Demographic heterogeneity, cohort selection, and population growth

Des différences, pourquoi? Transmission, maintenance and effects of phenotypic variance

Despite the observed distribution of variable individual phenotypes, survival and reproductive performance in wild populations, models of population dynamics often focus on mean demographic rates. Populations are constituted by individuals with different phenotypes and thus different performances. However, many models of population dynamics provide no understanding of the influence of this phenotypic variation on population dynamics. In this paper, we investigate how the relationships between demographic rates and phenotype distribution influence the transmission and the upholding of phenotypic variation, and population dynamics. We used integral projection models to measure associations between differences of phenotypic trait (size or mass) among individuals and demographic rates, growth and inheritance, and then quantify the influence of phenotypic variation on population dynamics. We build an analytical and general model resulting from simplifications assuming small phenotypic variance. We illustrate our model with two case studies: a short- and a long-lived life history. Population growth rate r is determined by a Lotka style equation in which survival and fertility are averaged over a phenotypic distribution that changes with age. Here, we further decomposed r to show how much it is affected by shifts in phenotypic average as well as variance. We derived the elasticities of r to the first and second derivative of each demographic rate. In particular, we show that the nonlinearity of change in selective pressure with phenotype matters more to population dynamics than the strength of this selection. In other words, the variance of a given trait will be most important when the strength of selection increases (or decreases) nonlinearly with that trait. Inheritance shapes the distribution of newborn phenotypes. Even if newborns have a fixed average phenotype, the variance among newborns increases with phenotypic variance among mothers, strength of inheritance and developmental variation. We explain how the components of inheritance can influence phenotypic variance and thus the demographic rates and population dynamics. In particular, when mothers of different ages produce offspring of different mean phenotype, the inheritance function can have a large influence on both the mean and variance of the trait at different ages and thus on the population growth rate. We provide new tools to understand how phenotypic variation influences population dynamics and discuss in which life histories we expect this influence to be large. For instance, in our short-lived life history, individual variability has larger effect than in our long-lived life history. We conclude by indicating future directions of analysis.

Quantifying the influence of measured and unmeasured individual differences on demography

1. Demographic rates can vary not only with measured individual characters like age, sex and mass but also with unmeasured individual variables like behaviour, genes and health. 2. Predictions from population models that include measured individual characteristics often differ from models that exclude them. Similarly, unmeasured individual differences have the potential to impact predictions from population models. However, unmeasured individual differences are rarely included in population models. 3. We construct stage- and age-structured models (where stage is mass) of a roe deer population, which are parameterized from statistical functions that either include, or ignore, unmeasured individual differences. 4. We found that mass and age structures substantially impacted model parameters describing population dynamics, as did temporal environmental variation, while unmeasured individual differences impacted parameters describing population dynamics to a much smaller extent once individual heterogeneity related to mass and age has been included in the model. We discuss how our assumptions (unmeasured individual differences only in mean trait values) could have influenced our findings and under what circumstances unmeasured individual differences could have had a larger impact on population dynamics. 5. There are two reasons explaining the relative small influence of unmeasured individual differences on population dynamics in roe deer. First, individual body mass and age both capture a large amount of individual differences in roe deer. Second, in large populations of long-lived animals, the average quality of individuals (independent of age and mass) within the population is unlikely to show substantial variation over time, unless rapid evolution is occurring. So even though a population consisting of high-quality individuals would have much higher population growth rate than a population consisting of low-quality individuals, the probability of observing a population consisting only of high-quality individuals is small.

Individual heterogeneity in life histories and eco-evolutionary dynamics

Individual heterogeneity in life history shapes eco-evolutionary processes, and unobserved heterogeneity can affect demographic outputs characterising life history and population dynamical properties. Demographic frameworks like matrix models or integral projection models represent powerful approaches to disentangle mechanisms linking individual life histories and population-level processes. Recent developments have provided important steps towards their application to study eco-evolutionary dynamics, but so far individual heterogeneity has largely been ignored. Here, we present a general demographic framework that incorporates individual heterogeneity in a flexible way, by separating static and dynamic traits (discrete or continuous). First, we apply the framework to derive the consequences of ignoring heterogeneity for a range of widely used demographic outputs. A general conclusion is that besides the long-term growth rate lambda, all parameters can be affected. Second, we discuss how the framework can help advance current demographic models of eco-evolutionary dynamics, by incorporating individual heterogeneity. For both applications numerical examples are provided, including an empirical example for pike. For instance, we demonstrate that predicted demographic responses to climate warming can be reversed by increased heritability. We discuss how applications of this demographic framework incorporating individual heterogeneity can help answer key biological questions that require a detailed understanding of eco-evolutionary dynamics.

Spatially variable habitat quality contributes to within-population variation in reproductive success

Variation in habitat quality is common across terrestrial, freshwater, and marine habitats. We investigated how habitat quality influenced the reproductive potential of mud crabs across 30 oyster reefs that were degraded to different extents. We further coupled this field survey with a laboratory experiment designed to mechanistically determine the relationship between resource consumption and reproductive performance. We show a >10-fold difference in average reproductive potential for crabs across reefs of different quality. Calculated consumption rates for crabs in each reef, based on a type II functional response, suggest that differences in reproductive performance may be attributed to resource limitation in poor quality reefs. This conclusion is supported by results of our laboratory experiment where crabs fed a higher quality diet of abundant animal tissue had greater reproductive performance. Our results demonstrate that spatial variation in habitat quality can be a considerable contributor to within-population individual variation in reproductive success (i.e., demographic heterogeneity). This finding has important implications for assessing population extinction risk.

Population Biology of Aging in the Wild

Empirical studies reveal aging occurs in wild populations. Consideration of the ecological and evolutionary consequences of these findings is critical for many areas of research, including life-history evolution, sexual selection, behavior, and applied ecology. Variation in the patterns of age-dependent declines of phenotypic traits has been found both within and among individuals, and this raises future questions aimed at understanding what determines these trajectories across traits and across the tree of life. The presence of older, aging, individuals in populations can have transgenerational effects on offspring and can influence how individuals interact. In some species older individuals in populations can have positive impacts, influencing knowledge and leadership, postreproductive care, and population cycle stabilization. Aging and long life span also need to be recognized in an applied ecology context including management plans, vector-borne disease transmission, and ecotoxicology.

Carryover effects and climatic conditions influence the postfledging survival of greater sage-grouse

Prebreeding survival is an important life history component that affects both parental fitness and population persistence. In birds, prebreeding can be separated into pre- and postfledging periods; carryover effects from the prefledging period may influence postfledging survival. We investigated effects of body condition at fledging, and climatic variation, on postfledging survival of radio-marked greater sage-grouse (Centrocercus urophasianus) in the Great Basin Desert of the western United States. We hypothesized that body condition would influence postfledging survival as a carryover effect from the prefledging period, and we predicted that climatic variation may mediate this carryover effect or, alternatively, would act directly on survival during the postfledging period. Individual body condition had a strong positive effect on postfledging survival of juvenile females, suggesting carryover effects from the prefledging period. Females in the upper 25th percentile of body condition scores had a postfledging survival probability more than twice that (Φ = 0.51 ± 0.06 SE) of females in the bottom 25th percentile (Φ = 0.21 ± 0.05 SE). A similar effect could not be detected for males. We also found evidence for temperature and precipitation effects on monthly survival rates of both sexes. After controlling for site-level variation, postfledging survival was nearly twice as great following the coolest and wettest growing season (Φ = 0.77 ± 0.05 SE) compared with the hottest and driest growing season (Φ = 0.39 ± 0.05 SE). We found no relationships between individual body condition and temperature or precipitation, suggesting that carryover effects operated independently of background climatic variation. The temperature and precipitation effects we observed likely produced a direct effect on mortality risk during the postfledging period. Conservation actions that focus on improving prefledging habitat for sage-grouse may have indirect benefits to survival during postfledging, due to carryover effects between the two life phases.

Consequences of dispersal heterogeneity for population spread and persistence

Dispersal heterogeneity is increasingly being observed in ecological populations and has long been suspected as an explanation for observations of non-Gaussian dispersal. Recent empirical and theoretical studies have begun to confirm this. Using an integro-difference model, we allow an individual's diffusivity to be drawn from a trait distribution and derive a general relationship between the dispersal kernel's moments and those of the underlying heterogeneous trait distribution. We show that dispersal heterogeneity causes dispersal kernels to appear leptokurtic, increases the population's spread rate, and lowers the critical reproductive rate required for persistence in the face of advection. Wavespeed has been shown previously to be determined largely by the form of the dispersal kernel tail. We qualify this by showing that when reproduction is low, the precise shape of the tail is less important than the first few dispersal moments such as variance and kurtosis. If the reproductive rate is large, a dispersal kernel's asymptotic tail has a greater influence over wavespeed, implying that estimating the prevalence of traits which correlate with long-range dispersal is critical. The presence of multiple dispersal behaviors has previously been characterized in terms of long-range versus short-range dispersal, and it has been found that rare long-range dispersal essentially determines wavespeed. We discuss this finding and place it within a general context of dispersal heterogeneity showing that the dispersal behavior with the highest average dispersal distance does not always determine wavespeed.

Impacts of breeder loss on social structure, reproduction and population growth in a social canid

The importance of individuals to the dynamics of populations may depend on reproductive status, especially for species with complex social structure. Loss of reproductive individuals in socially complex species could disproportionately affect population dynamics by destabilizing social structure and reducing population growth. Alternatively, compensatory mechanisms such as rapid replacement of breeders may result in little disruption. The impact of breeder loss on the population dynamics of social species remains poorly understood. We evaluated the effect of breeder loss on social stability, recruitment and population growth of grey wolves (Canis lupus) in Denali National Park and Preserve, Alaska using a 26-year dataset of 387 radiocollared wolves. Harvest of breeding wolves is a highly contentious conservation and management issue worldwide, with unknown population-level consequences. Breeder loss preceded 77% of cases (n = 53) of pack dissolution from 1986 to 2012. Packs were more likely to dissolve if a female or both breeders were lost and pack size was small. Harvest of breeders increased the probability of pack dissolution, likely because the timing of harvest coincided with the breeding season of wolves. Rates of denning and successful recruitment were uniformly high for packs that did not experience breeder loss; however, packs that lost breeders exhibited lower denning and recruitment rates. Breeder mortality and pack dissolution had no significant effects on immediate or longer term population dynamics. Our results indicate the importance of breeding individuals is context dependent. The impact of breeder loss on social group persistence, reproduction and population growth may be greatest when average group sizes are small and mortality occurs during the breeding season. This study highlights the importance of reproductive individuals in maintaining group cohesion in social species, but at the population level socially complex species may be resilient to disruption and harvest through strong compensatory mechanisms.

A method for detecting positive growth autocorrelation without marking individuals

In most ecological studies, within-group variation is a nuisance that obscures patterns of interest and reduces statistical power. However, patterns of within-group variability often contain information about ecological processes. In particular, such patterns can be used to detect positive growth autocorrelation (consistent variation in growth rates among individuals in a cohort across time), even in samples of unmarked individuals. Previous methods for detecting autocorrelated growth required data from marked individuals. We propose a method that requires only estimates of within-cohort variance through time, using maximum likelihood methods to obtain point estimates and confidence intervals of the correlation parameter. We test our method on simulated data sets and determine the loss in statistical power due to the inability to identify individuals. We show how to accommodate nonlinear growth trajectories and test the effects of size-dependent mortality on our method's accuracy. The method can detect significant growth autocorrelation at moderate levels of autocorrelation with moderate-sized cohorts (for example, statistical power of 80% to detect growth autocorrelation ρ² = 0.5 in a cohort of 100 individuals measured on 16 occasions). We present a case study of growth in the red-eyed tree frog. Better quantification of the processes driving size variation will help ecologists improve predictions of population dynamics. This work will help researchers to detect growth autocorrelation in cases where marking is logistically infeasible or causes unacceptable decreases in the fitness of marked individuals.

Individual heterogeneity in reproductive rates and cost of reproduction in a long-lived vertebrate

Individual variation in reproductive success is a key feature of evolution, but also has important implications for predicting population responses to variable environments. Although such individual variation in reproductive outcomes has been reported in numerous studies, most analyses to date have not considered whether these realized differences were due to latent individual heterogeneity in reproduction or merely random chance causing different outcomes among like individuals. Furthermore, latent heterogeneity in fitness components might be expressed differently in contrasted environmental conditions, an issue that has only rarely been investigated. Here, we assessed (i) the potential existence of latent individual heterogeneity and (ii) the nature of its expression (fixed vs. variable) in a population of female Weddell seals (Leptonychotes weddellii), using a hierarchical modeling approach on a 30-year mark–recapture data set consisting of 954 individual encounter histories. We found strong support for the existence of latent individual heterogeneity in the population, with “robust” individuals expected to produce twice as many pups as “frail” individuals. Moreover, the expression of individual heterogeneity appeared consistent, with only mild evidence that it might be amplified when environmental conditions are severe. Finally, the explicit modeling of individual heterogeneity allowed us to detect a substantial cost of reproduction that was not evidenced when the heterogeneity was ignored.

Modeling reproductive trajectories of roe deer females: fixed or dynamic heterogeneity?

The relative role of dynamic and fixed heterogeneity in shaping the individual heterogeneity observed in most life-history traits remains difficult to quantify. In a recent work, Tuljapurkar et al. (2009) suggested modeling individual heterogeneity in lifetime reproductive success by a null model building reproductive trajectories from a first-order Markov chain. According to this model, among-individual differences in reproductive trajectories would be generated by the stochastic transitions among reproductive states (such as breeder and non-breeder) due to dynamic heterogeneity. In this work, we analyze the individual variation in three reproductive metrics (reproductive status, fecundity, and reproductive success) in two populations of roe deer intensively monitored using Tuljapurkar et al. (2009)’s dynamic model. Moreover, we challenge the Tuljapurkar model previously used as a biological null model to test whether the observed distribution of reproductive success over the lifetime was generated by a stochastic process by modifying two steps of the previous model to build a full stochastic model. We show that a distribution generated by the full dynamic model proposed by Tuljapurkar et al. (2009) can be consistently interpreted as only generated from a stochastic biological process provided that the probabilities of transition among reproductive states used are independent of the current reproductive state and that the positive covariation that usually occurs between survival and reproduction among individuals is removed. Only the reproductive status of roe deer females could be restricted to a stochastic process described by the full stochastic model, probably because most females (>90%) were breeders in a given year. The fecundity of roe deer females could not be adequately described by the full dynamic and full stochastic model, and the observed distribution of female reproductive success differed from the one generated by a full dynamic model in which each individual reproductive trajectory was independent of the individual lifespan (second step of the full dynamic model changed). While there was clear evidence that dynamic heterogeneity occurred and accounted for a large part of the observed among-individual variation in reproductive trajectories of roe deer females, a stochastic process did not provide a suitable model for all reproductive metrics. Consequently, models including additional fixed and dynamic traits need to be built in order to separate the relative role of fixed and dynamic heterogeneities in generating reproductive trajectories.

Separating intrinsic and environmental contributions to growth and their population consequences

Among-individual heterogeneity in growth is a commonly observed phenomenon that has clear consequences for population and community dynamics yet has proved difficult to quantify in practice. In particular, observed among-individual variation in growth can be difficult to link to any given mechanism. Here, we develop a Bayesian state-space framework for modeling growth that bridges the complexity of bioenergetic models and the statistical simplicity of phenomenological growth models. The model allows for intrinsic individual variation in traits, a shared environment, process stochasticity, and measurement error. We apply the model to two populations of steelhead trout (Oncorhynchus mykiss) grown under common but temporally varying food conditions. Models allowing for individual variation match available data better than models that assume a single shared trait for all individuals. Estimated individual variation translated into a roughly twofold range in realized growth rates within populations. Comparisons between populations showed strong differences in trait means, trait variability, and responses to a shared environment. Together, individual- and population-level variation have substantial implications for variation in size and growth rates among and within populations. State-dependent life-history models predict that this variation can lead to differences in individual life-history expression, lifetime reproductive output, and population life-history diversity.

Variation among individuals in cone production in Pinus palustris (Pinaceae)

PREMISE OF THE STUDY

Reproductive output varies considerably among individuals within plant populations, and this is especially so in cone production of conifers. While this variation can have substantial effects on populations, little is known about its magnitude or causes.

METHODS

We studied variation in cone production for 2 years within a population of Pinus palustris Mill. (longleaf pine; Pinaceae). Using hurdle models, we evaluated the importance of burn treatments, tree size (dbh), canopy status (open, dominant, subordinate), and number of conspecific neighbors within 4 m (N(4)).

KEY RESULTS

Cone production of individuals-even after accounting for other variables-was strongly correlated between years. Trees in plots burned every 1, 2, or 5 years produced more cones than those burned every 7 years, or unburned. Larger trees tend to produce more cones, but the large effects of the other factors studied caused substantial scatter in the dbh-cone number relationship. Among trees in the open, dbh had little explanatory power. Subordinate trees with three neighbors produced no cones.

CONCLUSIONS

Tree size alone was a weak predictor of cone production. Interactions with neighbors play an important role in generating reproductive heterogeneity, and must be accounted for when relating cone production to size. The strong between-year correlation, together with the large variance in cone production among trees without neighbors, suggests that still more of the variance may be explainable, but requires factors outside of our study.