The age-structured lottery model

The lottery model of competition between species in a variable environmental has been influential in understanding how coexistence may result from interactions between fluctuating environmental and competitive factors. Of most importance, it has led to the concept of the storage effect as a mechanism of species coexistence. Interactions between environment and competition in the lottery model stem from the life-history assumption that environmental variation and competition affect recruitment to the adult population, but not adult survival. The strong role of life-history attributes in this coexistence mechanism implies that its robustness should be checked for a variety of life-history scenarios. Here, age structure is added to the adult population, and the results are compared with the original lottery model. This investigation uses recently developed shape characteristics for mortality and fecundity schedules to quantify the effects of age structure on the long-term low-density growth rate of a species in competition with its competitor when applying the standard invasibility coexistence criterion. Coexistence conditions are found to be affected to a small degree by the presence of age structure in the adult population: Type III mortality broadens coexistence conditions, and type I mortality makes them narrower. The rates of recovery from low density for coexisting species, and the rates of competitive exclusion in other cases, are modified to a greater degree by age structure. The absolute rates of recovery or decline of a species from low density are increased by type I mortality or early peak reproduction, but reduced by type III mortality or late peak reproduction. Analytical approximations show how the most important effects can be considered as simple modifications of the long-term low-density growth rates for the original lottery model.     

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.     

Species synchrony and its drivers: neutral and nonneutral community dynamics in fluctuating environments

Independent species fluctuations are commonly used as a null hypothesis to test the role of competition and niche differences between species in community stability. This hypothesis, however, is unrealistic because it ignores the forces that contribute to synchronization of population dynamics. Here we present a mechanistic neutral model that describes the dynamics of a community of equivalent species under the joint influence of density dependence, environmental forcing, and demographic stochasticity. We also introduce a new standardized measure of species synchrony in multispecies communities. We show that the per capita population growth rates of equivalent species are strongly synchronized, especially when endogenous population dynamics are cyclic or chaotic, while their long-term fluctuations in population sizes are desynchronized by ecological drift. We then generalize our model to nonneutral dynamics by incorporating temporal and nontemporal forms of niche differentiation. Niche differentiation consistently decreases the synchrony of species per capita population growth rates, while its effects on the synchrony of population sizes are more complex. Comparing the observed synchrony of species per capita population growth rates with that predicted by the neutral model potentially provides a simple test of deterministic asynchrony in a community.     

Why are population growth rate estimates of past and present hunter–gatherers so different?

Hunter–gatherer population growth rate estimates extracted from archaeological proxies and ethnographic data show remarkable differences, as archaeological estimates are orders of magnitude smaller than ethnographic and historical estimates. This could imply that prehistoric hunter–gatherers were demographically different from recent hunter–gatherers. However, we show that the resolution of archaeological human population proxies is not sufficiently high to detect actual population dynamics and growth rates that can be observed in the historical and ethnographic data. We argue that archaeological and ethnographic population growth rates measure different things; therefore, they are not directly comparable. While ethnographic growth rate estimates of hunter–gatherer populations are directly linked to underlying demographic parameters, archaeological estimates track changes in the long-term mean population size, which reflects changes in the environmental productivity that provide the ultimate constraint for forager population growth. We further argue that because of this constraining effect, hunter–gatherer populations cannot exhibit long-term growth independently of increasing environmental productivity.This article is part of the theme issue ‘Cross-disciplinary approaches to prehistoric demography’.     

Jensen’s Inequality and the Impact of Short-Term Environmental Variability on Long-Term Population Growth Rates

It is well established in theory that short-term environmental fluctuations could affect the long-term growth rates of wildlife populations, but this theory has rarely been tested and there remains little empirical evidence that the effect is actually important in practice. Here we develop models to quantify the effects of daily, seasonal, and yearly temperature fluctuations on the average population growth rates, and we apply them to long-term data on the endangered Black-faced Spoonbill (Platalea minor); an endothermic species whose population growth rates follow a concave relationship with temperature. We demonstrate for the first time that the current levels of temperature variability, particularly seasonal variability, are already large enough to substantially reduce long-term population growth rates. As the climate changes, our results highlight the importance of considering the ecological effects of climate variability and not just average conditions.     

Coexistence resulting from an alternation of density dependent and density independent growth

When two species compete with each other, one is likely to displace or exclude the other. Several circumstances under which they may coexist indefinitely have been presented in the literature; the present contribution presents examples of one more. Under circumstances where both populations are repeatedly decreased (for example because of annual environmental changes) then subsequent to each decrease both species grow unrestrictedly and then interact with each other in a competitive fashion. If the species that grows more rapidly under unrestricted conditions is at a disadvantage during competitive phases of growth, this effect prolongs coexistence but may not prevent eventual extinction of one or the other species. However, it is shown that there are certain broad ranges of conditions for population growth that lead to permanent cyclical stability. The stability described here is such that the ecosystem will return to the same dynamic balance even when severely perturbed. It is also shown that this kind of stability can be either favored or prevented in certain cases by random fluctuations in the environment affecting season length, kill factor, etc.     

EVOLUTIONARY RESPONSES TO ENVIRONMENTAL CHANGES: HOW DOES COMPETITION AFFECT ADAPTATION?

The role and importance of ecological interactions for evolutionary responses to environmental changes is to large extent unknown. Here it is shown that interspecific competition may slow down rates of adaptation substantially and fundamentally change patterns of adaptation to long-term environmental changes. In the model investigated here, species compete for resources distributed along an ecological niche space. Environmental change is represented by a slowly moving resource maximum and evolutionary responses of single species are compared with responses of coalitions of two and three competing species. In scenarios with two and three species, species that are favored by increasing resource availability increase in equilibrium population size whereas disfavored species decline in size. Increased competition makes it less favorable for individuals of a disfavored species to occupy a niche close to the maximum and reduces the selection pressure for tracking the moving resource distribution. Individual-based simulations and an analysis using adaptive dynamics show that the combination of weaker selection pressure and reduced population size reduces the evolutionary rate of the disfavored species considerably. If the resource landscape moves stochastically, weak evolutionary responses cause large fluctuations in population size and thereby large extinction risk for competing species, whereas a single species subject to the same environmental variability may track the resource maximum closely and maintain a much more stable population size. Other studies have shown that competitive interactions may amplify changes in mean population sizes due to environmental changes and thereby increase extinction risks. This study accentuates the harmful role of competitive interactions by illustrating that they may also decrease rates of adaptation. The slowdown in evolutionary rates caused by competition may also contribute to explain low rates of morphological change in spite of large environmental fluctuations found in fossil records.     

Estimating the growth of a newly established moose population using reproductive value

Estimating the population growth rate and environmental stochasticity of long-lived species is difficult because annual variation in population size is influenced by temporal autocorrelations caused by fluctuations in the age-structure. Here we use the dynamics of the reproductive value to estimate the long-term growth rate s and the environmental variance of a moose population that recently colonized the island of Vega in northern Norway. We show that the population growth rate was high (ŝ=0.26). The major stochastic influences on the population dynamics were due to demographic stochasticity, whereas the environmental variance was not significantly different from 0. This supports the suggestion that population growth rates of polytocous ungulates are high, and that demographic stochasticity must be assessed when estimating the growth of small ungulate populations.     

Habitat dependence and correlations between elasticities of long-term growth rates

In population biology, elasticity is a measure of the importance of a demographic rate on population growth. A relatively small amount of stochasticity can substantially impact the dynamics of a population whose growth is a function of deterministic and stochastic processes. Analyses of natural populations frequently neglect the latter. Even in a population that fluctuates substantially with time, the results of a deterministic perturbation analysis correlated strongly with results of a perturbation analysis of the long-run stochastic growth rate. Population growth was, however, not uniformly sensitive to demographic rates across different environmental conditions. The overall correlation between deterministic and stochastic perturbation analysis may be high, but environmental variability can dramatically alter the contributions of demographic rates in different environmental conditions. This potentially informative detail is neglected by deterministic analysis, yet it highlights one difficulty when extrapolating results from long-term analysis to shorter-term environmental change.     

Pattern of variation in avian population growth rates

A central question in population ecology is to understand why population growth rates differ over time. Here, we describe how the long-term growth of populations is not only influenced by parameters affecting the expected dynamics, for example form of density dependence and specific population growth rate, but is also affected by environmental and demographic stochasticity. Using long-term studies of fluctuations of bird populations, we show an interaction between the stochastic and the deterministic components of the population dynamics: high specific growth rates at small densities r(1) are typically positively correlated with the environmental variance sigma(e)(2). Furthermore, theta, a single parameter describing the form of the density regulation in the theta-logistic density-regulation model, is negatively correlated with r(1). These patterns are in turn correlated with interspecific differences in life-history characteristics. Higher specific growth rates, larger stochastic effects on the population dynamics and stronger density regulation at small densities are found in species with large clutch sizes or high adult mortality rates than in long-lived species. Unfortunately, large uncertainties in parameter estimates, as well as strong stochastic effects on the population dynamics, will often make even short-term population projections unreliable. We illustrate that the concept of population prediction interval can be useful in evaluating the consequences of these uncertainties in the population projections for the choice of management actions.     

Effects of temporal variability on rare plant persistence in annual systems

Traditional conservation biology regards environmental fluctuations as detrimental to persistence, reducing long-term average growth rates and increasing the probability of extinction. By contrast, coexistence models from community ecology suggest that for species with dormancy, environmental fluctuations may be essential for persistence in competitive communities. We used models based on California grasslands to examine the influence of interannual fluctuations in the environment on the persistence of rare forbs competing with exotic grasses. Despite grasses and forbs independently possessing high fecundity in the same types of years, interspecific differences in germination biology and dormancy caused the rare forb to benefit from variation in the environment. Owing to the buildup of grass competitors, consecutive favorable years proved highly detrimental to forb persistence. Consequently, negative temporal autocorrelation, a low probability of a favorable year, and high variation in year quality all benefited the forb. In addition, the litter produced by grasses in a previously favorable year benefited forb persistence by inhibiting its germination into highly competitive grass environments. We conclude that contrary to conventional predictions of conservation and population biology, yearly fluctuations in climate may be essential for the persistence of rare species in invaded habitats.     

Population and prehistory I: Food-dependent population growth in constant environments

We present a demographic model that describes the feedbacks between food supply, human mortality and fertility rates, and labor availability in expanding populations, where arable land area is not limiting. This model provides a quantitative framework to describe how environment, technology, and culture interact to influence the fates of preindustrial agricultural populations. We present equilibrium conditions and derive approximations for the equilibrium population growth rate, food availability, and other food-dependent measures of population well-being. We examine how the approximations respond to environmental changes and to human choices, and find that the impact of environmental quality depends upon whether it manifests through agricultural yield or maximum (food-independent) survival rates. Human choices can complement or offset environmental effects: greater labor investments increase both population growth and well-being, and therefore can counteract lower agricultural yield, while fertility control decreases the growth rate but can increase or decrease well-being. Finally we establish equilibrium stability criteria, and argue that the potential for loss of local stability at low population growth rates could have important consequences for populations that suffer significant environmental or demographic shocks.     

Extinctions in competitive communities forced by coloured environmental variation

Understanding the relationships between environmental fluctuations, population dynamics and species interactions in natural communities is of vital theoretical and practical importance. This knowledge is essential in assessing extinction risks in communities that are, for example, pressed by changing environmental conditions and increasing exploitation. We developed a model of density dependent population renewal, in a Lotka–Volterra competitive community context, to explore the significance of interspecific interactions, demographic stochasticity, population growth rate and species abundance on extinction risk in populations under various autocorrelation (colour) regimes of environmental forcing. These factors were evaluated in two cases, where either a single species or the whole community was affected by the external forcing. Species' susceptibility to environmental noise with different autocorrelation structure depended markedly on population dynamics, species' position in the abundance hierarchy and how similarly community members responded to external forcing. We also found interactions between demographic stochasticity and environmental noise leading to a reversal in extinction probabilities from under- to overcompensatory dynamics. We compare our results with studies of single species populations and contrast possible mechanisms leading to extinctions. Our findings indicate that abundance rank, the form of population dynamics, and the colour of environmental variation interact in affecting species extinction risk. These interactions are further modified by interspecific interactions within competitive communities as the interactions filter and modulate the environmental noise.     

Evaluating the demographic buffering hypothesis with vital rates estimated for Weddell seals from 30 years of mark-recapture data

1. Life-history theory predicts that those vital rates that make larger contributions to population growth rate ought to be more strongly buffered against environmental variability than are those that are less important. Despite the importance of the theory for predicting demographic responses to changes in the environment, it is not yet known how pervasive demographic buffering is in animal populations because the validity of most existing studies has been called into question because of methodological deficiencies. 2. We tested for demographic buffering in the southern-most breeding mammal population in the world using data collected from 5558 known-age female Weddell seals over 30 years. We first estimated all vital rates simultaneously with mark-recapture analysis and then estimated process variance and covariance in those rates using a hierarchical Bayesian approach. We next calculated the population growth rate's sensitivity to changes in each of the vital rates and tested for evidence of demographic buffering by comparing properly scaled values of sensitivity and process variance in vital rates. 3. We found evidence of positive process covariance between vital rates, which indicates that all vital rates are affected in the same direction by changes in annual environment. Despite the positive correlations, we found strong evidence that demographic buffering occurred through reductions in variation in the vital rates to which population growth rate was most sensitive. Process variation in vital rates was inversely related to sensitivity measures such that variation was greatest in breeding probabilities, intermediate for survival rates of young animals and lowest for survival rates of older animals. 4. Our work contributes to a small but growing set of studies that have used rigorous methods on long-term, detailed data to investigate demographic responses to environmental variation. The information from these studies improves our understanding of life-history evolution in stochastic environments and provides useful information for predicting population responses to future environmental change. Our results for an Antarctic apex predator also provide useful baselines from a marine ecosystem when its top- and middle-trophic levels were not substantially impacted by human activity.     

Adaptation of timing of life history traits and population dynamic responses to climate change in spatially structured populations

Changes in the seasonal timing of life history events are documented effects of climate change. We used a general model to study how dispersal and competitive interactions affect eco-evolutionary responses to changes in the temporal distribution of resources over the season. Specifically, we modeled adaptation of the timing of reproduction and population dynamic responses in two competing populations that disperse between two habitats characterized by an early and late resource peak. We investigated three scenarios of environmental change: (1) food peaks advance in both habitats, (2) in the late habitat only and (3) in the early habitat only. At low dispersal rates the evolutionarily stable timing of reproduction closely matched the local resource peak and the environmental change typically caused population decline. Larger dispersal rates rendered less intuitive eco-evolutionary population responses. First, dispersal caused mismatch between evolutionarily stable timing of reproduction and local resource peaks and as a result, reproductive output for subpopulations could increase as well as decrease when resource availability underwent temporal shifts. Second, population responses were contingent on competition between populations. This could accelerate population declines and cause extinctions or even reverse population trends from negative to positive compared to the low dispersal case. When dispersal rate was large and the early resource peak was advanced available niche space was reduced. Hence, even when a population survived the environmental change and obtained positive equilibrium population density, subsequent adaptation of competing populations could drive it to extinction due to convergent evolution and competitive exclusion. These results shed new light on the role of competition and dispersal for the evolution of timing of life history events and provide guidelines for understanding short and long-term population response to climate change.     

克隆和有性亲体效应及其调控机制

植物表型受自身基因型、所处环境及其亲体所经历环境的共同影响;其中,亲体环境对子代表型的影响被称为亲体效应。亲体效应不仅可通过有性繁殖产生的种子传递给后代(即有性亲体效应),也可以通过克隆生长等无性繁殖产生的分株传递给后代(即克隆亲体效应)。亲体效应对植物种群,特别是对有性繁殖受限、缺乏遗传变异的克隆植物种群的长期进化可能发挥着极其重要的作用,因此,对亲体效应研究进展的梳理非常必要。对克隆亲体效应和有性亲体效应的内涵进行了阐释,并论述了克隆和有性亲体效应对子代表型、适合度、种内/种间竞争能力以及种群/群落结构和功能的潜在影响;阐述了亲体效应的潜在调控机制,包括供给机制、代谢物质调控机制、表观遗传机制等;论述了克隆亲体效应在克隆植物适应进化中的作用。未来可以就克隆亲体效应的遗传稳定性及其对克隆生活史性状变异的贡献程度,以及克隆和有性亲体效应引起的表型多样性对种内/种间关系、种群/群落多样性及生态系统结构、功能和稳定性的影响开展深入研究。     

Population effects of increased climate variation

Global circulation models predict and numerous observations confirm that anthropogenic climate change has altered high-frequency climate variability. However, it is not yet well understood how changing patterns of environmental variation will affect wildlife population dynamics and other ecological processes. Theory predicts that a population's long-run growth rate is diminished and the chance of population extinction is increased as environmental variation increases. This results from the fact that population growth is a multiplicative process and that long-run population growth rate is the geometric mean of growth rates over time, which is always less than the arithmetic mean. However, when population growth rates for unstructured populations are related nonlinearly to environmental drivers, increasing environmental variation can increase a population's long-run growth rate. This suggests that patterns of environmental variation associated with different aspects of climate change may affect population dynamics in different ways. Specifically, increasing variation in rainfall might result in diminished long-run growth rates for many animal species while increasing variation in temperature might result in increased long-run growth rates. While the effect of rainfall is theoretically well understood and supported by data, the hypothesized effect of temperature is not. Here, I analyse two datasets to study the effect of fluctuating temperatures on growth rates of zooplankton. Results are consistent with the prediction that fluctuating temperatures should increase long-run growth rates and the frequency of extreme demographic events.     

Population dynamics and the colour of environmental noise.

The effect of red, white and blue environmental noise on discrete-time population dynamics is analyzed. The coloured noise is superimposed on Moran-Ricker and Maynard Smith dynamics, the resulting power spectra are less than examined. Time series dominated by short- and long-term fluctuations are said to be blue and red, respectively. In the stable range of the Moran-Ricker dynamics, environmental noise of any colour will make population dynamics red or blue depending the intrinsic growth rate. Thus, telling apart the colour of the noise from the colour of the population dynamics may not be possible. Population dynamics subjected to red and blue environmental noises show, respectively, more red or blue power spectra than those subjected to white noise. The sensitivity to differences in the noise colours decreases with increasing complexity and ultimately disappears in the chaotic range of the population dynamics. These findings are duplicated with the Maynard Smith model for high growth rates when the strength of density dependence changes. However, for low growth rates the power spectra of the population dynamics with noise are red in stable, periodic and aperiodic ranges irrespective of the noise colour. Since chaotic population fluctuations may show blue spectra in the deterministic case, this implies that blue deterministic chaos may become red under any colour of the noise.     

Diffusion analysis and stationary distribution of the two-species lottery competition model

The lottery model is a stochastic population model in which juveniles compete for space. Examples include sedentary organisms such as trees in a forest and members of marine benthic communities. The behavior of this model appears to be characteristic of that found in other sorts of stochastic competition models. In a community with two species, it was previously demonstrated that coexistence of the species is possible if adult death rates are small and environmental variation is large. Environmental variation is incorporated by assuming that the birth rates and death rates are random variables. Complicated conditions for coexistence and competitive exclusion have been derived elsewhere. In this paper, simple and easily interpreted conditions are found by using the technique of diffusion approximation. Formulae are given for the stationary distribution and means and variances of population fluctuations. The shape of the stationary distribution allows the stability of the coexistence to be evaluated.     

A shift from exploitation to interference competition with increasing density affects population and community dynamics

Intraspecific competition influences population and community dynamics and occurs via two mechanisms. Exploitative competition is an indirect effect that occurs through use of a shared resource and depends on resource availability. Interference competition occurs by obstructing access to a resource and may not depend on resource availability. Our study tested whether the strength of interference competition changes with protozoa population density. We grew experimental microcosms of protozoa and bacteria under different combinations of protozoan density and basal resource availability. We then solved a dynamic predator–prey model for parameters of the functional response using population growth rates measured in our experiment. As population density increased, competition shifted from exploitation to interference, and competition was less dependent on resource levels. Surprisingly, the effect of resources was weakest when competition was the most intense. We found that at low population densities, competition was largely exploitative and resource availability had a large effect on population growth rates, but the effect of resources was much weaker at high densities. This shift in competitive mechanism could have implications for interspecific competition, trophic interactions, community diversity, and natural selection. We also tested whether this shift in the mechanism of competition with protozoa density affected the structure of the bacterial prey community. We found that both resources and protozoa density affected the structure of the bacterial prey community, suggesting that competitive mechanism may also affect trophic interactions.