero-inflation in the augmented dataset (Royle & Dorazio, 2008;Link & Barker, 2010;Kéry & Schaub, 2012).Each individual carries its own survival history, z i,j , a binary character specifying whether individual i was alive or dead on the j th capture occasion.For the initial capture occasion, z is modelled as a Bernoulli variable with probability β s,j , where s refers to site, and β represents the entry probability of an individual into the study area, conditional on previous sampling occasions.Thus, β s,1 is simply the likelihood that an individual is already present and available for capture from the outset of the study.For all subsequent occasions, individuals available for capture come from two sources: surviving from the previous sampling occasion, jÀ1, with probability Φ, and becoming available for capture for the first time with probability β s,j , conditional on whether a given individual was already present in the study area.Survival was assigned a vague beta prior, and entry probabilities are drawn from a Dirichlet distribution, scaled to ensure all probabilities sum to 1.
To relate the true states of individuals to the observed data when detection is imperfect (Kellner & Swihart, 2014), we modelled capture histories as Bernoulli processes such that: where the binary variable y i,j indicates whether individual i was observed on the j th capture occasion, p represents the probability of detection and w the probability of inclusion.Priors for year-specific inclusion probability were set based on whether successful metamorphosis was observed in the previous year.Due to the apparent rarity of inter-site movement (Brooks et al., 2019), site was assumed to be fixed for each individual.For individuals that were never observed, site was treated as a latent parameter to be estimated.The model was fit in R and WinBUGS using Markov chain Monte Carlo (MCMC) optimization (Spiegelhalter et al., 2004;R Core Team, 2018).Three chains of MCMC samples were generated from the posterior distributions of the model parameters, each of length 100 000 with the first 10 000 values being discarded as burn-in.To minimize autocorrelation, only every 50th sample was drawn for posterior summaries.Adequate convergence of chains was assessed via potential scale reduction factors b R < 1:1 .Reported point estimates are posterior medians, with 95% confidence intervals in parentheses.

Effective population size
First, we used demographic and life-history information to develop 'demographic' estimates of N b for both populations of flatwoods salamanders in two separate breeding years, treating these estimates as a theoretical expectation against which to compare empirical estimates made using genetic data (see below).Demographic estimates were made using the approach of Waples et al. (2011), as implemented in the AgeNe program.This method uses a life table with sex-and age-specific survival and fertility rates and a sex-specific scaling factor that accounts for reproductive variance (RV) among individuals within year-classes, to estimate the N b : N ratio.Our life tables assumed a 1:1 sex ratio, age at maturity of 1 year and 12 total age classes (Table S2).Age-specific survival and fertility rates were taken from Brooks (2020).To account for uncertainty, we estimated each cohort's N b : N ratio using low-end, best-guess and high-end estimates of survival, which bracketed our uncertainty about this key parameter, resulting in lower confidence interval, mean and upper confidence interval estimates respectively (Table S2).Once an N b : N ratio was calculated, we used the empirical (mark-recapture) estimate of adult N from that year to extract N b (hereafter 'N bÀAgeNe ') from the ratio.
Age-specific, among-individual RV is a key parameter affecting the N b : N ratio and thus any estimates derived from a given life table.In AgeNe, RV is incorporated via a sex-specific over-dispersion parameter ϕ ð Þ equal to the variance divided by the mean of the distribution of reproductive success.Initially, we estimated the N b : N ratio for each cohort when ϕ ¼ 1. Fixing ϕ to 1 assumes that reproductive success follows a Poisson distribution, such that RV is equal to the mean number of offspring produced.However, previous studies have shown that RV can be highly overdispersed in wild populations (Ruzzante et al., 2016), so for comparison, we made AgeNe estimates using the same life tables but with empirical estimates of ϕ that varied among the four cohorts.Using results from the pedigree analysis (see below), we generated distributions of reproductive success among breeders contributing to each cohort (Table S3).For each of the four cohorts, we included as candidate offspring all sampled juveniles and included as candidate parents all adults that had been captured at the drift fence around that site in that year.Models assumed a promiscuous mating strategy and a genotyping error rate of 0.01, utilized full likelihood searches with high precision, medium run length and averaged over three independent runs.Ackerman et al. (2017) showed the importance of allowing some genotyping error in accurate pedigree construction.We also experimented with error rates as high as 0.05, which had virtually no effect on parentage assignments.Each included adult could be assigned to anywhere from zero offspring to all offspring from a given cohort.From the resulting distributions of offspring counts by parent sex, we calculated the variances and means and used these to calculate ϕ for each sex for each cohort, using these values of ϕ in AgeNe models (Table S3).Note that because adult age was unknown, we could not parse age-specific, betweenindividual RV from all-age, between-individual RV.Our method thus assumes that within-age RV does not vary significantly enough among age classes to substantially affect our results.Mathematical methods are being developed that may help partition these quantities, in situations where substantial demographic information is available (Waples, 2022).
Second, we developed genetic estimates of b N b using Waples' ( 2006) bias-corrected linkage disequilibrium method, implemented in the program NeEstimator v2.1 (Do et al., 2014).We excluded alleles that occurred at a frequency <0.02 (Waples & Do, 2010) and estimated the 95% confidence interval by jackknifing (Jones, Ovenden, & Wang, 2016).Only juveniles (larvae and metamorphs) were included in this analysis.The model underlying NeEstimator assumes random (i.e.non-assortative) mating, non-overlapping generations and sampling of a single cohort.The second of these assumptions was violated, because flatwoods salamanders are iteroparous, which biases estimates of b N b .Fortunately, by incorporating information on simple life-history parameters, resulting biases can be reduced (Waples, Antao, & Luikart, 2014).Specifically, we converted 'raw' estimates of b N b from NeEstimator to unbiased estimates of b N bLD using the following equation from Waples et al. (2014) where AL is the adult lifespan and ɑ is the age at reproductive maturity.We assumed an AL of 12 years and an ɑ of 1 year (Palis, 1997;Brooks et al., 2020).We opted for this correction rather than the '3-parameter' correction because we lacked estimates of the coefficient of variation for adult lifespan.Third, we estimated b N b for each cohort using Wang & Santure's (2009) group-likelihood pedigree approach, as implemented in COLONY 2.0 (Wang, 2009).This approach works by genetically reconstructing the pedigree of a sampled cohort and using sibship frequencies (i.e.frequencies of full-and potentially half-sibling dyads) to infer b N bSF for the cohort.Input datasets and model settings were as described in the section on estimating ϕ.As stated above, we assumed a modest genotyping error rate of 0.01, but note that assuming an error rate as high as 0.05 increased b N bSF only slightly (1-3 individuals per cohort, data not shown).Unlike the linkage disequilibrium method, the sibship frequency approach does not assume random mating (Wang & Santure, 2009).Note that to improve accuracy, adult genotypes were used in the reconstruction of pedigrees, but that data from adults had no influence on the calculations of b N bSF from those pedigrees (Wang, 2009).Nonetheless, for comparison, we also estimated b N bSF in COLONY excluding adult genotypes from the pedigree reconstruction.
For each cohort, we estimated the weighted harmonic mean ( b N bLDþSF ) of the individual b N bLD and b N bSF estimates, weighting each estimator inversely by the width of its confidence interval.We reasoned that this would improve the accuracy and precision of our genetic estimates of b N b (Waples, 2016).However, no methods currently exist for estimating confidence intervals for a weighted mean, so only point estimates could be derived from this method.

Results
Over the duration of the drift fence study, terrestrial flatwoods salamanders were detected on 402 separate sampling nights yielding 1297 captures of 606 unique individuals at Site 1 and 598 captures of 293 unique individuals at Site 2. Recapture rates differed markedly between individuals, with some individuals captured 13 times and others never recaptured.Despite two opportunities per year to encounter individuals as they move to and from breeding sites, annual detection probabilities were only 0.63 (CI:0.60-0.67).In line with the known life history of ambystomatid salamanders, populations exhibited uneven, staggered entry; in some years (2010)(2011)(2014)(2015) more than 100 individuals became available for capture, whereas no new individuals entered the population in 2012-2013, 2013-2014 or 2016-2017.Estimates of population size were highest in 2014-2015 following successful recruitment, and lowest in 2013-2014 following 3 years with no recruitment as a result of inadequate hydroperiods during a drought.Despite fluctuations in population size across the duration of the study, the overall trend appeared relatively flat.Estimates of N and associated uncertainties for all years are presented in Table 1.Demographic estimates of N b from AgeNe (hereafter N bAgeNe ) provide a theoretical expectation for what we might expect genetic b N b to be in populations with certain demographic and life-history characteristics.When RV was assumed to be Poisson distributed ϕ ¼ 1 ð Þ, N bAgeNe was perfectly correlated with N over time and space, and the Nb : N ratio was a constant 0.96, indicating that the range of survival and fertility schedules we assumed did little to reduce N b relative to N (Figure 1, Table 2).On the other hand, when assuming variable, over-dispersed reproductive variance and estimated ϕ from pedigrees, N bAgeNe was still tightly correlated with N over time and space, but the resulting N b : N ratios varied from 0.44 (Site 1, 2013-14) to 0.77 (Site 2, 2015-16), indicating the strong influence of RV on reducing N b relative to N (Figure 1, Table 2).Although N was lower at both sites in the second than the first year, estimated ϕ (i.e.RV) was also lower at both sites in the second than the first year (Table S3), which resulted in higher N b : N ratios in the second year.Overall, estimated ϕ, ranged from 2.8 to 16.6 for males and from 4.1 to 11.0 for females.Estimates of ϕ did not vary consistently between sexes, but like N was consistently higher at Site 1 compared with Site 2 and consistently higher in the second breeding year compared with the first (Table S3).
Like N and N bAgeNe , genetic estimates of b N b generally indicated a greater population size at Site 1 than Site 2 and an increase in population size over time at both sites, and genetic estimators of b N b exhibited overlapping confidence intervals for three of the four cohorts (Figure 1).However, genetic estimators varied in how strongly they correlated with demographic trends, and in their ratios with N and N bAgeNe .Both b N bSF and b N bLDþSF were strongly correlated with N across space and time, whereas b N bLD was less strongly correlated with N, primarily because the estimate of b N bLD for Site 2 in 2015-16 was higher than expected based on N (Figure 1).This estimate also had wide confidence intervals and so contributed little to the weighted harmonic genetic mean.Resulting b N b : N ratios ranged across cohorts from 0.21 to 0.72, 0.19 to 0.36 and 0.21 to 0.45 for b N bLD , b N bSF and b N bLDþSF , respectively, and thus were more variable for N b-LD than for the other two estimators (Table 2).Although not shown, exclusion of adult (candidate parent) genotypes from COLONY pedigree assignments had little effect, adding only 1-2 individuals to b N bSF estimates and altering the widths of confidence individuals by only AE3 individuals.
Across cohorts, b N b : N ratios for all three genetic estimators were negatively correlated with N .In other words, as census population size decreased, the b N b : N ratio increased.In the first breeding year, all three genetic estimates of N b were similar to the demographic expectation of N bAgeNe assuming over-dispersed ϕ.In contrast, in the second breeding year, five of the six genetic estimates (all except b N b : N at Site 2 in 2015-16) were less than one third of the demographic expectation based on N bAgeNe (Figure 1, Table 2).

Discussion
Accurate knowledge of population trends is critical to the management and conservation of endangered species.Genetic estimates of effective size could be an efficient way to monitor population trends, however, the scarcity of studies that jointly estimate N , demographic N b and genetic b N b makes it challenging to draw firm conclusions as to the relationship between genetic and demographic approaches and the reliability of each method (Nunziata, Scott, & Lance, 2015;Nunziata et al., 2017;Pierson et al., 2018).Our long-term dataset allowed us to evaluate multiple estimators of effective number of breeders that leverage different types of genetic information and compare them with markrecapture estimates of the total number of adults in each population (which in the genetics literature is often referred to as the census population size).Our work adds confidence to the utility of these methods and provides useful information for flatwoods salamander recovery efforts.
To be useful for conservation purposes, an estimator must be able to estimate N b with high precision.Across years, sites and estimators, however, there was considerable variation in the confidence intervals associated with N b estimates.As Wang (2016) observed, the LD approach appears sensitive to violations of assumptions like non-overlapping generations and random mating, which may have been violated to varying (unknown) degrees by the populations in our study.Our two single-sample genetic estimators utilize largely independent information, so in theory, combining information across these methods should leverage more information from the data, increase precision and accuracy and therefore be the best approach (Waples, 2016;Olah et al., 2021).Leveraging the availability of multiple single-sample methods (LD and SF) buffered the impact of occasional imprecise estimates (e.g.b N bLD at Site 2 in 2015-2016), which were down-weighted in the averaging process, and our datasets appeared to meet assumptions closely enough to be appropriate for the use of both these methods.In contrast, due to the short timescale of our study (less than a full generation), 'temporal' methods for estimating b N b would likely have resulted in biased estimates (Waples and Yokota, 2007).
Of the four site/year samples, the weighted-average genetic b N bLDþSF estimates closely reflected relative differences in census population sizes, indicating a consistently smaller population at Site 2 but a consistent increase at both sites between 2013-2014 and 2015-2016.Other studies also have shown good correspondence between single-sample b N b or b N e and N estimates over time and space in other iteroparous species (Charlier, Laikre, & Ryman, 2012;Duong et al., 2013;Baalsrud et al., 2014), including in other Ambystoma salamanders (Wang et al., 2011;Whiteley, McGarigal, & Schwartz, 2014; but see Nunziata, Scott, & Lance, 2015).The ranges of b N bLDþSF : N ratios we observed for each site (0.21-0.42 for Site 1 and 0.25-0.45for Site 2) are similar to each other and on the high end of the range of ratios reported for other imperilled species (mean = 0.28, SD = 0.15) by Palstra & Ruzzante (2008).Life-history tactics such as sperm storage and polygamy of both sexes may help ensure relatively high and widespread reproductive success of flatwoods salamanders.Notably, although genetic b N b and N tracked each other well, the relationship was non-linear in that the b N b : N ratio increased as population size decreased.Such a relationship has been shown for other amphibians (e.g.Jehle et al., 2005;Capellà-Marzo, Sánchez-Montes, & Martínez-Solano, 2020) and is often attributed to genetic compensation, and may help buffer small populations from genetic drift (Palstra & Ruzzante, 2008).Importantly, this non-linearity makes it unlikely that one can be consistently derived from the other without additional information on the degree of skew in reproductive success at various population sizes.
Our results demonstrate that estimates of N b derived from life tables can be highly sensitive to assumptions regarding variance in reproductive success.If genetic data are available, one solution is to treat ϕ as a latent variable, such that estimates of b N b are used to infer what degree of reproductive variance is consistent with the genetic data (Ruzzante et al., 2016).In the absence of genetic material, however, the utility of demographic estimates of N b is highly dependent on having accurate information on reproductive variance among individuals in a population.When reproductive variance was assumed to be Poisson distributed, our demographic estimates of N b were more similar to N than to genetic estimates of b N b .In an applied context, failure to accurately account for reproductive variance when deriving effective population sizes from demography could result in biased assessments of population status and/or erroneously concluding that management interventions are not necessary.When over-dispersion in reproductive variance was accounted for, our demographic estimates of N b more closely corresponded to genetic estimates of b N b .Obtaining accurate estimates of reproductive variance should therefore be a priority for those wishing to use demographic methodologies to infer effective population size.For flatwoods salamanders, this will require ageing individuals to derive age-specific RV values, as well as discerning the reasons for changes in RV through time.More generally, conservationists should design studies to identify the ecological and environmental factors that cause the greatest imbalances in reproductive success (Nunney, 1991).Such studies will require detailed information on the mating system and life history of a species, coupled with multiple years of genetic data that captures a range of reproductive variance.
Translocation efforts for flatwoods salamanders are already underway.Given our best genetic estimates of b N b (20-37 individuals per cohort), it appears likely that the populations in our study cannot persist in isolation but can persist as part of a connected metapopulation (Kimura & Ohta, 1969;Hanski et al., 1995;Hanski, 1998;Green, 2003;Frankham et al., 2014).Several wetland-breeding species have been shown to exist at relatively small populations with seemingly negligible fitness consequences (Sagvik, Uller, & Olsson, 2005;Shoemaker et al., 2013;Cayuela et al., 2017), but the loss of breeding wetlands may have isolated flatwoods salamander populations to such a degree that genetic issues will emerge (Shaffer, 1981;Newman & Pilson, 1997;Palis, Aresco, & Kilpatrick, 2006;Frankham et al., 2014;Wendt et al., 2021).Consequently, restoring connectivity between wetlands through translocations may be necessary for species recovery efforts (Hanski, 1989(Hanski, , 1999;;Harrison & Quinn, 1989;Harper, Rittenhouse, & Semlitsch, 2008).However, we stress that caution must be taken to avoid jeopardizing the integrity of source populations as a result of translocation activities (Easton, Bishop, & Whigham, 2020).In the absence of natural history information, genetic estimates like those presented here will provide the most reliable assessment of whether sustained harvest is possible and help to identify the best candidate sites to act as source populations (Capellà-Marzo, Sánchez-Montes, & Martínez-Solano, 2020;Luikart et al., 2021;Mitchell et al., 2022).Here, we find evidence for genetic compensation, indicating that these populations may harbour a genetic surplus, that is, a pool of individuals that could be removed for translocation purposes with minimal impact on the b N b of the source population.However, for this concept to be of practical use, managers must obtain multiple years of both N and b N b across a wide range of conditions to identify the inflection points in b N b : N ratios and set appropriate take limits.
Moving forward, estimates like those presented here provide the best method to determine the outcome of habitat restoration and translocation efforts.Although we have used absence versus occupancy as an indicator of habitat quality (e.g.Gorman, Bishop, & Haas, 2009;Brooks et al., 2019), so many factors unrelated to habitat characteristics can cause local absences of an endangered species, and a more refined metric of habitat quality based on effective population size or population trajectories would be much more informative.In 2023, flatwoods salamander larvae were detected at two recipient sites in our study area, representing the first successful translocation of the species.Now that individuals have become established, repeated measures of b N b at translocation sites will help to ascertain population trajectories and the probability of long-term persistence.If new populations quickly blink out following establishment, this could indicate issues with the habitat at recipient sites or a mismatch between the local adaptations of source animals and their new environment (Gibbs, 2000;Amezaga, Santamaría, & Green, 2002;Urban, 2011).Again, genetic information will be the only viable approach to measure the effectiveness of management practices designed to address these issues and to achieve recovery goals by providing quick, accurate population assessments for decision-makers (Houde, Garner, & Neff, 2015;Whiteley et al., 2017;Mitchell et al., 2022).

Figure 1
Figure1Single-season estimates for reticulated flatwood salamanders of census population size and effective number of breeders for (a) Site 1 and (b) Site 2 for the 2 years of genetic sampling.Bars indicate 95% confidence intervals around each mean, except in the case of the 'genetic mean' (SF+LD), which was the weighted harmonic mean of b N bLD and b N bSF , for which a pooled variance could not be calculated.

Table 1
Annual population size N are reported.Numbers at Site 2 in 2010-2011 were artificially low because sampling began several weeks later than at Site 1; in all subsequent years, both sites had equal sampling effort.Seasons highlighted in bold are those in which genetic samples were collected.

Table 2
Single-season estimates of total and effective population sizes, and resulting N b :N ratios, for flatwoods salamanders for two sites (breeding wetland) at two different times Where estimable, mean values are followed by 95% confidence intervals (in parentheses).The genetic means are weighted harmonic means of the linkage disequilibrium (LD) and sibship frequency (SF) estimates, and there are no measures of variance associated with these values, and thus no confidence intervals.