Effective size of fluctuating populations with two sexes and overlapping generations

We derive formulas that can be applied to estimate the effective population size N(e) for organisms with two sexes reproducing once a year and having constant adult mean vital rates independent of age. Temporal fluctuations in population size are generated by demographic and environmental stochasticity. For populations with even sex ratio at birth, no deterministic population growth and identical mean vital rates for both sexes, the key parameter determining N(e) is simply the mean value of the demographic variance for males and females considered separately. In this case Crow and Kimura's generalization of Wright's formula for N(e) with two sexes, in terms of the effective population sizes for each sex, is applicable even for fluctuating populations with different stochasticity in vital rates for males and females. If the mean vital rates are different for the sexes then a simple linear combination of the demographic variances determines N(e), further extending Wright's formula. For long-lived species an expression is derived for N(e) involving the generation times for both sexes. In the general case with nonzero population growth and uneven sex ratio of newborns, we use the model to investigate numerically the effects of different population parameters on N(e). We also estimate the ratio of effective to actual population size in six populations of house sparrows on islands off the coast of northern Norway. This ratio showed large interisland variation because of demographic differences among the populations. Finally, we calculate how N(e) in a growing house sparrow population will change over time.     

Weakened purifying selection leads to elevated mutation load under environmental sex determination

In many gonochoristic taxa, sex is influenced by developmental environment, a system that can lead to temporal fluctuations in offspring sex ratio. Demographic models suggest that only short‐lived species with environmental sex determination (ESD) are negatively impacted by sex‐ratio fluctuations, yet these models fail to account for the potential mutation load associated with reductions in genetically effective population sizes. In this study, we developed a series of individual‐based simulation models that explore the fixation rates of mildly deleterious alleles under different sex‐determining systems and examine the impacts of variation in lifespan and offspring sex ratio. Populations with ESD exhibited increases in fixation rates in both short‐ and long‐lived populations, but substantial increases were limited to populations characterized by a combination of high sex‐ratio variation and short lifespan. Fixation rates were negatively associated with effective population size, indicating that purifying selection operates less efficiently under ESD relative to genotypic sex determination. Reductions in effective population size could be attributed to both intragenerational forces (unequal sex ratio) and intergenerational forces (variable census population sizes). Levels of temporal sex‐ratio variation calculated from wild populations of ESD species were capable of yielding large increases in fixation rates, although this relationship was strongly mediated by lifespan. Our results may help to explain the limited phylogenetic distribution of ESD in short‐lived taxa.     

Effect of Harvest on a Brown Bear Population in Alaska

There is a long and contentious history of brown bear (Ursus arctos) harvest management in Alaska, USA, the state that hosts the largest brown bear population in North America. In the mid-1990s, the Alaska Board of Game set the population objective for brown bears in Game Management Unit 13 A, located in interior southcentral Alaska, to be reduced by 50% to improve survival of moose (Alces alces) calves. The Board began further liberalizing brown bear harvest regulations for the unit beginning in regulatory year 1995, though adult females and their dependent offspring (i.e., cubs <2 yrs old) were protected. To evaluate progress toward this abundance objective, we captured and collared bears between 2006 and 2011 and conducted a capture-mark-resight density survey during summer 2011 for comparison to a similar baseline survey conducted in 1998. We report the results of the density survey and vital rates estimated from resight histories of collared bears and harvest information spanning from 1985 (10 years before establishment of the population objective) to 2012. There was a 25–40% reduction in abundance between 1998 and 2011. Population growth rates derived from density estimates and a matrix population projection model indicated that the population declined by 2.3–4.2% annually. We estimated harvest rates to be 8–15% annually, but harvest composition data indicated no changes in skull size, age distribution, or overall sex ratio. There was evidence of an increase in the proportion of older females in the harvest. Demographic analysis indicated high reproductive output and recruitment, potentially indicating a density-dependent compensatory response to reduced population size. Despite 13 years of harvest rates in excess of what had previously been considered to be sustainable for this population, the objective of reducing bear abundance by 50% had not been achieved as of 2011. The protection of females and dependent offspring in our study population appears to be a sufficient safeguard against a precipitous population decline while still permitting progress toward the population objective through high harvest on other segments of the population. © 2020 The Wildlife Society.     

Temporal genetic variation of mitochondrial DNA and the female effective population size of red drum (Sciaenops ocellatus) in the northern Gulf of Mexico

We studied genetic drift of mitochondrial DNA (mtDNA) haplotype frequencies in a natural population of red drum (Sciaenops ocellatus) from the northern Gulf of Mexico (Gulf). The amount of genetic drift observed across temporally adjacent year classes (1986–89) was used to estimate variance effective (female) population size (N_ef). N_ef was estimated to be 14 308 and the ratio of female effective size to adult female census size was approximately 0.004, which is among the lowest value reported for vertebrate animals. Low effective size relative to census size among red drum in the northern Gulf may result from yearly fluctuations in the number of breeding females, high variance in female reproductive success, or both. Despite low genetic effective size relative to census size, the genetic effective population size of red drum in the northern Gulf appears sufficiently large to preclude potentially deleterious effects of inbreeding.     

REPLICATED ORIGIN OF FEMALE‐BIASED ADULT SEX RATIO IN INTRODUCED POPULATIONS OF THE TRINIDADIAN GUPPY (POECILIA RETICULATA)

There are many theoretical and empirical studies explaining variation in offspring sex ratio but relatively few that explain variation in adult sex ratio. Adult sex ratios are important because biased sex ratios can be a driver of sexual selection and will reduce effective population size, affecting population persistence and shapes how populations respond to natural selection. Previous work on guppies (Poecilia reticulata) gives mixed results, usually showing a female‐biased adult sex ratio. However, a detailed analysis showed that this bias varied dramatically throughout a year and with no consistent sex bias. We used a mark‐recapture approach to examine the origin and consistency of female‐biased sex ratio in four replicated introductions. We show that female‐biased sex ratio arises predictably and is a consequence of higher male mortality and longer female life spans with little effect of offspring sex ratio. Inconsistencies with previous studies are likely due to sampling methods and sampling design, which should be less of an issue with mark‐recapture techniques. Together with other long‐term mark‐recapture studies, our study suggests that bias in offspring sex ratio rarely contributes to adult sex ratio in vertebrates. Rather, sex differences in adult survival rates and longevity determine vertebrate adult sex ratio.     

Population Dynamics of Breeding Mallards in the Great Lakes States

Abstract: Mallard (Anas platyrhynchos) populations in the United States portion of the Great Lakes region increased through the 1990s but have since declined. To promote sustainable growth of this population, managers need to understand how perturbation of vital rates will affect annual population growth rate (Λ). We developed a stage-based model representing the female mallard population in the Great Lakes using vital rates generated from a landscape-level study documenting reproductive parameters from 2001 to 2003. We conducted perturbation analyses (i.e., sensitivity analyses) to identify vital rates that most influence Λ and variance decomposition analyses to determine the proportion of variation in Λ explained by variation in each vital rate. Perturbation analyses indicated that Λ was most sensitive to changes in nonbreeding survival, duckling survival, and nest success. Therefore, changes in these vital rates would be expected to result in the greatest ΔΛ. Process variation in breeding season parameters accounted for 63% of variation in Λ. Breeding season parameters explaining the most variation were duckling survival (32%) and nest success (16%). Survival of adult females outside the breeding season accounted for 36% of variation in Λ. Harvest derivation, high harvest, and high sensitivity of Λ to nonbreeding survival for Great Lakes female mallards suggests there is a strong potential for managing the Great Lakes mallard population via harvest management. Because Λ was highly sensitive to changes in duckling survival, we suggest programs that emphasize wetland protection, enhancement, and restoration as a management strategy to improve population growth for breeding mallards.     

Stochastic exits from dormancy give rise to heavy‐tailed distributions of descendants in bacterial populations

Variance in reproductive success is a major determinant of the degree of genetic drift in a population. While many plants and animals exhibit high variance in their number of progeny, far less is known about these distributions for microorganisms. Here, we used a strain barcoding approach to quantify variability in offspring number among replicate bacterial populations and developed a Bayesian method to infer the distribution of descendants from this variability. We applied our approach to measure the offspring distributions for five strains of bacteria from the genus Streptomyces after germination and growth in a homogenous laboratory environment. The distributions of descendants were heavy‐tailed, with a few cells effectively ‘winning the jackpot’ to become a disproportionately large fraction of the population. This extreme variability in reproductive success largely traced back to initial populations of spores stochastically exiting dormancy, which provided early‐germinating spores with an exponential advantage. In simulations with multiple dormancy cycles, heavy‐tailed distributions of descendants decreased the effective population size by many orders of magnitude and led to allele dynamics differing substantially from classical population genetics models with matching effective population size. Collectively, these results demonstrate that extreme variability in reproductive success can occur even in growth conditions that are far more homogeneous than the natural environment. Thus, extreme variability in reproductive success might be an important factor shaping microbial population dynamics with implications for predicting the fate of beneficial mutations, interpreting sequence variability within populations and explaining variability in infection outcomes across patients.     

Effective size of density‐dependent two‐sex populations: the effect of mating systems

Density dependence in vital rates is a key feature affecting temporal fluctuations of natural populations. This has important implications for the rate of random genetic drift. Mating systems also greatly affect effective population sizes, but knowledge of how mating system and density regulation interact to affect random genetic drift is poor. Using theoretical models and simulations, we compare N_e in short‐lived, density‐dependent animal populations with different mating systems. We study the impact of a fluctuating, density‐dependent sex ratio and consider both a stable and a fluctuating environment. We find a negative relationship between annual N_e/N and adult population size N due to density dependence, suggesting that loss of genetic variation is reduced at small densities. The magnitude of this decrease was affected by mating system and life history. A male‐biased, density‐dependent sex ratio reduces the rate of genetic drift compared to an equal, density‐independent sex ratio, but a stochastic change towards male bias reduces the N_e/N ratio. Environmental stochasticity amplifies temporal fluctuations in population size and is thus vital to consider in estimation of effective population sizes over longer time periods. Our results on the reduced loss of genetic variation at small densities, particularly in polygamous populations, indicate that density regulation may facilitate adaptive evolution at small population sizes.     

Sociality and the rate of molecular evolution

The molecular clock does not tick at a uniform rate in all taxa but may be influenced by species characteristics. Eusocial species (those with reproductive division of labor) have been predicted to have faster rates of molecular evolution than their nonsocial relatives because of greatly reduced effective population size; if most individuals in a population are nonreproductive and only one or few queens produce all the offspring, then eusocial animals could have much lower effective population sizes than their solitary relatives, which should increase the rate of substitution of "nearly neutral" mutations. An earlier study reported faster rates in eusocial honeybees and vespid wasps but failed to correct for phylogenetic nonindependence or to distinguish between potential causes of rate variation. Because sociality has evolved independently in many different lineages, it is possible to conduct a more wide-ranging study to test the generality of the relationship. We have conducted a comparative analysis of 25 phylogenetically independent pairs of social lineages and their nonsocial relatives, including bees, wasps, ants, termites, shrimps, and mole rats, using a range of available DNA sequences (mitochondrial and nuclear DNA coding for proteins and RNAs, and nontranslated sequences). By including a wide range of social taxa, we were able to test whether there is a general influence of sociality on rates of molecular evolution and to test specific predictions of the hypothesis: (1) that social species have faster rates because they have reduced effective population sizes; (2) that mitochondrial genes would show a greater effect of sociality than nuclear genes; and (3) that rates of molecular evolution should be correlated with the degree of sociality. We find no consistent pattern in rates of molecular evolution between social and nonsocial lineages and no evidence that mitochondrial genes show faster rates in social taxa. However, we show that the most highly eusocial Hymenoptera do have faster rates than their nonsocial relatives. We also find that social parasites (that utilize the workers from related species to produce their own offspring) have faster rates than their social relatives, which is consistent with an effect of lower effective population size on rate of molecular evolution. Our results illustrate the importance of allowing for phylogenetic nonindependence when conducting investigations of determinants of variation in rate of molecular evolution.     

Impact of Spatial and Temporal Variation in Calf Survival on the Growth of Elk Populations

Abstract: The realized impact of a vital rate on population growth (λ) is determined by both the relative influence of the vital rate on λ (elasticity) and its magnitude of variability. We estimated mean survival and reproductive rates in elk (Cervus elaphus) and spatial and temporal variation in these rates from 37 sources located primarily across the Rocky Mountain region and northwestern United States. We removed sampling variance from estimates of process variance both within and across vital-rate data sets using the variance discounting method developed by White (2000). Deterministic elasticities calculated from a population matrix model parameterized with these mean vital rates ranked adult female survival (e_Scow = 0.869) much higher than calf survival (e_Scalf = 0.131). However, process variance in calf survival was >11 times greater than process variance in female survival across data sets and 10 times greater on average within studies. We conducted Life-Stage Simulation Analysis to incorporate both vital-rate elasticity patterns and empirical estimates of variability to identify those vital rates most influential in elk population dynamics. The overwhelming magnitude of variation in calf survival explained 75% of the variation in the population growth rates generated from 1,000 matrix replicates, compared to just 16% of the variation in λ explained by variation in female survival. Variation in calf survival greatly impacts elk population growth and calls into question the utility of classical elasticity analysis alone for guiding elk management. These results also suggest that the majority of interannual variability that wildlife managers document in late-winter and spring elk surveys is attributable to variation in calf survival over the previous year and less influenced by variation in the harvest of females during the preceding autumn. To meet elk population size objectives, managers should consider the inherent variation in calf survival, and its apparent sensitivity to management, in addition to female harvest.     

EFFECTIVE POPULATION SIZE IN A CONTINUOUSLY DISTRIBUTED POPULATION

An individual-based simulation model was created to examine genetic variability, time until fixation and spatial genetic structure in a continuously distributed population. Previous mathematical models for continuously distributed populations have the difficulty that the assumption of independent reproduction and independent dispersal of offspring cause clumped spatial distribution and thus violate an assumption of random spatial distribution. In this study, this problem is avoided by considering the dispersal behavior of offspring. The simulation results showed that the inbreeding effective population size estimated by the rate of decrease of heterozygosity during the first 15 generations corresponds to the neighborhood size calculated by the standard deviation of the dispersal distance (σ_T). This inbreeding effective population size does not greatly change with the area of simulation when the densities and σ_T are the same. However, the inbreeding effective population size estimated by heterozygosity using the first 500 generations is larger than the neighborhood size calculated by the dispersal distance and increases with the area of simulation with the same densities. The variance effective population size, estimated by time until fixation of alleles, increases with dispersal distance (σ_T) and with the area of simulation given the same densities. The inbreeding effective population size and variance effective population size were smaller than the actual population size unless σ_T is sufficiently large (2 σ_T > approximate L/2, where L is a side of the simulation square).     

The effects of density-dependent offspring mortality on the synchrony of reproduction

Mortality rates often depend on the size of a population. Using ideal free theory to model the optimal timing of reproduction in model populations, I considered how the specific relationship between density-dependent offspring mortality and population size affects the optimal temporal distribution of reproduction. The results suggest that the specific form of the relationship between density-dependent mortality and the number of offspring produced determines the degree to which reproduction within a population is synchronous. Specifically, reproductive synchrony decreases as density-dependent mortality becomes increasingly inversely related to the number of offspring produced and is highest when density-dependent mortality is directly density-dependent. These findings support the suggestion that predation pressure selects for greater reproductive synchrony in species where mortality is directly density-dependent, but does not affect the timing of reproduction in species with density-independent rates of mortality. This revised version was published online in July 2006 with corrections to the Cover Date.     

Competitive exclusion and coexistence for a quasilinear size-structured population model

We present a quasilinear size-structured model which describes the dynamics of a population with n competing ecotypes. We assume that the vital rates of each subpopulation depend on the total population due to competition. We provide conditions on the individual rates which guarantee competitive exclusion in the case of closed reproduction (offspring always belongs to the same ecotype as the parent). In particular, our results suggest that the ratio of the reproduction and mortality rates is a good measure to determine the winning ecotype. Meanwhile, we show that in the case of open reproduction all ecotypes coexist.     

Population ecology and conservation of endangered megafauna: the case of European bison in Białowieża Primeval Forest, Poland

The European bison Bison bonasus is an example of nearly extinct 'charismatic megafauna'. The Białowieża Primeval Forest in Poland is among the few places where they still live in the wild. The management of this free-living herd has to reconcile to the conservation needs of a species and the economic and environmental objectives of their habitat: protected as well as commercial woodlands of Białowieża. Here we present a detailed account of the population development and analyse variation in vital rates based on monitoring that started in 1952 and continued until 2002. The population was allowed to grow freely until 1970, when removal started with the aim to stabilize population size. We found that recruitment rate, but not mortality, was density dependent, suggesting that the population density was not very high relative to resource levels. Winters with much snow and cold temperature had a strong negative effect on survival. May temperature of the previous year positively affected recruitment rates. Masting (oak seed) also positively affected recruitment rates, which provides a rare account of masting affecting the performance of a large ruminant. Sex ratio of offspring was even and was not strongly affected by density or climate. We use an age-structured matrix model to show how this knowledge of intrinsic and extrinsic factors affecting vital rates may help managerial decisions by providing explicit links between given environmental conditions and the population growth rates.     

Effect of paternal age on the birth sex ratio in captive populations of aye‐aye (Daubentonia madagascariensis (Gmelin))

For the management of captive populations of zoo animals, it is important to elucidate factors that affect the offspring birth sex ratio. On the basis of the sex allocation theory, the Trivers–Willard and mate attractive/quality hypotheses predict that maternal and paternal conditions affect offspring birth sex ratios. We examined these predictions for the birth sex ratio of aye‐aye Daubentonia madagascariensis (Gmelin) by analyzing the pedigree information in the International Studbook. We found that the birth sex ratio of the aye‐aye was affected by the paternal age, but not maternal age and other environmental factors (birth year, season, and institution). The younger the sire, the more the offspring sex ratio was biased toward males. These results are useful for the effective population management of captive aye‐aye and illustrated the usefulness of the sex allocation theory in the sex ratio management of zoo animals.     

Effects of maternal age and environment on offspring vital rates in the oleander aphid (Hemiptera: Aphididae)

Maternal effects have the potential to affect population dynamics and evolution. To affect population dynamics, maternal effects must influence offspring vital rates (birth, death, or movement). Here, we explore the magnitude of nongenetic maternal influence on the vital rates of an insect herbivore and explore predictability of maternal effects with reference to published studies. We experimentally studied the effects of maternal age, host plant species (two Asclepias spp.), and density on offspring vital rates in Aphis nerii, the oleander aphid. Older mothers produced offspring that lived shorter lives, consistent with the "Lansing Effect." Older mothers also produced offspring that matured at a younger age. As maternal age increased, offspring mass at maturity decreased when mothers were on Asclepias syriaca. However, offspring mass was highest from intermediate aged mothers on A. viridis. The absence of maternal density effects seems to exclude maternal density as a potential source of delayed density dependence in A. nerii. Our results indicate that maternal effects have some influence on A. nerii vital rates. However, references to published studies suggest that only the Lansing Effect is a predictable response to maternal age in insects. Moreover, the magnitude of observed effects was generally low.     

Dynamics of neutral and selected alleles when the offspring distribution is skewed

We analyze the dynamics of two alternative alleles in a simple model of a population that allows for large family sizes in the distribution of offspring number. This population model was first introduced by Eldon and Wakeley, who described the backward-time genealogical relationships among sampled individuals, assuming neutrality. We study the corresponding forward-time dynamics of allele frequencies, with or without selection. We derive a continuum approximation, analogous to Kimura's diffusion approximation, and we describe three distinct regimes of behavior that correspond to distinct regimes in the coalescent processes of Eldon and Wakeley. We demonstrate that the effect of selection is strongly amplified in the Eldon-Wakeley model, compared to the Wright-Fisher model with the same variance effective population size. Remarkably, an advantageous allele can even be guaranteed to fix in the Eldon-Wakeley model, despite the presence of genetic drift. We compute the selection coefficient required for such behavior in populations of Pacific oysters, based on estimates of their family sizes. Our analysis underscores that populations with the same effective population size may nevertheless experience radically different forms of genetic drift, depending on the reproductive mechanism, with significant consequences for the resulting allele dynamics.     

Reconstructing shifts in vital rates driven by long‐term environmental change: a new demographic method based on readily available data

Frequently, vital rates are driven by directional, long‐term environmental changes. Many of these are of great importance, such as land degradation, climate change, and succession. Traditional demographic methods assume a constant or stationary environment, and thus are inappropriate to analyze populations subject to these changes. They also require repeat surveys of the individuals as change unfolds. Methods for reconstructing such lengthy processes are needed. We present a model that, based on a time series of population size structures and densities, reconstructs the impact of directional environmental changes on vital rates. The model uses integral projection models and maximum likelihood to identify the rates that best reconstructs the time series. The procedure was validated with artificial and real data. The former involved simulated species with widely different demographic behaviors. The latter used a chronosequence of populations of an endangered cactus subject to increasing anthropogenic disturbance. In our simulations, the vital rates and their change were always reconstructed accurately. Nevertheless, the model frequently produced alternative results. The use of coarse knowledge of the species' biology (whether vital rates increase or decrease with size or their plausible values) allowed the correct rates to be identified with a 90% success rate. With real data, the model correctly reconstructed the effects of disturbance on vital rates. These effects were previously known from two populations for which demographic data were available. Our procedure seems robust, as the data violated several of the model's assumptions. Thus, time series of size structures and densities contain the necessary information to reconstruct changing vital rates. However, additional biological knowledge may be required to provide reliable results. Because time series of size structures and densities are available for many species or can be rapidly generated, our model can contribute to understand populations that face highly pressing environmental problems.     

Demographics of an Experimentally Released Population of Elk in Great Smoky Mountains National Park

ABSTRACT We assessed the potential for reestablishing elk (Cervus elaphus) in Great Smoky Mountains National Park (GSMNP), USA, by estimating vital rates of experimentally released animals from 2001 to 2006. Annual survival rates for calves ranged from 0.333 to 1.0 and averaged 0.592. Annual survival for subadult and adult elk (i.e., ≥ 1 yr of age) ranged from 0.690 to 0.933, depending on age and sex. We used those and other vital rates to model projected population growth and viability using a stochastic individual-based model. The annual growth rate (λ) of the modeled population over a 25-year period averaged 0.996 and declined from 1.059 the first year to 0.990 at year 25. The modeled population failed to attain a positive 25-year mean growth rate in 46.0% of the projections. Poor calf recruitment was an important determinant of low population growth. Predation by black bears (Ursus americanus) was the dominant calf mortality factor. Most of the variance of growth projections was due to demographic variation resulting from the small population size (n = 61). Management actions such as predator control may help increase calf recruitment, but our projections suggest that the GSMNP elk population may be at risk for some time because of high demographic variation.     

Assessing the roles of population density and predation risk in the evolution of offspring size in populations of a placental fish

Population density is an ecological variable that is hypothesized to be a major agent of selection on offspring size. In high-density populations, high levels of intraspecific competition are expected to favor the production of larger offspring. In contrast, lower levels of intraspecific competition and selection for large offspring should be weaker and more easily overridden by direct selection for increased fecundity in low-density populations. Some studies have found associations between population density and offspring size consistent with this hypothesis. However, their interpretations are often clouded by a number of issues. Here, we use data from a 10-year study of nine populations of the least killifish, Heterandria formosa, to describe the associations of offspring size with habitat type, population density, and predation risk. We found that females from spring populations generally produced larger offspring than females from ponds; however, the magnitude of this difference varied among years. Across all populations, larger offspring were associated with higher densities and lower risks of predation. Interestingly, the associations between the two ecological variables (density and predation risk) and offspring size were largely independent of one another. Our results suggest that previously described genetic differences in offspring size are due to density-dependent natural selection.