The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.     

The ideal free distribution as an evolutionarily stable strategy

We examine the evolutionary stability of strategies for dispersal in heterogeneous patchy environments or for switching between discrete states (e.g. defended and undefended) in the context of models for population dynamics or species interactions in either continuous or discrete time. There have been a number of theoretical studies that support the view that in spatially heterogeneous but temporally constant environments there will be selection against unconditional, i.e. random, dispersal, but there may be selection for certain types of dispersal that are conditional in the sense that dispersal rates depend on environmental factors. A particular type of dispersal strategy that has been shown to be evolutionarily stable in some settings is balanced dispersal, in which the equilibrium densities of organisms on each patch are the same whether there is dispersal or not. Balanced dispersal leads to a population distribution that is ideal free in the sense that at equilibrium all individuals have the same fitness and there is no net movement of individuals between patches or states. We find that under rather general assumptions about the underlying population dynamics or species interactions, only such ideal free strategies can be evolutionarily stable. Under somewhat more restrictive assumptions (but still in considerable generality), we show that ideal free strategies are indeed evolutionarily stable. Our main mathematical approach is invasibility analysis using methods from the theory of ordinary differential equations and nonnegative matrices. Our analysis unifies and extends previous results on the evolutionary stability of dispersal or state-switching strategies.     

Spatio‐temporal dynamics of density‐dependent dispersal during a population colonisation

Predicting population colonisations requires understanding how spatio‐temporal changes in density affect dispersal. Density can inform on fitness prospects, acting as a cue for either habitat quality, or competition over resources. However, when escaping competition, high local density should only increase emigration if lower‐density patches are available elsewhere. Few empirical studies on dispersal have considered the effects of density at the local and landscape scale simultaneously. To explore this, we analyze 5 years of individual‐based data from an experimental introduction of wild guppies Poecilia reticulata. Natal dispersal showed a decrease in local density dependence as density at the landscape level increased. Landscape density did not affect dispersal among adults, but local density‐dependent dispersal switched from negative (conspecific attraction) to positive (conspecific avoidance), as the colonisation progressed. This study demonstrates that densities at various scales interact to determine dispersal, and suggests that dispersal trade‐offs differ across life stages.     

The effects of climate change on density‐dependent population dynamics of aquatic invertebrates

Global climate change has the potential to alter aquatic communities through changes in evapotranspiration and increased variability in precipitation. We used aquatic mesocosms to test the impacts of variable precipitation on population dynamics of common mosquito (Culicidae) and midge (Chironomidae) larvae that inhabit vernal pools. In a mixed deciduous forest in northern Vermont, USA, we orthogonally crossed seven levels of mean water level (increased rainfall) with seven levels of water level coefficient of variation (more variable rainfall) to simulate a broad array of climate change scenarios in 49 experimental mesocosms. The average abundance of Culicidae was highest at low water levels, whereas the average abundance of Chironomidae was highest at higher water levels and low variability in water level. Treatments and environmental and spatial covariates collectively explained 49% of the variance in mean abundance. For both taxa, we fit hierarchical Bayesian models to each 16‐week time series to estimate the parameters in a Gompertz logistic equation of population growth with density dependence. We found that Culicidae population growth rate increased with decreasing water levels and that 87% of the variance in Chironomidae density dependence could be explained by treatment. Collectively, these results suggest that climate change can alter abundances aquatic invertebrate taxa but not necessarily through the same mechanism on all populations. In the case of Culicidae the abundance is affected by changes in growth rate, and in Chironomidae by changes in the strength of density dependence.     

Infanticide as an evolutionarily stable strategy

An evolutionarily stable strategies analysis of infanticide, expressed as two pure strategies, shows that the equilibrial frequency of infanticide depends on only two parameters: the relative advantage of infanticide when others are also infanticidal and the relative advantage of a non-infanticidal strategy if others are non-infanticidal. The possible equilibrial conditions of strictly infanticidal, strictly non-infanticidal, stably polymorphic or history-dependent populations correspond to various earlier models of infanticide. Thus, these earlier models may be subsumed as special cases of the ESS analysis. This permits the comparison of alternative theories of infanticide in specific cases of infanticide in natural populations. In particular, it is argued that if infanticide confers a relative advantage on the perpetrator when other population members are non-infanticidal, this is sufficient to reject a ‘maladaptive’ explanation for infanticide. The potential existence of history-dependent equilibria suggests there will be extreme difficulty with non-experimental methods that attempt to test the adaptiveness of infanticidal behaviour.     

Density‐dependent and density‐independent drivers of population change in Barton Springs salamanders

Understanding population change is essential for conservation of imperiled species, such as amphibians. Worldwide amphibian declines have provided an impetus for investigating their population dynamics, which can involve both extrinsic (density‐independent) and intrinsic (density‐dependent) drivers acting differentially across multiple life stages or age classes. In this study, we examined the population dynamics of the endangered Barton Springs Salamander (Eurycea sosorum) using data from a long‐term monitoring program. We were interested in understanding both the potential environmental drivers (density‐independent factors) and demographic factors (interactions among size classes, negative density dependence) to better inform conservation and management activities. We used data from three different monitoring regimes and multivariate autoregressive state‐space models to quantify environmental effects (seasonality, discharge, algae, and sediment cover), intraspecific interactions among three size classes, and intra‐class density dependence. Results from our primary data set revealed similar patterns among sites and size classes and were corroborated by our out‐of‐sample data. Cross‐correlation analysis showed juvenile abundance was most strongly correlated with a 9‐month lag in aquifer discharge, which we suspect is related to inputs of organic carbon into the aquifer. However, sedimentation limited juvenile abundance at the surface, emphasizing the importance of continued sediment management. Recruitment from juveniles to the sub‐adult size class was evident, but negative density‐dependent feedback ultimately regulated each size class. Negative density dependence may be an encouraging sign for the conservation of E. sosorum because populations that can reach carrying capacity are less likely to go extinct compared to unregulated populations far below their carrying capacity. However, periodic population declines coupled with apparent migration into the aquifer complicate assessments of species status. Although both density‐dependent and density‐independent drivers of population change are not always apparent in time series of animal populations, both have important implications for conservation and management of E. sosorum.     

Partitioning the sources of demographic variation reveals density‐dependent nest predation in an island bird population

Ecological factors often shape demography through multiple mechanisms, making it difficult to identify the sources of demographic variation. In particular, conspecific density can influence both the strength of competition and the predation rate, but density‐dependent competition has received more attention, particularly among terrestrial vertebrates and in island populations. A better understanding of how both competition and predation contribute to density‐dependent variation in fecundity can be gained by partitioning the effects of density on offspring number from its effects on reproductive failure, while also evaluating how biotic and abiotic factors jointly shape demography. We examined the effects of population density and precipitation on fecundity, nest survival, and adult survival in an insular population of orange‐crowned warblers (Oreothlypis celata) that breeds at high densities and exhibits a suite of traits suggesting strong intraspecific competition. Breeding density had a negative influence on fecundity, but it acted by increasing the probability of reproductive failure through nest predation, rather than through competition, which was predicted to reduce the number of offspring produced by successful individuals. Our results demonstrate that density‐dependent nest predation can underlie the relationship between population density and fecundity even in a high‐density, insular population where intraspecific competition should be strong.     

Evolutionary stability of mutualism: interspecific population regulation as an evolutionarily stable strategy

Interspecific mutualisms are often vulnerable to instability because low benefit : cost ratios can rapidly lead to extinction or to the conversion of mutualism to parasite-host or predator-prey interactions. We hypothesize that the evolutionary stability of mutualism can depend on how benefits and costs to one mutualist vary with the population density of its partner, and that stability can be maintained if a mutualist can influence demographic rates and regulate the population density of its partner. We test this hypothesis in a model of mutualism with key features of senita cactus (Pachycereus schottii)-senita moth (Upiga virescens) interactions, in which benefits of pollination and costs of larval seed consumption to plant fitness depend on pollinator density. We show that plants can maximize their fitness by allocating resources to the production of excess flowers at the expense of fruit. Fruit abortion resulting from excess flower production reduces pre-adult survival of the pollinating seed-consumer, and maintains its density beneath a threshold that would destabilize the mutualism. Such a strategy of excess flower production and fruit abortion is convergent and evolutionarily stable against invasion by cheater plants that produce few flowers and abort few to no fruit. This novel mechanism of achieving evolutionarily stable mutualism, namely interspecific population regulation, is qualitatively different from other mechanisms invoking partner choice or selective rewards, and may be a general process that helps to preserve mutualistic interactions in nature.     

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.     

Delayed density‐dependent onset of spring reproduction in a fluctuating population of field voles

Delayed density‐dependent demographic processes are thought to be the basis for multi‐annual cyclic fluctuations in small rodent populations, but evidence for delayed density dependence of a particular demographic trait is rare. Here, using capture–recapture data from 22 sites collected over nine years, we demonstrate a strong effect of population density with a one‐year lag on the timing of the onset of spring reproduction in a cyclically fluctuating population of field voles Microtus agrestis in northern England. The mean date for the onset of spring reproduction was delayed by about 24 days for every additional 100 voles ha^?1 in the previous spring. This delayed density dependence is sufficient to generate the type of cyclic population dynamics described in the study system.     

Non‐additive effects of density‐dependent and density‐independent factors on brown trout vital rates

Interactions between density‐dependent and density‐independent processes can lead to variation in both growth and survival rates. Detecting such effects, however, will often require sampling on an individual level and at the appropriate spatial and temporal scale. This study documents substantial variation in survival and growth of stream‐dwelling brown trout Salmo trutta from a small Norwegian stream. The data is based on seasonal capture–recaptures of individually marked trout on fixed stations during eight years. The fish were small‐sized, rarely reaching sizes larger than 20 cm and ages older than seven years. Density varied between 0.2–0.8 fish m^?2. Variation in survival and recapture probabilities was analysed using program MARK. Apparent survival (the probability of being alive and present within the study area) generally decreased with increasing trout density and increasing drought level (measured as lowest observed water flow) during both winter and summer. Further, there was a significant interaction effect between density and water flow, indicating that density‐dependent effects on survival predominated when environmental conditions were benign (no drought), while density‐independent processes were most important under harsh environmental conditions (drought). Observed length‐at‐age during autumn indicated a more or less linear growth trajectory throughout life, and no effect of density, water flow or temperature was found. However, using the individual‐based capture–recapture data to estimated specific growth rate, significant positive effects of water flow and temperature and a negative effect of density were identified. Thus, the capture–recapture data suggest a strong potential for population regulation at the rather low densities found in this stream, and regulation may occur both through effects on survival and growth.     

Indirect evidence of density‐dependent population regulation in Aponomma hydrosauri (Acari: Ixodidae), an ectoparasite of reptiles

Abstract The extent to which density‐dependent processes regulate natural populations is the subject of an ongoing debate. We contribute evidence to this debate showing that density‐dependent processes influence the population dynamics of the ectoparasite Aponomma hydrosauri (Acari: Ixodidae), a tick species that infests reptiles in Australia. The first piece of evidence comes from an unusually long‐term dataset on the distribution of ticks among individual hosts. If density‐dependent processes are influencing either host mortality or vital rates of the parasite population, and those distributions can be approximated with negative binomial distributions, then general host–parasite models predict that the aggregation coefficient of the parasite distribution will increase with the average intensity of infections. We fit negative binomial distributions to the frequency distributions of ticks on hosts, and find that the estimated aggregation coefficient k increases with increasing average tick density. This pattern indirectly implies that one or more vital rates of the tick population must be changing with increasing tick density, because mortality rates of the tick's main host, the sleepy lizard, Tiliqua rugosa, are unaffected by changes in tick burdens. Our second piece of evidence is a re‐analysis of experimental data on the attachment success of individual ticks to lizard hosts using generalized linear modelling. The probability of successful engorgement decreases with increasing numbers of ticks attached to a host. This is direct evidence of a density‐dependent process that could lead to an increase in the aggregation coefficient of tick distributions described earlier. The population‐scale increase in the aggregation coefficient is indirect evidence of a density‐dependent process or processes sufficiently strong to produce a population‐wide pattern, and thus also likely to influence population regulation. The direct observation of a density‐dependent process is evidence of at least part of the responsible mechanism.     

Effective size of density‐dependent populations in fluctuating environments

Reliable estimates of effective population size are of central importance in population genetics and evolutionary biology. For populations that fluctuate in size, harmonic mean population size is commonly used as a proxy for (multi‐) generational effective size. This assumes no effects of density dependence on the ratio between effective and actual population size, which limits its potential application. Here, we introduce density dependence on vital rates in a demographic model of variance effective size. We derive an expression for the ratio in a density‐regulated population in a fluctuating environment. We show by simulations that yearly genetic drift is accurately predicted by our model, and not proportional to as assumed by the harmonic mean model, where N is the total population size of mature individuals. We find a negative relationship between and N. For a given N, the ratio depends on variance in reproductive success and the degree of resource limitation acting on the population growth rate. Finally, our model indicate that environmental stochasticity may affect not only through fluctuations in N, but also for a given N at a given time. Our results show that estimates of effective population size must include effects of density dependence and environmental stochasticity.     

The ideal free distribution and predator-prey populations

The ideal free distribution, a theoretical model of the distribution of competitors between habitat patches, has recently undergone a number of modifications and extensions. These fall into two main categories: those that assume that equilibrium is attained, and those that establish whether it is attained. The modifications suggest ways in which behavioural properties of individuals might affect the distribution of competitors, and clear a path for further empirical tests.     

Neural correlates to flight‐related density‐dependent phase characteristics in locusts

Locust phase polymorphism is an extreme example of behavioral plasticity; in response to changes in population density, locusts dramatically alter their behavior. These changes in behavior facilitate the appearance of various morphological and physiological phase characteristics. One of the principal behavioral changes is the more intense flight behavior and improved flight performance of gregarious locusts compared to solitary ones. Surprisingly, the neurophysiological basis of the behavioral phase characteristics has received little attention. Here we present density‐dependent differences in flight‐related sensory and central neural elements in the desert locust. Using techniques already established for gregarious locusts, we compared the response of locusts of both phases to controlled wind stimuli. Gregarious locusts demonstrated a lower threshold for wind‐induced flight initiation. Wind‐induced spiking activity in the locust tritocerebral commissure giants (TCG, a pair of identified interneurons that relay input from head hair receptors to thoracic motor centers) was found to be weaker in solitary locusts compared to gregarious ones. The solitary locusts' TCG also demonstrated much stronger spike frequency adaptation in response to wind stimuli. Although the number of forehead wind sensitive hairs was found to be larger in solitary locusts, the stimuli conveyed to their flight motor centers were weaker. The tritocerebral commissure dwarf (TCD) is an inhibitory flight‐related interneuron in the locust that responds to light stimuli. An increase in TCD spontaneous activity in dark conditions was significantly stronger in gregarious locusts than in solitary ones. Thus, phase‐dependent differences in the activity of flight‐related interneurons reflect behavioral phase characteristics. © 2003 Wiley Periodicals, Inc. J Neurobiol 57: 152–162, 2003     

Evolution of density‐dependent movement during experimental range expansions

Range expansions and biological invasions are prime examples of transient processes that are likely impacted by rapid evolutionary changes. As a spatial process, range expansions are driven by dispersal and movement behaviour. Although it is widely accepted that dispersal and movement may be context‐dependent, for instance density‐dependent, and best represented by reaction norms, the evolution of density‐dependent movement during range expansions has received little experimental attention. We therefore tested current theory predicting the evolution of increased movement at low densities at range margins using highly replicated and controlled range expansion experiments across multiple genotypes of the protist model system Tetrahymena thermophila. Although rare, we found evolutionary changes during range expansions even in the absence of initial standing genetic variation. Range expansions led to the evolution of negatively density‐dependent movement at range margins. In addition, we report the evolution of increased intrastrain competitive ability and concurrently decreased population growth rates in range cores. Our findings highlight the importance of understanding movement and dispersal as evolving reaction norms and plastic life‐history traits of central relevance for range expansions, biological invasions and the dynamics of spatially structured systems in general.     

Exact compensation of stream drift as an evolutionarily stable strategy

The colonization cycle hypothesis predicts that adults of stream-dwelling insects preferentially disperse in the upstream direction in order to compensate for larval drift. Upstream biased dispersal has indeed been shown in many, albeit not all, natural populations. Based on a recently published analysis, we develop a simple stochastic model for the competition of genotypes with different dispersal strategies in a stream habitat. By means of an invasion analysis, we show that exact compensation of larval drift by upstream biased adult dispersal is an evolutionarily stable strategy. Exact compensation means that, on average, the net movement of individuals from birth to the time of reproduction is zero. At the population level, we show that, in general, upstream biased dispersal is not necessary for persistence, unless the reproductive rate is very low. Under all conditions, however, populations of exact compensators attain highest sizes or persistence times, respectively. Although selection pressure towards exact compensation is arguably very general in populations subject to stream drift, trade-offs or constraints might change the outcome of selection. Therefore, the analysis presented in this paper has to be viewed as a null model for optimal dispersal behavior in stream habitats.     

Balancing food and density‐dependence in the spatial distribution of an interference‐prone forager

Foraging distributions are thought to be density‐dependent, because animals not only select for a high availability and quality of resources, but also avoid conspecific interference. Since these processes are confounded, their relative importance in shaping foraging distributions remains poorly understood. Here we aimed to rank the contribution of density‐dependent and density‐independent effects on the spatio‐temporal foraging patterns of eurasian oystercatchers. In our intertidal study area, tides caused continuous variation in oystercatcher density, providing an opportunity to disentangle conspecific interference and density‐independent interactions with the food landscape. Spatial distributions were quantified using high‐resolution individual tracking of foraging activity and location. In a model environment that included a realistic reconstruction of both the tides and the benthic food, we tested a family of behaviour‐based optimality models against these tracking data. Density‐independent interactions affected spatial distributions much more strongly than conspecific interference, even in an interference‐prone species like oystercatchers. Spatial distributions were governed by avoidance of bill injury costs, selection for high interference‐free intake rates and a decreasing availability of benthic bivalve prey after their exposure. These density‐independent interactions outweighed interference competition in terms of effect size. We suggest that the bottleneck in our mechanistic understanding of foraging distributions may be primarily the role of density‐independent prey attributes unrelated to intake rates, like damage costs in the case of oystercatchers foraging on perilous prey. At a landscape scale, above the finest inter‐individual distances, effects of conspecific interaction on spatial distributions may have been overemphasised.