Intraspecific trait variation across scales: implications for understanding global change responses

Recognition of the importance of intraspecific variation in ecological processes has been growing, but empirical studies and models of global change have only begun to address this issue in detail. This review discusses sources and patterns of intraspecific trait variation and their consequences for understanding how ecological processes and patterns will respond to global change. We examine how current ecological models and theories incorporate intraspecific variation, review existing data sources that could help parameterize models that account for intraspecific variation in global change predictions, and discuss new data that may be needed. We provide guidelines on when it is most important to consider intraspecific variation, such as when trait variation is heritable or when nonlinear relationships are involved. We also highlight benefits and limitations of different model types and argue that many common modeling approaches such as matrix population models or global dynamic vegetation models can allow a stronger consideration of intraspecific trait variation if the necessary data are available. We recommend that existing data need to be made more accessible, though in some cases, new experiments are needed to disentangle causes of variation.     

Selective consequences of catastrophes for growth rates in a stream-dwelling salmonid

Optimal life histories in a fluctuating environment are likely to differ from those that are optimal in a constant environment, but we have little understanding of the consequences of bounded fluctuations versus episodic massive mortality events. Catastrophic disturbances, such as floods, droughts, landslides and fires, substantially alter the population dynamics of affected populations, but little has been done to investigate how catastrophes may act as a selective agent for life-history traits. We use an individual-based model of population dynamics of the stream-dwelling salmonid marble trout (Salmo marmoratus) to investigate how trade-offs between the growth and mortality of individuals and density-dependent body growth can lead to the maintenance of a wide or narrow range of individual variation in body growth rates in environments that are constant (i.e., only demographic stochasticity), variable (i.e., environmental stochasticity), or variable with catastrophic events that cause massive mortalities (e.g., flash floods). We find that occasional episodes of massive mortality can substantially reduce persistent variability in individual growth rates. Lowering the population density reduces density dependence and allows for higher fitness of more opportunistic strategies (rapid growth and early maturation) during the recovery period.     

Estimation of a Nonlinear Density-Dependence Parameter for Wild Turkey

Abstract: Although previous research and theory has suggested that wild turkey (Meleagris gallopavo) populations may be subject to some form of density dependence, there has been no effort to estimate and incorporate a density-dependence parameter into wild turkey population models. To estimate a functional relationship for density dependence in wild turkey, we analyzed a set of harvest-index time series from 11 state wildlife agencies. We tested for lagged correlations between annual harvest indices using partial autocorrelation analysis. We assessed the ability of the density-dependent theta-Ricker model to explain harvest indices over time relative to exponential or random walk growth models. We tested the homogeneity of the density-dependence parameter estimates (θ) from 3 different harvest indices (spring harvest no. reported harvest/effort, survey harvest/effort) and calculated a weighted average based on each estimate's variance and its estimated covariance with the other indices. To estimate the potential bias in parameter estimates from measurement error, we conducted a simulation study using the theta-Ricker with known values and lognormally distributed measurement error. Partial autocorrelation function analysis indicated that harvest indices were significantly correlated only with their value at the previous time step. The theta-Ricker model performed better than the exponential growth or random walk models for all 3 indices. Simulation of known parameters and measurement error indicated a strong positive upward bias in the density-dependent parameter estimate, with increasing measurement error. The average density-dependence estimate, corrected for measurement error ranged 0.25 ≤ θC ≤ 0.49, depending on the amount of measurement error and assumed spring harvest rate. We infer that density dependence is nonlinear in wild turkey, where growth rates are maximized at 39-42% of carrying capacity. The annual yield produced by density-dependent population growth will tend to be less than that caused by extrinsic environmental factors. This study indicates that both density-dependent and density-independent processes are important to wild turkey population growth, and we make initial suggestions on incorporating both into harvest management strategies.     

Long-term demographic analysis in goshawk <Emphasis Type="Italic">Accipiter gentilis</Emphasis>: the role of density dependence and stochasticity

Density dependence and environmental stochasticity are both potentially important processes influencing population demography and long-term population growth. Quantifying the importance of these two processes for population growth requires both long-term population as well as individual-based data. I use a 30-year data set on a goshawk Accipiter gentilis population from Eastern Westphalia, Germany, to describe the key vital rate elements to which the growth rate is most sensitive and test how environmental stochasticity and density dependence affect long-term population growth. The asymptotic growth rate of the fully age-structured mean matrix model was very similar to the observed one (0.7% vs. 0.3% per annum), and population growth was most elastic to changes in survival rate at age classes 1-3. Environmental stochasticity led only to a small change in the projected population growth rate (between -0.16% and 0.67%) and did not change the elasticities qualitatively, suggesting that the goshawk life history of early reproduction coupled with high annual fertility buffers against a variable environment. Age classes most crucial to population growth were those in which density dependence seemed to act most strongly. This emphasises the importance of density dependence as a regulatory mechanism in this goshawk population. It also provides a mechanism that might enable the population to recover from population lows, because a mean matrix model incorporating observed functional responses of both vital rates to population density coupled with environmental stochasticity reduced long-term extinction risk of 30% under density-independent environmental stochasticity and 60% under demographic stochasticity to zero.     

Population-level ecological effect assessment: estimating the effect of toxic chemicals on density-dependent populations

We examined the relationship between individual-level and population-level effects of toxic chemicals, employing the equilibrium population size as an index of population-level effects. We first analyzed two-stage matrix models considering four life-history types and four density-dependent models, and then we analyzed ecotoxicological and life-history data of the fathead minnow (Pimephales promelas) and brook trout (Salvelinus fontinalis) as real examples. Our elasticity analysis showed that toxic impacts on density-dependent populations depended largely on the differences in density-dependence and in life histories of the organisms. In particular, the importance of adult survivability was considerably increased in iteroparous organisms with density-dependent juvenile survivability or fertility. Our results also suggested that population-level effects, as indicated by the percentage reduction in equilibrium population size, were often greater than the percentage reductions in vital rates of individuals. Our analysis indicates that assessing population-level risk and developing a risk-reduction strategy without considering density-dependence can be risky.     

What have two decades of laboratory life-history evolution studies onDrosophila melanogaster taught us?

A series of laboratory selection experiments onDrosophila melanogaster over the past two decades has provided insights into the specifics of life-history tradeoffs in the species and greatly refined our understanding of how ecology and genetics interact in life-history evolution. Much of what has been learnt from these studies about the subtlety of the microevolutionary process also has significant implications for experimental design and inference in organismal biology beyond life-history evolution, as well as for studies of evolution in the wild. Here we review work on the ecology and evolution of life-histories in laboratory populations ofD. melanogaster, emphasizing how environmental effects on life-history-related traits can influence evolutionary change. We discuss life-history tradeoffs—many unexpected—revealed by selection experiments, and also highlight recent work that underscores the importance to life-history evolution of cross-generation and cross-life-stage effects and interactions, sexual antagonism and sexual dimorphism, population dynamics, and the possible role of biological clocks in timing life-history events. Finally, we discuss some of the limitations of typical selection experiments, and how these limitations might be transcended in the future by a combination of more elaborate and realistic selection experiments, developmental evolutionary biology, and the emerging discipline of phenomics.     

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.     

Geographic variation in density-dependent dynamics impacts the synchronizing effect of dispersal and regional stochasticity

Explanations for the ubiquitous presence of spatially synchronous population dynamics have assumed that density-dependent processes governing the dynamics of local populations are identical among disjunct populations, and low levels of dispersal or small amounts of regionalized stochasticity (Moran effect) can act to synchronize populations. In this study we used historical spatially referenced data on gypsy moth (Lymantria dispar) outbreaks to document that density-dependent processes can vary substantially across geographical landscapes. This variation may be due in part to geographical variation in habitat (e.g., variation in forest composition). We then used a second-order log-linear stochastic model to explore how inter-population variation in density-dependent processes affects synchronization via either synchronous stochastic forcing or dispersal. We found that geographical variation in direct density-dependence (first order) greatly diminishes synchrony caused by stochasticity but only slightly decreases synchronization via dispersal. Variation in delayed density-dependence (second order) diluted synchrony caused by regional stochasticity to a lesser extent than first-order variation, but it did not have any influence on synchrony caused by dispersal. In general, synchronization caused by dispersal was primarily dependent upon the instability of populations and only weakly, if at all, affected by similarities in density-dependence among populations. We conclude that studies of synchrony should carefully consider both the nature of the synchronizing agents and the pattern of local density-dependent processes, including how these vary geographically.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Optimal age of maturity in fluctuating environments under r‐ and K‐selection

Optimality models for evolution of life histories have shown that increased environmental stochasticity promotes early age of maturity. Here we argue that if r‐selection for early maturation implies a tradeoff making those phenotypes more sensitive to a change in population size than phenotypes maturing at older ages, K‐selection can favor delayed onset of maturation. We analyze a general stochastic Leslie‐matrix model with a simplified density regulation affecting all survivals equally through a function of the population vector, often called the ‘critical age class’. We show that the outcome of such an age‐dependent r‐ and K‐selection is that the expected value of the ‘critical age class’ is maximized by evolution, a strategy strongly influenced by the magnitude of the environmental stochasticity. We also demonstrate that evolution caused by such density‐dependent selection influences the population dynamics, showing a possible reciprocal effect between ecology and evolution in age‐structured populations. This modeling approach reveals that changes in population size affecting the fitness of phenotypes with different age of maturity may be an important selective agent for variation in onset of reproduction in fluctuating environments. This provides a testable hypothesis for how patterns in the population dynamics should affect life history variation.     

Comparative population dynamics of large and small mammals in the Northern Hemisphere: deterministic and stochastic forces

Deterministic feedbacks within populations interact with extrinsic, stochastic processes to generate complex patterns of animal abundance over time and space. Animals inherently differ in their responses to fluctuating environments due to differences in body sizes and life history traits. However, controversy remains about the relative importance of deterministic and stochastic forces in shaping population dynamics of large and small mammals. We hypothesized that effects of environmental stochasticity and density dependence are stronger in small mammal populations relative to their effects in large mammal populations and thus differentiate the patterns of population dynamics between them. We conducted an extensive, comparative analysis of population dynamics in large and small mammals to test our hypothesis, using seven population parameters to describe general dynamic patterns for 23 (14 species) time series of observations of abundance of large mammals and 38 (21 species) time series for small mammals. We used state‐space models to estimate the strength of direct and delayed density dependence as well as the strength of environmental stochasticity. We further used phylogenetic comparative analysis to detect differences in population dynamic patterns and individual population parameters, respectively, between large and small mammals. General population dynamic patterns differed between large and small mammals. However, the strength of direct and delayed density dependence was comparable between large and small mammals. Moreover, the variances of population growth rates and environmental stochasticity were greater in small mammals than in large mammals. Therefore, differences in population response to stochastic forces and strength of environmental stochasticity are the primary factor that differentiates population dynamic patterns between large and small mammal species.     

Patterns and processes of population dynamics with fluctuating habitat size: a case study of a marine copepod inhabiting tide pools

The logistic model is a fundamental population model often used as the basis for analyzing wildlife population dynamics. In the classic logistic model, however, population dynamics may be difficult to characterize if habitat size is temporally variable because population density can vary at a constant abundance, which results in variable strength of density‐dependent feedback for a given population size. To incorporate habitat size variability, we developed a general population model in which changes in population abundance, density, and habitat size are taken into account. From this model, we deduced several predictions for patterns and processes of population dynamics: 1) patterns of fluctuation in population abundance and density can diverge, with respect of their correlation and relative variability; and 2) along with density dependence, habitat size fluctuation can affect population growth with a time lag because changes in habitat size result in changes in population density. In order to test these predictions, we applied our model to population dynamics data of 36 populations of Tigriopus japonicus, a marine copepod inhabiting tide pools of variable sizes caused by weather processes. As expected, we found a significant difference in the fluctuation patterns of population abundance and density of T. japonicus populations with respect to the correlation between abundance and density and their relative variability, which correlates positively with the variability of habitat size. In addition, we found direct and lagged‐indirect effects of weather processes on population growth, which were associated with density dependence and impose regulatory forces on local and regional population dynamics. These results illustrate how changes in habitat size can have an impact on patterns and processes of wildlife population dynamics. We suggest that without knowledge of habitat size fluctuation, measures of population size and its variability as well as inferences about the processes of population dynamics may be misleading.     

Natural selection and population dynamics

To what extent, and under which circumstances, are population dynamics influenced by concurrent natural selection? Density dependence and environmental stochasticity are generally expected to subsume any selective modulation of population growth rate, but theoretical considerations point to conditions under which selection can have an appreciable impact on population dynamics. By contrast, empirical research has barely scratched the surface of this fundamental question in population biology. Here, we present a diverse body of mostly empirical evidence that demonstrates how selection can influence population dynamics, including studies of small populations, metapopulations, cyclical populations and host-pathogen interactions. We also discuss the utility, in this context, of inferences from molecular genetic data, placing them within the broader framework of quantitative genetics and life-history evolution.     

Density regulation in the Mediterranean leaf-toed gecko <Emphasis Type="Italic">Euleptes europaea</Emphasis>

Isolated populations are particularly prone to extinction, and understanding their temporal dynamics is relevant for conservation and management. In this study, the abundance of a population of the nocturnal leaf-toed gecko Euleptes europaea was estimated by mark-recapture over a 12-year period in northwest Italy. Simulation tests showed the presence of density-dependence, and autoregressive analyses indicated that direct density dependence was responsible for a large part of the variation in population growth rates. Density-dependent recruitment was suggested as the main demographic mechanism controlling population dynamics, which was also affected by solar radiation measured during the active gecko season. These results may contribute to implement conservation strategies in other small and isolated leaf-toed gecko populations.     

Estimating density dependence in time-series of age-structured populations

For a life history with age at maturity alpha, and stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time-lags of from 1 to alpha years. Contrary to current interpretations, the coefficients for different time-lags in the autoregressive dynamics do not simply measure delayed density dependence, but also depend on life-history parameters. We define a new measure of total density dependence in a life history, D, as the negative elasticity of population growth rate per generation with respect to change in population size, D = - partial differential lnlambda(T)/partial differential lnN, where lambda is the asymptotic multiplicative growth rate per year, T is the generation time and N is adult population size. We show that D can be estimated from the sum of the autoregression coefficients. We estimated D in populations of six avian species for which life-history data and unusually long time-series of complete population censuses were available. Estimates of D were in the order of 1 or higher, indicating strong, statistically significant density dependence in four of the six species.     

Resolving discrepancies between deterministic population models and individual-based simulations

ABSTRACT This work ties together two distinct modeling frameworks for population dynamics: an individual-based simulation and a set of coupled integrodifferential equations involving population densities. The simulation model represents an idealized predator-prey system formulated at the scale of discrete individuals, explicitly incorporating their mutual interactions, whereas the population-level framework is a generalized version of reaction-diffusion models that incorporate population densities coupled to one another by interaction rates. Here I use various combinations of long-range dispersal for both the offspring and adult stages of both prey and predator species, providing a broad range of spatial and temporal dynamics, to compare and contrast the two model frameworks. Taking the individual-based modeling results as given, two examinations of the reaction-dispersal model are made: linear stability analysis of the deterministic equations and direct numerical solution of the model equations. I also modify the numerical solution in two ways to account for the stochastic nature of individual-based processes, which include independent, local perturbations in population density and a minimum population density within integration cells, below which the population is set to zero. These modifications introduce new parameters into the population-level model, which I adjust to reproduce the individual-based model results. The individual-based model is then modified to minimize the effects of stochasticity, producing a match of the predictions from the numerical integration of the population-level model without stochasticity.     

Density-Dependent Harvest Modeling for the Eastern Wild Turkey

Abstract Many current wild turkey (Meleagris gallopavo) harvest models assume density-independent population dynamics. We developed an alternative model incorporating both nonlinear density-dependence and stochastic density-independent effects on wild turkey populations. We examined model sensitivity to parameter changes in 5% increments and determined mean spring and fall harvests and their variability in the short term (3 yr) and long term (10 yr) from proportional harvesting under these conditions. In the long term, population growth rates were most sensitive to poult:female ratios and the form of density dependence. The nonlinear density-dependent effect produced a population that maximized yield at 40% carrying capacity. The model indicated that a spring or fall proportional harvest could be maximized for fall harvest rates between 0% and 13% of the population, assuming a 15% spring male harvest and 5% spring illegal female kill. Combined spring and fall harvests could be maximized at a 9% fall harvest, under the same assumptions. Variability in population growth and harvest rates increased uncertainty in spring and fall harvests and the probability of overharvesting annual yield, with growth rate variation having the strongest effect. Model simulations suggested fall harvest rates should be conservative (≤9%) for most management strategies.     

Viability and Management of an Endangered Capercaillie (Tetrao urogallus) Metapopulation in the Jura Mountains, Western Switzerland

The populations of Capercaillie (Tetrao urogallus), the largest European grouse, have seriously declined during the last century over most of their distribution in western and central Europe. In the Jura mountains, the relict population is now isolated and critically endangered (about 500 breeding adults). We developed a simulation software (TetrasPool) that accounts for age and spatial structure as well as stochastic processes, to perform a viability analysis and explore management scenarios for this population, capitalizing on a 24 years-long series of field data. Simulations predict a marked decline and a significant extinction risk over the next century, largely due to environmental and demographic stochasticity (average values of life-history parameters would otherwise allow stability). Variances among scenarios mainly stem from uncertainties about the shape and intensity of density dependence. Uncertainty analyses suggest to focus conservation efforts on enhancing, not only adult survival (as often advocated for long-lived species), but also recruitment. The juvenile stage matters when local populations undergo extinctions, because it ensures connectivity and recolonization. Besides limiting human perturbations, a silvicultural strategy aimed at opening forest structure should improve the quality and surface of available patches, independent of their size and localization. Such measures are to be taken urgently, if the population is to be saved.     

Relative importance of density-dependent regulation and environmental stochasticity for butterfly population dynamics

The relative contribution of density-dependent regulation and environmental stochasticity to the temporal dynamics of animal populations is one of the central issues of ecology. In insects, the primary role of the latter factor, typically represented by weather patterns, is widely accepted. We have evaluated the impact of density dependence as well as density-independent factors, including weather and mowing regime, on annual fluctuations of butterfly populations. As model species, we used Maculinea alcon and M. teleius living in sympatry and, consequently, we also analysed the effect of their potential competition. Density dependence alone explained 62 and 42% of the variation in the year-to-year trends of M. alcon and M. teleius, respectively. The cumulative Akaike weight of models with density dependence, which can be interpreted as the probability that this factor should be contained in the most appropriate population dynamics model, exceeded 0.97 for both species. In contrast, the impacts of inter-specific competition, mowing regime and weather were much weaker, with their cumulative weights being in the range of 0.08–0.21; in addition, each of these factors explained only 2–5% of additional variation in Maculinea population trends. Our results provide strong evidence for density-dependent regulation in Maculinea, while the influence of environmental stochasticity is rather minor. In the light of several recent studies on other butterflies that detected significant density-dependent effects, it would appear that density-dependent regulation may be more widespread in this group than previously thought, while the role of environmental stochasticity has probably been overestimated. We suggest that this misconception is the result of deficiencies in the design of most butterfly population studies in the past, including (1) a strong focus on adults and a neglect of the larval stage in which density-dependent effects are most likely to occur; (2) an almost exclusive reliance on transect count results that may confound the impact of environmental stochasticity on butterfly numbers with its impact on adult longevity. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Regulation of local populations of a coral reef fish via joint effects of density- and number-dependent mortality

Density-dependent mortality can regulate local populations - effectively minimizing the likelihood of local extinctions and unchecked population growth. It is considered particularly important for many marine reef organisms with demographically open populations that lack potential regulatory mechanisms tied to local reproduction. While density-dependent mortality has been documented frequently for reef fishes, few studies have explored how the strength of density-dependence varies with density, or how density-dependence may be modified by numerical effects (i.e., number-dependent mortality). Both issues can have profound effects on spatial patterns of abundance and the regulation of local populations. I address these issues through empirical studies in Moorea, French Polynesia, of the six bar wrasse (Thalassoma hardwicke), a reef fish that settles to isolated patch reefs. Per capita mortality rates of newly settled wrasse increased as a function of density and were well approximated by the Beverton-Holt function for both naturally formed and experimentally generated juvenile cohorts. Average instantaneous mortality rates were a decelerating function of initial densities, indicating the per capita strength of density-dependence decreased with density. Results of a factorial manipulation of density and group size indicate that per capita mortality rates were simultaneously density- and number-dependent; fish at higher densities and/or in groups had higher probabilities of disappearing from patch reefs compared with fish that were solitary and/or at lower densities. Mortality rates were ~30% higher for fish at densities of 0.5 fish/m² than at 0.25 fish/m². Similarly, mortality rates increased by ~45% when group size was increased from 1 to 2 individuals per patch, even when density was kept constant. These observations suggest that the number of interacting individuals, independent of patch size (i.e., density-independent effects) can contribute to regulation of local populations. Overall, this work highlights a greater need to consider numerical effects in addition to density effects when exploring sources of population regulation.     

Modelling the local dynamics of the zebra mussel (Dreissena polymorpha)

1. The bivalve Dreissena polymorpha has invaded many freshwater ecosystems worldwide in recent decades. Because of their high fecundity and ability to settle on almost any solid substratum, zebra mussels usually outcompete the resident species and cause severe damage to waterworks. Time series of D. polymorpha densities display a variety of dynamical patterns, including very irregular behaviours. Unfortunately, there is a lack of mathematical modelling that could explain these patterns. 2. Here, we propose a very simple discrete‐time population model with age structure and density dependence that can generate realistic dynamics. Most of the model parameters can be derived from existing data on D. polymorpha. Some of them are quite variable: with respect to these we perform a sensitivity analysis of the model behaviour and verify that non‐equilibrial regimes (either periodic or chaotic) are the rule rather than the exception. 3. Even in circumstances where the model dynamics are aperiodic it is possible to predict total density peaks from previous peaks. This turns out to be true also in the presence of environmental stochasticity. 4. Using the stochastic model we explore the effects of age‐selective predation. Quite surprisingly, larger removal rates of adults do not always result in smaller population densities and mussel biomasses. Moreover, non‐selective predation can result in skewed size‐frequency distributions which, therefore, are not necessarily the footprint of predators’ preference for larger or smaller zebra mussels.