Energy storage and the evolution of population dynamics

We explore the mutual dependence of life history evolution and population dynamics by modeling a structured rotifer population that preys on a dynamic food supply. We focus on the ecological role of energy storage. A physiologically based submodel describes how individual predators allocate assimilated energy among growth, reproduction, and storage. We use invasibility analyses to predict evolutionary stable strategies for energy allocation. Various proxy measures of fitness based on measurable biological quantities, such as average population size or average per-capita fecundity, fail to predict evolutionary stable strategies. The predicted strategies indicate that selection strongly favors storage allocation for juveniles, but only for adults when prey densities are high. With the evolution of energy storage, population dynamics can shift from aperiodic to stable cycles without any need to invoke group selection.     

Optimal strategies of spatial distribution: the Olli effect

The selection of strategies of spatial distribution of individuals has been studied. In case of non-monotonous dependence of reproduction coefficient on the mean population density, a cluster formation is possible. At low mean densities, parity strategies of spatial distribution are realized, and at high densities, non-parity ones. A generalized notion of parity strategy of spatial distribution has been proposed. It includes such expenditures as expenditure for the movement of an individual, defense of the territory etc. A problem of evolutionary stability of different strategies of spatial distribution has been discussed.     

Sinks without borders: snowshoe hare dynamics in a complex landscape

A full understanding of population dynamics of wide-ranging animals should account for the effects that movement and habitat use have on individual contributions to population growth or decline. Quantifying the per-capita, habitat-specific contribution to population growth can clarify the value of different patch types, and help to differentiate population sources from population sinks. Snowshoe hares, Lepus americanus , routinely use various habitat types in the landscapes they inhabit in the contiguous US, where managing forests for high snowshoe hare density is a priority for conservation of Canada lynx, Lynx canadensis . We estimated density and demographic rates via mark–recapture live trapping and radio-telemetry within four forest stand structure (FSS) types at three study areas within heterogeneous managed forests in western Montana. We found support for known fate survival models with time-varying individual covariates representing the proportion of locations in each of the FSS types, with survival rates decreasing as use of open young and open mature FSS types increased. The per-capita contribution to overall population growth increased with use of the dense mature or dense young FSS types and decreased with use of the open young or open mature FSS types, and relatively high levels of immigration appear to be necessary to sustain hares in the open FSS types. Our results support a conceptual model for snowshoe hares in the southern range in which sink habitats (open areas) prevent the buildup of high hare densities. More broadly, we use this system to develop a novel approach to quantify demographic sources and sinks for animals making routine movements through complex fragmented landscapes.     

A general model of site-dependent population regulation: population-level regulation without individual-level interactions

In this paper, we use a modeling approach to explore the population regulatory consequences of individual choices for where to breed in heterogeneous environments. In contrast to standard models, we focus on individuals that interact only indirectly through their choices of breeding sites (i.e., individuals preempt the occupation of a breeding site by others when they choose to breed there). We consider the consequences of individuals choosing breeding sites either randomly or sequentially from best to worst. Our analysis shows that average per-capita fecundity of the population is independent of the number of occupied breeding sites if individuals choose sites at random and that variation in average per-capita fecundity increases as population size declines. In contrast, if individuals choose breeding sites sequentially from highest to lowest quality, then as population size increases average per-capita fecundity declines and variation in average per-capita fecundity increases. Consequently, aggregate population-level demographic rates can change in ways that generate population regulation, even when change in population size does not change the demographic performance of any individual on any particular breeding site. However, such regulation occurs only when individuals make adaptive choices of where to breed. Because variation in average per-capita fecundity decreases when population size declines, populations regulated in a site-dependent manner should be much less susceptible to the vicissitudes of small population size than those which choose breeding sites at random.     

Scramble in behaviour and ecology

Nicholson's distinction between 'scramble' and 'contest' modes of competition has received widespread attention in ecology and in behaviour, though the emphasis has been different between the two disciplines. In ecology the focus has been on the effects on population; in behavioural ecology the focus has been on the consequences at the individual level. This paper reviews and develops a theory of scramble competition at the individual level, deriving a general evolutionarily stable strategy (ESS) for individual scramble expenditure in a patchy habitat in which individuals compete in local groups for available resources, and examines two population consequences. The critical parameter determining the relationship between individual scramble expenditure and the number of competitors in a patch is the expected resource per capita. If resource input, R, to a patch is constant and independent of the number of competitors, n, then as the number of competitors increases, the per-capita resources declines as R/n, and the ESS scramble level declines (in proportion to (n-1)/n2). However, if the resource input to a patch is positively related to the number of competitors in the patch, scramble expenditure may increase with the number of competitors. In the case where the per-capita resource input stays constant (i.e. R(n) = Rn), the scramble level increases with competitor number (in proportion to (n-1) /n). There are plausible ecological reasons why either of these extreme limits may be approached in nature, making it important to ascertain the relationship between R and n before predicting individual scramble expenditure. For example, resource input may be constant when groups of competitors are constrained to remain together in given patches, and constant per-capita resources may be approached when ideal-free foraging rules apply. However, in the latter case, scramble expenditure must be accounted for in determining the ideal-free distribution. An analysis shows that this leads to 'undermatching', i.e. the ratio of numbers of competitors for good/bad patches becomes progressively less than the ratio of input rates for good/bad patches as the difference between the good and bad patches increases. A second population consequence of the scramble ESS relates to the fact that scrambles may dramatically affect fitness. The per-capita gain in energy can be reduced by a factor of up to 1/n as a result of scramble expenditure, potentially reducing realized population size to as little as the square root of the maximum potential carrying capacity, though reasons are given why such large reductions are unlikely.     

Sex, sex-ratios, and the dynamics of pelagic copepod populations

I examine how the population biology of pelagic copepods depends on their mating biology using field data and a simple demographic model. Among calanoid copepods, two distinct patterns emerge. Firstly, copepods that lack seminal receptacle and require repeated mating to stay fertilized have near equal adult sex ratios in field populations. Winter population densities are orders of magnitude less than the critical population density required for population persistence, but populations survive winter seasons as resting eggs in the sediment. Population growth in these species is potentially high because they have on average a factor of 2 higher egg production rates than other pelagic copepods. Secondly, other copepods require only one mating to stay fertile, and populations of these species have strongly female-skewed adult sex-ratios in field populations. Resting eggs have not been described within this group. Winter population sizes are well predicted by the critical density required for population persistence which, in turn, is closely related to the body-size-dependent mate-search capacity. Thus, the different requirements for mating lead in the first case to a more opportunistic reproductive strategy that implies rapid colonization of the pelagic during productive seasons, and in the second case to a strategy that allows maintenance of a pelagic populations during unproductive seasons. Positive density dependent population growth during periods of low population density (‘Allee effect’) amplifies population density variation during winter into the subsequent summer, thus explaining why summer densities appear to depend more on winter densities than on current growth opportunities in pelagic copepods.     

Anthropogenically-Mediated Density Dependence in a Declining Farmland Bird

Land management intrinsically influences the distribution of animals and can consequently alter the potential for density-dependent processes to act within populations. For declining species, high densities of breeding territories are typically considered to represent productive populations. However, as density-dependent effects of food limitation or predator pressure may occur (especially when species are dependent upon separate nesting and foraging habitats), high territory density may limit per-capita productivity. Here, we use a declining but widespread European farmland bird, the yellowhammer Emberiza citrinella L., as a model system to test whether higher territory densities result in lower fledging success, parental provisioning rates or nestling growth rates compared to lower densities. Organic landscapes held higher territory densities, but nests on organic farms fledged fewer nestlings, translating to a 5 times higher rate of population shrinkage on organic farms compared to conventional. In addition, when parental provisioning behaviour was not restricted by predation risk (i.e., at times of low corvid activity), nestling provisioning rates were higher at lower territory densities, resulting in a much greater increase in nestling mass in low density areas, suggesting that food limitation occurred at high densities. These findings in turn suggest an ecological trap, whereby preferred nesting habitat does not provide sufficient food for rearing nestlings at high population density, creating a population sink. Habitat management for farmland birds should focus not simply on creating a high nesting density, but also on ensuring heterogeneous habitats to provide food resources in close proximity to nesting birds, even if this occurs through potentially restricting overall nest density but increasing population-level breeding success.     

Oscillatory dynamics in evolutionary games are suppressed by heterogeneous adaptation rates of players

Game dynamics in which three or more strategies are cyclically competitive, as represented by the rock-scissors-paper game, have attracted practical and theoretical interests. In evolutionary dynamics, cyclic competition results in oscillatory dynamics of densities of individual strategists. In finite-size populations, it is known that oscillations blow up until all but one strategies are eradicated if without mutation. In the present paper, we formalize replicator dynamics with players who have different adaptation rates. We show analytically and numerically that the heterogeneous adaptation rate suppresses the oscillation amplitude. In social dilemma games with cyclically competing strategies and homogeneous adaptation rates, altruistic strategies are often relatively weak and cannot survive in finite-size populations. In such situations, heterogeneous adaptation rates save coexistence of different strategies and hence promote altruism. When one strategy dominates the others without cyclic competition, fast adaptors earn more than slow adaptors. When not, mixture of fast and slow adaptors stabilizes population dynamics, and slow adaptation does not imply inefficiency for a player.     

Identification of age-structured models: cell cycle phase transitions

A methodology is developed that determines age-specific transition rates between cell cycle phases during balanced growth by utilizing age-structured population balance equations. Age-distributed models are the simplest way to account for varied behavior of individual cells. However, this simplicity is offset by difficulties in making observations of age distributions, so age-distributed models are difficult to fit to experimental data. Herein, the proposed methodology is implemented to identify an age-structured model for human leukemia cells (Jurkat) based only on measurements of the total number density after the addition of bromodeoxyuridine partitions the total cell population into two subpopulations. Each of the subpopulations will temporarily undergo a period of unbalanced growth, which provides sufficient information to extract age-dependent transition rates, while the total cell population remains in balanced growth. The stipulation of initial balanced growth permits the derivation of age densities based on only age-dependent transition rates. In fitting the experimental data, a flexible transition rate representation, utilizing a series of cubic spline nodes, finds a bimodal G(0)/G(1) transition age probability distribution best fits the experimental data. This resolution may be unnecessary as convex combinations of more restricted transition rates derived from normalized Gaussian, lognormal, or skewed lognormal transition-age probability distributions corroborate the spline predictions, but require fewer parameters. The fit of data with a single log normal distribution is somewhat inferior suggesting the bimodal result as more likely. Regardless of the choice of basis functions, this methodology can identify age distributions, age-specific transition rates, and transition-age distributions during balanced growth conditions.     

Modelling horse management in the Australian Alps

Management of the feral Horse (Equus caballus) in the Australian Alps bioregion is a difficult and emotive issue, with interested parties working from vastly differing perspectives. Compounding this, information regarding ecology and distribution of horses, and the cost and effectiveness of management strategies is often unknown or uncertain. Resolving these issues requires an objective approach with the flexibility to incorporate different potential scenarios. We used a spatially explicit population model to compare the potential effects of two different management strategies on populations of horses in the Australian Alps bioregion: culling from helicopters versus trapping and mustering. We populated the model using the results of population surveys conducted in 2014, vegetation data and cost estimates. We then provided an estimate of the effect of each strategy on population size across the Alps, and their corresponding costs, compared to no management. To account for uncertainties, we simulated different scenarios for horse population densities, dispersal rates and population growth rates. Management using aerial culling was more effective than mustering in every scenario modelled, and three to six times cheaper. Aerial culling was only slightly more effective within its control region. However, because mustering is necessarily restricted by road access, this translated to a substantial improvement in population control – up to 2000 horses where growth and dispersal rates were high. Our results unequivocally suggest aerial culling as the only strategy that could effectively control horses within the modelled range of scenarios; this result stands in addition to its other potential benefits of lower cost, animal stress and landscape disturbance. A major advantage of this modelling approach is that we can easily update it with new data, test different measures of effectiveness and add new scenarios to adapt to the rapidly changing situation on the ground, both in terms of the ecology and the political climate.     

Revisiting the Role of Individual Variability in Population Persistence and Stability

Populations often exhibit a pronounced degree of individual variability and this can be important when constructing ecological models. In this paper, we revisit the role of inter-individual variability in population persistence and stability under predation pressure. As a case study, we consider interactions between a structured population of zooplankton grazers and their predators. Unlike previous structured population models, which only consider variability of individuals according to the age or body size, we focus on physiological and behavioural structuring. We first experimentally demonstrate a high degree of variation of individual consumption rates in three dominant species of herbivorous copepods (Calanus finmarchicus, Calanus glacialis, Calanus euxinus) and show that this disparity implies a pronounced variation in the consumption capacities of individuals. Then we construct a parsimonious predator-prey model which takes into account the intra-population variability of prey individuals according to behavioural traits: effectively, each organism has a ‘personality’ of its own. Our modelling results show that structuring of prey according to their growth rate and vulnerability to predation can dampen predator-prey cycles and enhance persistence of a species, even if the resource stock for prey is unlimited. The main mechanism of efficient top-down regulation is shown to work by letting the prey population become dominated by less vulnerable individuals when predator densities are high, while the trait distribution recovers when the predator densities are low.     

Building integral projection models with nonindependent vital rates

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co‐vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs and include cases where the processes co‐vary as a function of time (temporal variation), co‐vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population‐level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life‐history evolution.     

The Allee-type ideal free distribution

The ideal free distribution (IFD) in a two-patch environment where individual fitness is positively density dependent at low population densities is studied. The IFD is defined as an evolutionarily stable strategy of the habitat selection game. It is shown that for low and high population densities only one IFD exists, but for intermediate population densities there are up to three IFDs. Population and distributional dynamics described by the replicator dynamics are studied. It is shown that distributional stability (i.e., IFD) does not imply local stability of a population equilibrium. Thus distributional stability is not sufficient for population stability. Results of this article demonstrate that the Allee effect can strongly influence not only population dynamics, but also population distribution in space.     

Natural enemy ravine revisited: the importance of sample size for determining population growth

Abstract. 1. The population growth of three aphid species, Metopolophium dirhodum (Walker), Rhopalosiphum padi (L.), and Sitobion avenae (F.), on winter wheat, was analysed by regression. The calculations were based on censuses of aphids made in 268 plots at 3- or 7-day intervals for 10 years on leaves and 6 years on ears. The calculations were made separately for each plot each year, then repeated on the pooled data from all plots monitored in a year.
2. At the level of individual plots, no population growth was detected at very low densities. At high densities, the populations grew exponentially and the growth rates did not decrease with increasing aphid density.
3. Significant growth was always detected in the pooled data. These growth rates decreased significantly at the highest densities. Field estimates of the intrinsic rate of increase derived from these data ranged from 0.010 to 0.026 for M. dirhodum , 0.0071–0.011 for R. padi , and 0.00078–0.0061 and 0.0015–0.13 for S. avenae , on leaves and ears respectively .
4. The apparent lack of growth in the individual plots at low densities is attributable to small sample size. It is concluded that the natural enemy ravine in the population dynamics of cereal aphids, identified by Southwood and Comins (1976), is a consequence of low population densities at which population increase is undetectable unless very large samples are taken.     

Arms races and the evolution of big fierce societies

The causes of biological gigantism have received much attention, but only for individual organisms. What selection pressures might favour the evolution of gigantic societies? Here we consider the largest single-queen insect societies, those of the Old World army ant Dorylus, single colonies of which can have 20 million workers. We propose that colony gigantism in Dorylus arises as a result of an arms race and test this prediction by developing a size-structured mathematical model. We use this model for exploring and potentially explaining differences in colony size, colony aggression and colony propagation strategies in populations of New World army ants Eciton and Old World army ants Dorylus. The model shows that, by determining evolutionarily stable strategies (ESSs), differences in the trophic levels at which these army ants live feed forwards into differences in their densities and collision rates and, hence, into different strategies of growth, aggression and propagation. The model predicts large colony size and the occurrence of battles and a colony-propagation strategy involving highly asymmetrical divisions in Dorylus and that Eciton colonies should be smaller, non-combative and exhibit equitable binary fission. These ESSs are in excellent agreement with field observations and demonstrate that gargantuan societies can arise through arms races.     

Plastic reproductive allocation as a buffer against environmental stochasticity – linking life history and population dynamics to climate

Empirical work suggest that long‐lived organisms have adopted risk sensitive reproductive strategies where individuals trade the amount of resources spent on reproduction versus survival according to expected future environmental conditions. Earlier studies also suggest that climate affects population dynamics both directly by affecting population vital rates and indirectly through long‐term changes in individual life histories. Using a seasonal and state‐dependent individual‐based model we investigated how environmental variability affects the selection of reproductive strategies and their effect on population dynamics. We found that: (1) dynamic, i.e. plastic, reproductive strategies were optimal in a variable climate. (2) Females in poor and unpredictable climatic regimes allocated fewer available resources in reproduction and more in own somatic growth. This resulted in populations with low population densities, and a high average female age and body mass. (3) Strong negative density dependence on offspring body mass and survival, along with co‐variation between climatic severity and population density, resulted in no clear negative climatic effects on reproductive success and offspring body mass. (4) Time series analyses of population growth rates revealed that populations inhabiting benign environments showed the clearest response to climatic perturbations as high population density prohibited an effective buffering of adverse climatic effects as individuals were not able to gain sufficient body reserves during summer. Regularly occurring harsh winters ‘harvested’ populations, resulting in persistent low densities, and released them from negative density dependent effects, resulting in high rewards for a given resource allocation.     

不同密度猪毛菜形态结构性状及生物量分配策略的异速关系

植物的生长特性随环境条件的变化具有可塑性,而不同的环境因素对植物可塑性的影响也不尽相同。利用异速分析的方法,通过模拟退化草地恢复过程中猪毛菜（Salsola collina）的不同种群密度（16、44、100、400株/m²）,研究其形态结构性状及生物量分配策略的异速关系在种群密度间的差异。结果表明,种群密度增大能抑制猪毛菜的生长,而且对猪毛菜的株高、根长、一级分枝数、二级分枝数、三级分枝数以及总分枝长均产生了极显著的影响,表明种群密度的变化使得植物的高生长和侧向生长发生了显著变化。种群密度的变化也引起了植物生物量的变化,其中植物根、茎、叶间的生物关系是一种表观可塑性,植物的生长策略未发生改变,只是植物个体大小发生改变引起的生物量分配的变化。植物株高、总分枝长、一级分枝数及繁殖分配的变化,是由种群密度变化引起的,植物的适应策略发生了改变,是真正的可塑性。种群密度改变了植物的繁殖分配策略,而未改变植物叶的分配策略,说明当环境发生变化时,植物调整了其繁殖策略以适应环境因素的改变,以保证种群的生存繁衍。     

Nonlinear effects of consumer density on multiple ecosystem processes

1.?In the face of human-induced declines in the abundance of common species, ecologists have become interested in quantifying how changes in density affect rates of biophysical processes, hence ecosystem function. We manipulated the density of a dominant detritivore (the cased caddisfly, Limnephilus externus) in subalpine ponds to measure effects on the release of detritus-bound nutrients and energy. 2.?Detritus decay rates (k, mass loss) increased threefold, and the loss of nitrogen (N) and phosphorus (P) from detrital substrates doubled across a range of historically observed caddisfly densities. Ammonium and total soluble phosphorus concentrations in the water column also increased with caddisfly density on some dates. Decay rates, nutrient release and the change in total detritivore biomass all exhibited threshold or declining responses at the highest densities. 3.?We attributed these threshold responses in biophysical processes to intraspecific competition for limiting resources manifested at the population level, as density-dependent per-capita consumption, growth, development and case : body size in caddisflies was observed. Moreover, caddisflies increasingly grazed on algae at high densities, presumably in response to limiting detrital resources. 4.?These results provide evidence that changes in population size of a common species will have nonlinear, threshold effects on the rates of biophysical processes at the ecosystem level. Given the ubiquity of negative density dependence in nature, nonlinear consumer density-ecosystem function relationships should be common across species and ecosystems.     

Maternal control of offspring sex and male morphology in the Otitesella fig wasps

Models concerning the evolution of alternative mating tactics commonly assume that individuals determine their own strategies. Here we develop a computer-based ESS model that allows mothers, ovipositing in discrete patches, to choose both the sex and the male mating tactics (natal-patch mating or dispersing) of their offspring based only on how many other mothers have used the specific patch before them. Data for three species of nonpollinating fig wasps from the Otitesella genus agree quantitatively with the model's assumptions and predictions. This suggests that females respond to population densities at the level of individual figs. The alternative male tactics in the species we studied are probably a result of a conditional strategy exercised by the mother that laid them. In addition, as females were only allowed to lay one egg per patch, our results suggest a new mechanism that can skew population sex ratios towards a female bias.     

Evolutionary dynamics of prey exploitation in a metapopulation of predators

In well-mixed populations of predators and prey, natural selection favors predators with high rates of prey consumption and population growth. When spatial structure prevents the populations from being well mixed, such predators may have a selective disadvantage because they do not make full use of the prey's growth capacity and hence produce fewer propagules. The best strategy then depends on the degree to which predators can monopolize the exploitation of local prey populations, which in turn depends on the spatial structure, the number of migrants, and, in particular, the stochastic nature of the colonization process. To analyze the evolutionary dynamics of predators in a spatially structured predator-prey system, we performed simulations with a metapopulation model that has explicit local dynamics of nonpersistent populations, keeps track of the number of emigrants entering the migration pool, assumes individuals within local populations as well as within the migration pool to be well mixed, and takes stochastic colonization into account. We investigated which of the predator's exploitation strategies are evolutionarily stable and whether these strategies minimize the overall density of prey, as is the case in Lotka-Volterra-type models of competitive exclusion. This was analyzed by pairwise invasibility plots based on short-term simulations and tested by long-term simulation experiments of competition between resident and mutant predator-types that differed in one of the following parameters: the prey-to-predator conversion efficiency, the per capita prey consumption rate, or the per capita emigration rate from local populations. In addition, we asked which of these three strategies are most likely to evolve. Our simulations showed that under selection for conversion efficiency the predator-prey system always goes globally extinct yet persists under selection for consumption or emigration rates and that the evolutionarily stable (ES) exploitation strategies do not maximize local population growth rates. The most successful exploitation strategy minimizes the overall density of prey but does not make it settle exactly at the minimum. The system did not settle at the point where the mean time to co-invasion (i.e., immigration of a second predator in a local prey population) equals the mean local interaction time (an idea borne out from studies on host exploitation strategies in host-pathogen systems) but rather where the mean time to co-invasion was larger. The ES exploitation strategies represent more prudent strategies than the ones that minimize prey density. Finally, we show that-compared to consumption-emigration is a more likely target for selection to achieve prudent exploitation and that prudent exploitation strategies can evolve only provided the prey-to-predator conversion efficiency is subject to constraints.