A Monte Carlo simulation model for studying evolution in age-structured populations

This model provides for any number of genotypes defined by age-specific survival and fecundity rates in a population with completely overlapping generations and growing under the control of density-governing functions affecting survival or fecundity. It is tested in situations involving two alleles at one locus. Nonselection populations at Hardy–Weinberg equilibrium obey the ecogenetic law; i.e., each genotype follows Lotka's law regarding rate of increase and stable age distribution as if it were an independent true-breeding population. Populations experiencing age- and density-independent selection approximate this situation, and the changes in gene frequency are predicted by relative fitnesses bases on λ, the finite rate of increase of the genotypes. Polymorphic gene equilibria occurring at steady-state population sizes are determined by fitnesses based on R, the net reproductive rate. In examples involving differences in generation time produced by age-dependent differences in fecundity, the allele associated with longer generation time may be favored or opposed by selection, depending on whether the density-governing factor controlling population size affects survival or fecundity. If such genotypes have similar R's, a genetic equilibrium may be established if the population is governed by a density function acting upon fecundity. Received: August 23, 1999 / Accepted: July 13, 2000     

DOES INCREASED MORTALITY FAVOR THE EVOLUTION OF MORE RAPID SENESCENCE?

It is widely believed (following the 1957 hypothesis of G. C. Williams) that greater rates of “extrinsic” (age- and condition-independent) mortality favor more rapid senescence. However, a recent analysis of mammalian life tables failed to find a significant correlation between minimum adult mortality rate and the rate of senescence. This article presents a simple theoretical analysis of how extrinsic mortality should affect the rate of senescence (i.e., the rate at which probability of mortality increases with age) under different evolutionary and population dynamical assumptions. If population dynamics are density independent, extrinsic mortality should not alter the senescence rate favored by natural selection. If population growth is density dependent and populations are stable, the effect of extrinsic mortality depends on the age specificity of the density dependence and on whether survival or reproduction (or both) are functions of density. It is possible that higher extrinsic mortality will increase the rate of senescence at all ages, decrease the rate at all ages, or increase it at some ages while decreasing it at others. Williams's hypothesis is most likely to be supported when density dependence acts primarily on fertility and does not differentially decrease the fertilities of older individuals. Patterns contrary to Williams's prediction are possible when density dependence acts primarily on the survival or fertility of later ages or when most variation in mortality rates is due to variation in nonextrinsic mortality.     

Genome‐wide SNP analysis reveals a genetic basis for sea‐age variation in a wild population of Atlantic salmon (Salmo salar)

Delaying sexual maturation can lead to larger body size and higher reproductive success, but carries an increased risk of death before reproducing. Classical life history theory predicts that trade‐offs between reproductive success and survival should lead to the evolution of an optimal strategy in a given population. However, variation in mating strategies generally persists, and in general, there remains a poor understanding of genetic and physiological mechanisms underlying this variation. One extreme case of this is in the Atlantic salmon (Salmo salar), which can show variation in the age at which they return from their marine migration to spawn (i.e. their ‘sea age’). This results in large size differences between strategies, with direct implications for individual fitness. Here, we used an Illumina Infinium SNP array to identify regions of the genome associated with variation in sea age in a large population of Atlantic salmon in Northern Europe, implementing individual‐based genome‐wide association studies (GWAS) and population‐based F_ST outlier analyses. We identified several regions of the genome which vary in association with phenotype and/or selection between sea ages, with nearby genes having functions related to muscle development, metabolism, immune response and mate choice. In addition, we found that individuals of different sea ages belong to different, yet sympatric populations in this system, indicating that reproductive isolation may be driven by divergence between stable strategies. Overall, this study demonstrates how genome‐wide methodologies can be integrated with samples collected from wild, structured populations to understand their ecology and evolution in a natural context.     

A graphical analysis of life history evolution in biennial plants

Graphical analysis was done on the lfie history evolution of biennials (or monocarpic perennials). The age of seed production (x), the probability of surviving to agex [l(x)], and the number of seeds produced at agex[b(x)] determine the ultimate rate of population increase (r). The ages whenr=max andr=0 define the optimal and critical age for seed production, respectively, which depend on the shape and combination of thel(x) andb(x) curves. The otpimal age of seed production appears only for the convex function of the natural logarithm of the net reproductive rate [R ₀(x)], while the critical age appears irrespective of the shape of theR ₀(x) curves. The effects of environmental change on the optimal and critical ages are, analyzed, with the conclusion that in an environment imposing higher mortality or lower fecundity, delayed reproduction is favored. Age- and size-dependent productions of seeds have different effects on the variation ofr in a changing environment.     

Predicting evolutionary responses to selection on polyandry in the wild: additive genetic covariances with female extra-pair reproduction

The evolutionary forces that underlie polyandry, including extra-pair reproduction (EPR) by socially monogamous females, remain unclear. Selection on EPR and resulting evolution have rarely been explicitly estimated or predicted in wild populations, and evolutionary predictions are vulnerable to bias due to environmental covariances and correlated selection through unmeasured traits. However, evolutionary responses to (correlated) selection on any trait can be directly predicted as additive genetic covariances (cov_A) with appropriate components of relative fitness. I used comprehensive life-history, paternity and pedigree data from song sparrows (Melospiza melodia) to estimate cov_A between a female''s liability to produce extra-pair offspring and two specific fitness components: relative annual reproductive success (ARS) and survival to recruitment. All three traits showed non-zero additive genetic variance. Estimates of cov_A were positive, predicting evolution towards increased EPR, but 95% credible intervals overlapped zero. There was therefore no conclusive prediction of evolutionary change in EPR due to (correlated) selection through female ARS or recruitment. Negative environmental covariance between EPR and ARS would have impeded evolutionary prediction from phenotypic selection differentials. These analyses demonstrate an explicit quantitative genetic approach to predicting evolutionary responses to components of (correlated) selection on EPR that should be unbiased by environmental covariances and unmeasured traits.     

Demographic variation and conservation of the narrow endemic plant Ranunculus weyleri

Ranunculus weyleri is a narrow endemic protected plant from Majorca Island. It is known from only five populations located in two mountain areas 48 km apart. Using demographic data collected from 2007 to 2010, we assessed the demographic status of two populations – font des Coloms (FC) and talaia Moreia (TM) – using Integral Projection Models (IPMs). We showed that none of the two populations were declining under a deterministic model. Population FC was stable (λ = 1.026, CI_95% = 0.965–1.093), while population TM showed sign of demographic expansion (λ = 1.113, CI_95% = 1.032–1.219). Plant survival, flowering probability and the mean number of seedlings per floral peduncle were lower in TM, whereas growth and the number of floral peduncles per reproductive plant were lower in FC. Elasticity analyses showed that management strategies increasing plant survival and growth would be the most efficient to increase λ for both populations. Herbivory pressure by goats has been shown to be high in TM, resulting in high predation rate on floral peduncles. Controlling goat pressure may thus represent a promising management option, provided that we can demonstrate a negative impact of herbivory by goats on survival and growth which are the most critical parts of the life cycle in this species. Meanwhile, initiating a long-term monitoring is of crucial importance to get more insights into the relationships between environmental variation, plant performance and population dynamics.     

Evolution of Peromyscus leucopus Mice in Response to a Captive Environment

Many wildlife species are propagated in captivity as models for behavioral, physiological, and genetic research or to provide assurance populations to protect threatened species. However, very little is known about how animals evolve in the novel environment of captivity. The histories of most laboratory strains are poorly documented, and protected populations of wildlife species are usually too small and too short-term to allow robust statistical analysis. To document the evolutionary change in captive breeding programs, we monitored reproduction and behavior across 18 generations in six experimental populations of Peromyscus leucopus mice started from a common set of 20 wild-caught founders. The mice were propagated under three breeding protocols: a strategy to retain maximal genetic diversity, artificial selection against stereotypic behaviors that were hypothesized to reflect poor adaptation to captivity, and random bred controls. Two replicates were maintained with each protocol, and inter-replicate crosses at generations 19 and 20 were used to reverse accumulated inbreeding. We found that one of the stereotypic behaviors (repetitive flipping) was positively associated with reproductive fitness, while the other (gnawing) was relatively invariant. Selection to reduce these stereotypic behaviors caused marked reduction in reproduction, and populations not under artificial selection to reduce these behaviors responded with large increases in flipping. In non-selected populations, there was rapid evolution toward much higher proportion of pairs breeding and more rapid conception. Litter size, pup survival, and weaning mass all declined slowly, to the extent that would be predicted based on inbreeding depression. Inter-crossing between replicate populations reversed these declines in fitness components but did not reverse the changes in behavior or the accelerated breeding. These findings indicate that adaptation to captivity can be rapid, affecting reproductive patterns and behaviors, even under breeding protocols designed to minimize the rate of genetic change due to random drift and inadvertent selection.     

Ecological–genetic approach in modeling the natural evolution of a population: Prospects and special aspects of verification

This study presents a complex approach for modeling the natural evolution of a population in terms of population number and dynamics of the genetic structure. A set of dynamic models that consider various types of natural selection was applied to describe possible mechanisms underlying the formation of existing genetic variations in litter sizes in coastal, inland, and farmed arctic fox populations (Alopex lagopus, family Canidae, order Carnivora). The r–K selection model for uniform population and the models with natural selection were assessed on various life cycle stages in a two-age population. The life cycle of arctic fox was fitted to the population model with two age stages. The different reproductive potentials and survivability of progeny on the early stage of life cycle were genetically determined using the model with a single diallelic gene. A monomorphism was obtained for a considered characteristic in a population of coastal arctic fox with constant food supply. Meanwhile, a polymorphism with cyclic fluctuations in population number and gene frequency was obtained in inland arctic fox populations, which could be due to cyclic fluctuations of prey. In farmed fox populations, the considered gene becomes pleiotropic (defines the survival rate of individuals on early and late stages of the life cycle) because of artificial selection performed by farmers to increase the reproductive success of breeders. The application of an appropriate model (with selection by pleiotropic gene) can be used to determine the elimination rate of low litter size alleles from the farmed populations. The possible applications of the proposed models for formulating and solving optimal control tasks in arctic fox populations are discussed too.     

PARTHENOGENESIS IN A FRESHWATER SNAIL: REPRODUCTIVE ASSURANCE VERSUS PARASITIC RELEASE

Two alternative (but not mutually exclusive) hypotheses were contrasted for their abilities to explain the distribution of parthenogenesis in the freshwater snail Potamopyrgus antipodarum: the reproductive assurance hypothesis, which predicts that parthenogenesis will be favored in sparse populations where mates are difficult to find, and the Red Queen hypothesis, which predicts that parthenogenesis will be favored in populations that have a low risk of parasitism. The results were inconsistent with the prediction of the reproductive assurance hypothesis; male frequency was not significantly or positively correlated with snail density. Thus, there was no support for any of the hypotheses for the maintenance of sex that rely on selection for reproductive assurance to explain the distribution of parthenogenesis (e.g., recombinational repair). The results, however, were consistent with the Red Queen hypothesis; male frequency was positively and significantly correlated with the frequency of individuals infected by trematodes. This correlation suggests that parthenogenetic females have replaced sexual females in populations where parasites are rare, and that sexual females have persisted in populations where parasites are common.     

SEXUAL SIZE DIMORPHISM AND SELECTION IN THE WILD IN THE WATERSTRIDER AQUARIUS REMIGIS: LIFETIME FECUNDITY SELECTION ON FEMALE TOTAL LENGTH AND ITS COMPONENTS

Darwin's fecundity advantage model is often cited as the cause of female biased size dimorphism, however, the empirical studies of lifetime selection on male and female body size that would be required to demonstrate this are few. As a component of a study relating sexual size dimorphism to lifetime selection in natural populations of the female size-biased waterstrider Aquarius remigis (Hemiptera: Gerridae), we estimated coefficients for daily fecundity selection, longevity selection, and lifetime fecundity selection acting on female body size and components of body size for two consecutive generations. Daily fecundity was estimated using females confined in field enclosures and reproductive survival was estimated by twice-weekly recaptures. We found that daily fecundity selection favored females with longer total length through direct selection acting on abdomen length. Longevity selection favored females with smaller total length. When daily fecundity and reproductive longevity were combined to estimate lifetime fecundity we found significant balancing selection acting on total length in both years. The relationship between daily fecundity and reproductive longevity also reveals a significant cost of reproduction in one of two years. We relate these selection estimates to previous estimates of sexual selection on male body size and consider the relationship between contemporary selection and sexual size dimorphism.     

Genetic analysis of male reproductive success in relation to density in the zebrafish, Danio rerio

Background

We used behavioural and genetic data to investigate the effects of density on male reproductive success in the zebrafish, Danio rerio. Based on previous measurements of aggression and courtship behaviour by territorial males, we predicted that they would sire more offspring than non-territorial males.

Results

Microsatellite analysis of paternity showed that at low densities territorial males had higher reproductive success than non-territorial males. However, at high density territorial males were no more successful than non-territorials and the sex difference in the opportunity for sexual selection, based on the parameter I _mates, was low.

Conclusion

Male zebrafish exhibit two distinct mating tactics; territoriality and active pursuit of females. Male reproductive success is density dependent and the opportunity for sexual selection appears to be weak in this species.     

Reproductive strategy of the invasive Oxalis pes-caprae: distribution patterns of floral morphs, ploidy levels and sexual reproduction

Oxalis pes-caprae, a tristylous flowering plant native to South Africa, is described in the western Mediterranean basin as an asexual—only 5x short-styled morph (5x S-morph) invasive weed losing all mating partners after introduction. The objective of this study was to reassess the patterns of floral morph and cytotype distribution and the sexual reproduction ability in this invaded range. For that, floral morph and cytotype composition were evaluated in 39 populations of O. pes-caprae in a methodical sampling. The reproductive success of natural populations was assessed as fruit and seed production and seed germination for all floral morphs and cytotypes detected. Self- and morph-incompatibility were also studied with controlled hand pollinations. A remarkable diversity in floral morph and cytotype composition was observed. Furthermore, we observed successful sexual reproduction in several localities across the surveyed area. The S-morph is still dominant in this invaded area, and although it was mostly 5x, an additional cytotype (4x) was also recorded. Records of both a mid-styled morph (M-morph) and an area with trimorphic populations of this species are reported here for the first time in the invasive range of the Mediterranean basin. The long-styled morph appears to occur randomly across the surveyed area, while the M-morph is concentrated mainly in Estremadura province (Portugal), where a breakdown in the incompatibility system was observed. These distribution patterns may result from events of sexual reproduction after incompatibility breakdown and/or from multiple introduction events from the native area. The ability to reproduce sexually, undetected so far, may have important impacts in the population dynamics and major consequences for the adaptation and selection potential of O. pes-caprae in this invaded area.     

Correlated responses to clonal selection in populations of Daphnia pulicaria: mechanisms of genetic correlation and the creative power of sex

Genetic correlations among traits alter evolutionary trajectories due to indirect selection. Pleiotropy, chance linkage, and selection can all lead to genetic correlations, but have different consequences for phenotypic evolution. We sought to assess the mechanisms contributing to correlations with size at maturity in the cyclic parthenogen Daphnia pulicaria. We selected on size in each of four populations that differ in the frequency of sex, and evaluated correlated responses in a life table. Size at advanced adulthood, reproductive output, and adult growth rate clearly showed greater responses in high‐sex populations, with a similar pattern in neonate size and r. This pattern is expected only when trait correlations are favored by selection and the frequency of sex favors the creation and demographic expansion of highly fit clones. Juvenile growth and age at maturity did not diverge consistently. The inter‐clutch interval appeared to respond more strongly in low‐sex populations, but this was not statistically significant. Our data support the hypothesis that correlated selection is the strongest driver of genetic correlations, and suggest that in organisms with both sexual and asexual reproduction, adaptation can be enhanced by recombination.     

Epistasis causes outbreeding depression in eucalypt hybrids

The genetic architecture underlying species differentiation is essential for understanding the mechanisms of speciation and post-zygotic reproductive barriers which exist between species. We undertook line-cross analysis of multiple hybrid (F₁, F₂ and backcrosses) and pure-species populations of two diploid eucalypt species from different subseries, Eucalyptus globulus and Eucalyptus nitens, to unravel the genetic architecture of their differentiation. The populations were replicated on two sites and monitored for growth and survival over a 14-year period. The hybrids exhibited severe outbreeding depression which increased with age. Of the composite additive, dominance and epistatic effects estimated, the additive × additive epistatic component was the most important in determining population divergence in both growth and survival. Significant dominance × dominance epistasis was also detected for survival at several ages. While favourable dominance and, in the case of survival, dominance × dominance epistasis could produce novel gene combinations which enhance hybrid fitness, at the population level, these effects were clearly overridden by adverse additive × additive epistasis which appears to be a major driver of overall outbreeding depression in the hybrid populations. The lack of model fit at older ages suggested that even high-order epistatic interactions may potentially have a significant contribution to outbreeding depression in survival. The estimated composite genetic parameters were generally stable across sites. Our results argue that the development of favourable epistasis is a key mechanism underlying the genetic divergence of eucalypt species, and epistasis is an important mechanism underlying the evolution of post-zygotic reproductive barriers.     

Plasticity of plant defense and its evolutionary implications in wild populations of Boechera stricta

Phenotypic plasticity is thought to impact evolutionary trajectories by shifting trait values in a direction that is either favored by natural selection (“adaptive” plasticity) or disfavored (“nonadaptive” plasticity). However, it is unclear how commonly each of these types of plasticity occurs in natural populations. To answer this question, we measured glucosinolate defensive chemistry and reproductive fitness in over 1500 individuals of the wild perennial mustard Boechera stricta, planted in four common gardens across central Idaho, United States. Glucosinolate profiles—including total glucosinolate concentration as well as the relative abundances and overall diversity of different compounds—were strongly plastic both among habitats and within habitats. Patterns of glucosinolate plasticity varied greatly among genotypes. Plasticity among sites was predicted to affect fitness in 27.1% of cases; more often than expected by chance, glucosinolate plasticity increased rather than decreased relative fitness. In contrast, we found no evidence for within‐habitat selection on glucosinolate reaction norm slopes (i.e., plasticity along a continuous environmental gradient). Together, our results indicate that glucosinolate plasticity may improve the ability of B. stricta populations to persist after migration to new habitats.     

Population demography of the endangered large blue butterfly <Emphasis Type="Italic">Maculinea arion</Emphasis> in Europe

Demographic parameters such as survival, sex ratio and abundance can profoundly affect the viability of populations and thus are of primary importance in species of conservation concern. Although numerous studies have been published on certain aspects of the ecology and evolution of the endangered Large Blue butterfly Maculinea arion, there is still a lack of detailed knowledge on its populations’ demography. Moreover, M. arion populates a variety of xerothermic habitats throughout its European range using various food plants and host ants, which leads to complications in its conservation. Our aim was to estimate demographic parameters of M. arion populations in different parts of its European range. Detailed mark-recapture sampling was conducted on populations in four different countries. We often found that daily apparent survival probability declined with increasing age of individuals, but there was no difference between male and female survival. In smaller populations, the sex ratio was rather female-biased. Our most interesting result was the lack of protandry in some populations that might be a consequence of selection against reproductive asynchrony in small populations or a polyandrous mating system. The perfect coincidence of male and female phenology can positively affect the effective population size, because the lack of reproductive asynchrony increases the chance of male–female encounters. Abundance of the studied populations ranged between 100 and 1,600 individuals, smaller populations were on the verge of extinction. Habitat of the threatened small populations was either overgrazed or abandoned, while habitat of larger, stable populations was lightly grazed.     

Ultra-low-density genotype panels for breed assignment of Angus and Hereford cattle

Angus and Hereford beef is marketed internationally for apparent superior meat quality attributes; DNA-based breed authenticity could be a useful instrument to ensure consumer confidence on premium meat products. The objective of this study was to develop an ultra-low-density genotype panel to accurately quantify the Angus and Hereford breed proportion in biological samples. Medium-density genotypes (13 306 single nucleotide polymorphisms (SNPs)) were available on 54 703 commercial and 4042 purebred animals. The breed proportion of the commercial animals was generated from the medium-density genotypes and this estimate was regarded as the gold-standard breed composition. Ten genotype panels (100 to 1000 SNPs) were developed from the medium-density genotypes; five methods were used to identify the most informative SNPs and these included the Delta statistic, the fixation (F_st) statistic and an index of both. Breed assignment analyses were undertaken for each breed, panel density and SNP selection method separately with a programme to infer population structure using the entire 13 306 SNP panel (representing the gold-standard measure). Breed assignment was undertaken for all commercial animals (n=54 703), animals deemed to contain some proportion of Angus based on pedigree (n=5740) and animals deemed to contain some proportion of Hereford based on pedigree (n=5187). The predicted breed proportion of all animals from the lower density panels was then compared with the gold-standard breed prediction. Panel density, SNP selection method and breed all had a significant effect on the correlation of predicted and actual breed proportion. Regardless of breed, the Index method of SNP selection numerically (but not significantly) outperformed all other selection methods in accuracy (i.e. correlation and root mean square of prediction) when panel density was ⩾300 SNPs. The correlation between actual and predicted breed proportion increased as panel density increased. Using 300 SNPs (selected using the global index method), the correlation between predicted and actual breed proportion was 0.993 and 0.995 in the Angus and Hereford validation populations, respectively. When SNP panels optimised for breed prediction in one population were used to predict the breed proportion of a separate population, the correlation between predicted and actual breed proportion was 0.034 and 0.044 weaker in the Hereford and Angus populations, respectively (using the 300 SNP panel). It is necessary to include at least 300 to 400 SNPs (per breed) on genotype panels to accurately predict breed proportion from biological samples.     

r‐ and K‐selection in fluctuating populations is determined by the evolutionary trade‐off between two fitness measures: Growth rate and lifetime reproductive success

In a stable environment, evolution maximizes growth rates in populations that are not density regulated and the carrying capacity in the case of density regulation. In a fluctuating environment, evolution maximizes a function of growth rate, carrying capacity and environmental variance, tending to r‐selection and K‐selection under large and small environmental noise, respectively. Here we analyze a model in which birth and death rates depend on density through the same function but with independent strength of density dependence. As a special case, both functions may be linear, corresponding to logistic dynamics. It is shown that evolution maximizes a function of the deterministic growth rate r₀ and the lifetime reproductive success (LRS) R₀, both defined at small densities, as well as the environmental variance. Under large noise this function is dominated by r₀ and average lifetimes are small, whereas R₀ dominates and lifetimes are larger under small noise. Thus, K‐selection is closely linked to selection for large R₀ so that evolution tends to maximize LRS in a stable environment. Consequently, different quantities (r₀ and R₀) tend to be maximized at low and high densities, respectively, favoring density‐dependent changes in the optimal life history.     

Evolutionary potential of Chamaecrista fasciculata in relation to climate change. I. Clinal patterns of selection along an environmental gradient in the great plains

Climate change will alter natural selection on native plant populations. Little information is available to predict how selection will change in the future and how populations will respond. Insight can be obtained by comparing selection regimes in current environments to selection regimes in environments similar to those predicted for the future. To mimic predicted temporal change in climate, three natural populations of the annual legume Chamaecrista fasciculata were sampled from a climate gradient in the Great Plains and progeny of formal crosses were reciprocally planted back into common gardens across this climate gradient. In each garden, native populations produced significantly more seed than the other populations, providing strong evidence of local adaptation. Phenotypic selection analysis conducted by site showed that plants with slower reproductive development, more leaves, and thicker leaves were favored in the most southern garden. Evidence of clinal variation in selection regimes was also found; selection coefficients were ordered according to the latitude of the common gardens. The adaptive value of native traits was indicated by selection toward the mean of local populations. Repeated clinal patterns in linear and nonlinear selection coefficients among populations and within and between sites were found. To the extent that temporal change in climate into the future will parallel the differences in selection across this spatial gradient, this study suggests that selection regimes will be displaced northward and different trait values will be favored in natural populations.     

Poor horse traders: large mammals trade survival for reproduction during the process of feralization

We investigated density dependence on the demographic parameters of a population of Camargue horses (Equus caballus), individually monitored and unmanaged for eight years. We also analysed the contributions of individual demographic parameters to changes in the population growth rates. The decrease in resources caused a loss of body condition. Adult male survival was not affected, but the survival of foals and adult females decreased with increasing density. Prime-aged females maintained high reproductive performance at high density, and their survival decreased. The higher survival of adult males compared with females at high density presumably results from higher investment in reproduction by mares. The high fecundity in prime-aged females, even when at high density, may result from artificial selection for high reproductive performance, which is known to have occurred in all the major domestic ungulates. Other studies suggest that feral ungulates including cattle and sheep, as these horses, respond differently from wild ungulates to increases in density, by trading adult survival for reproduction. As a consequence, populations of feral animals should oscillate more strongly than their wild counterparts, since they should be both more invasive (as they breed faster), and more sensitive to harsh environmental conditions (as the population growth rate of long-lived species is consistently more sensitive to a given proportional change in adult survival than to the same change in any other vital rate). If this principle proves to be general, it has important implications for management of populations of feral ungulates.