Emergent Allee effects in top predators feeding on structured prey populations

Top predators that forage in a purely exploitative manner on smaller stages of a size-structured prey population have been shown to exhibit an Allee effect. This Allee effect emerges from the changes that predators induce in the prey-population size distribution and represents a feedback of predator density on its own performance, in which the feedback operates through and is modified by the life history of the prey. We demonstrate that these emergent Allee effects will occur only if the prey, in the absence of predators, is regulated by density dependence in development through one of its juvenile stages, as opposed to regulation through adult fecundity. In particular, for an emergent Allee effect to occur, over-compensation is required in the maturation rate out of the regulating juvenile stage, such that a decrease in juvenile density will increase the total maturation rate to larger/older stages. If this condition is satisfied, predators with negative size selection, which forage on small prey, exhibit an emergent Allee effect, as do predators with positive size selection, which forage on large adult prey. By contrast, predators that forage on juveniles in the regulating stage never exhibit emergent Allee effects. We conclude that the basic life-history characteristics of many species make them prone to exhibiting emergent Allee effects, resulting in an increased likelihood that communities possess alternative stable states or exhibit catastrophic shifts in structure and dynamics.     

Self-organized dynamics in spatially structured populations

Self-organization and pattern formation represent the emergence of order in temporal and spatial processes. Self-organization in population ecology is gaining attention due to the recent advances concerning temporal fluctuations in the population size of dispersal-linked subunits. We shall report that spatially structured models of population renewal promote the emergence of a complex power law order in spatial population dynamics. We analyse a variety of population models showing that self-organization can be identified as a temporal match in population dynamics among local units, and how the synchrony changes in time. Our theoretical results are concordant with analyses of population data on the Canada lynx.     

Allee effects in stochastic populations

The Allee effect, or inverse density dependence at low population sizes, could seriously impact preservation and management of biological populations. The mounting evidence for widespread Allee effects has lately inspired theoretical studies of how Allee effects alter population dynamics. However, the recent mathematical models of Allee effects have been missing another important force prevalent at low population sizes: stochasticity. In this paper, the combination of Allee effects and stochasticity is studied using diffusion processes, a type of general stochastic population model that accommodates both demographic and environmental stochastic fluctuations. Including an Allee effect in a conventional deterministic population model typically produces an unstable equilibrium at a low population size, a critical population level below which extinction is certain. In a stochastic version of such a model, the probability of reaching a lower size a before reaching an upper size b , when considered as a function of initial population size, has an inflection point at the underlying deterministic unstable equilibrium. The inflection point represents a threshold in the probabilistic prospects for the population and is independent of the type of stochastic fluctuations in the model. In particular, models containing demographic noise alone (absent Allee effects) do not display this threshold behavior, even though demographic noise is considered an "extinction vortex". The results in this paper provide a new understanding of the interplay of stochastic and deterministic forces in ecological populations.     

Host resistance and coevolution in spatially structured populations

Natural, agricultural and human populations are structured, with a proportion of interactions occurring locally or within social groups rather than at random. This within-population spatial and social structure is important to the evolution of parasites but little attention has been paid to how spatial structure affects the evolution of host resistance, and as a consequence the coevolutionary outcome. We examine the evolution of resistance across a range of mixing patterns using an approximate mathematical model and stochastic simulations. As reproduction becomes increasingly local, hosts are always selected to increase resistance. More localized transmission also selects for higher resistance, but only if reproduction is also predominantly local. If the hosts disperse, lower resistance evolves as transmission becomes more local. These effects can be understood as a combination of genetic (kin) and ecological structuring on individual fitness. When hosts and parasites coevolve, local interactions select for hosts with high defence and parasites with low transmissibility and virulence. Crucially, this means that more population mixing may lead to the evolution of both fast-transmitting highly virulent parasites and reduced resistance in the host.     

Allee effects and resilience in stochastic populations

Allee effects, or positive functional relationships between a population’s density (or size) and its per unit abundance growth rate, are now considered to be a widespread if not common influence on the growth of ecological populations. Here we analyze how stochasticity and Allee effects combine to impact population persistence. We compare the deterministic and stochastic properties of four models: a logistic model (without Allee effects), and three versions of the original model of Allee effects proposed by Vito Volterra representing a weak Allee effect, a strong Allee effect, and a strong Allee effect with immigration. We employ the diffusion process approach for modeling single-species populations, and we focus on the properties of stationary distributions and of the mean first passage times. We show that stochasticity amplifies the risks arising from Allee effects, mainly by prolonging the amount of time a population spends at low abundance levels. Even weak Allee effects become consequential when the ubiquitous stochastic forces affecting natural populations are accounted for in population models. Although current concepts of ecological resilience are bound up in the properties of deterministic basins of attraction, a complete understanding of alternative stable states in ecological systems must include stochasticity.     

Searching for mechanisms of synchrony in spatially structured gamebird populations

1.  Time series data on five species of gamebird from the Dolomitic Alps were used to examine the relative importance of dispersal and common stochastic events in causing synchrony between spatially structured populations.
2.  Cross-correlation analysis of detrended time series was used to describe the spatial pattern of fluctuations in abundance, while standardized time series were used to describe both fluctuations and the trend in abundance. There were large variations in synchrony both within and between species and only weak negative relationships with distance.
3.  Species in neighbouring habitats were more likely to be in synchrony than species separated by several habitats. Species with similar density-dependent structure were more likely to be in synchrony.
4.  In order to estimate the relative importance of dispersal and environmental stochasticity, we modelled the spatial dynamics of each species using two different approaches. First, we used estimating functions and bootstrapping of time series data to calculate the relative importance of dispersal and stochastic effects for each species. Second, we estimated the intensity of environmental stochasticity from climatic records during the breeding season and then modelled the dispersal rate and dispersal distance for each species. The two models exhibited similar results for rock ptarmigan, black grouse, hazel grouse and rock partridge, while contrasting patterns were observed for capercaillie.
5.  The results suggest that environmental stochasticity plays the dominant role in synchronizing the fluctuations of these galliform species, although there will also be some dispersal between populations.     

Evolutionary dynamics of rhizopine within spatially structured rhizobium populations

Symbiosis between legumes and nitrogen-fixing bacteria is thought to bring mutual benefit to each participant. However, it is not known how rhizobia benefit from nodulating legume hosts because they fix nitrogen only after becoming bacteroids, which are terminally differentiated cells that cannot reproduce. Because undifferentiated rhizobia in and around the nodule can reproduce, evolution of symbiotic nitrogen fixation may depend upon kin selection. In some hosts, these kin may persist in the nodule as viable, undifferentiated bacteria. In other hosts, no viable rhizobia survive to reproduce after nodule senescence. Bacteroids in these hosts may benefit their free-living kin by enhancing production of plant root exudates. However, unrelated non-mutualists may also benefit from increased plant exudates. Rhizopines, compounds produced by bacteroids in nodules and catabolized only by related free-living rhizobia, may provide a mechanism by which bacteroids can preferentially benefit kin. Despite this apparent advantage, rhizopine genotypes are relatively rare. We constructed a mathematical model to examine how mixing within rhizobium populations influences the evolution of rhizopine genotypes. Our model predicts that the success of rhizopine genotypes is strongly dependent upon the spatial genetic structure of the bacterial population; rhizopine is more likely to dominate well-mixed populations. Further, for a given level of mixing, we find that rhizopine evolves under a positive frequency-dependent process in which stochastic accumulation of rhizopine alleles is necessary for rhizopine establishment. This process leads to increased spatial structure in rhizobium populations, and suggests that rhizopine may expand the conditions under which nitrogen fixation can evolve via kin selection.     

A phenomenological theory of spatially structured local synaptic connectivity

The structure of local synaptic circuits is the key to understanding cortical function and how neuronal functional modules such as cortical columns are formed. The central problem in deciphering cortical microcircuits is the quantification of synaptic connectivity between neuron pairs. I present a theoretical model that accounts for the axon and dendrite morphologies of pre- and postsynaptic cells and provides the average number of synaptic contacts formed between them as a function of their relative locations in three-dimensional space. An important aspect of the current approach is the representation of a complex structure of an axonal/dendritic arbor as a superposition of basic structures—synaptic clouds. Each cloud has three structural parameters that can be directly estimated from two-dimensional drawings of the underlying arbor. Using empirical data available in literature, I applied this theory to three morphologically different types of cell pairs. I found that, within a wide range of cell separations, the theory is in very good agreement with empirical data on (i) axonal–dendritic contacts of pyramidal cells and (ii) somatic synapses formed by the axons of inhibitory interneurons. Since for many types of neurons plane arborization drawings are available from literature, this theory can provide a practical means for quantitatively deriving local synaptic circuits based on the actual observed densities of specific types of neurons and their morphologies. It can also have significant implications for computational models of cortical networks by making it possible to wire up simulated neural networks in a realistic fashion.     

Invasion and adaptive evolution for individual-based spatially structured populations

The interplay between space and evolution is an important issue in population dynamics, that is particularly crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution are closely related. Here, we model the interplay between space and evolution starting with an individual-based approach and show the important role of parameter scalings on clustering and invasion. We consider a stochastic discrete model with birth, death, competition, mutation and spatial diffusion, where all the parameters may depend both on the position and on the phenotypic trait of individuals. The spatial motion is driven by a reflected diffusion in a bounded domain. The interaction is modelled as a trait competition between individuals within a given spatial interaction range. First, we give an algorithmic construction of the process. Next, we obtain large population approximations, as weak solutions of nonlinear reaction–diffusion equations. As the spatial interaction range is fixed, the nonlinearity is nonlocal. Then, we make the interaction range decrease to zero and prove the convergence to spatially localized nonlinear reaction–diffusion equations. Finally, a discussion of three concrete examples is proposed, based on simulations of the microscopic individual-based model. These examples illustrate the strong effects of the spatial interaction range on the emergence of spatial and phenotypic diversity (clustering and polymorphism) and on the interplay between invasion and evolution. The simulations focus on the qualitative differences between local and nonlocal interactions.      

The evolution of disease resistance and tolerance in spatially structured populations

THE UBIQUITOUS CHALLENGE FROM INFECTIOUS DISEASE HAS PROMPTED THE EVOLUTION OF DIVERSE HOST DEFENSES, WHICH CAN BE DIVIDED INTO TWO BROAD CLASSES: resistance (which limits pathogen growth and infection) and tolerance (which does not limit infection, but instead reduces or offsets its negative fitness consequences). Resistance and tolerance may provide equivalent short-term benefits, but have fundamentally different epidemiological consequences and thus exhibit different evolutionary behaviors. We consider the evolution of resistance and tolerance in a spatially structured population using a stochastic simulation model. We show that tolerance can invade a population of susceptible individuals (i.e., neither resistant nor tolerant) with higher cost than resistance, even though they each provide equivalent direct benefits to the host, because tolerant hosts impose higher disease burden upon vulnerable competitors. However, in spatially structured settings, tolerance can invade a population of resistant hosts only with lower cost than resistance due to spatial genetic structure and the higher local incidence of disease around invading tolerant individuals. The evolution of tolerance is therefore constrained by spatial genetic structure in a manner not previously revealed by nonspatially explicit models, suggesting mechanisms that could maintain variation or limit the occurrence of tolerance relative to resistance.     

Sources of stochasticity in models of sex allocation in spatially structured populations

There are many ways to include stochastic effects in models of sex allocation evolution. These include variability in the number of mating partners and fecundity in a rich literature that goes back 20 years. The effects of variance in the fecundity and number of mating partners have typically been considered separately from the stochastic effects of mortality. However, I show that these processes produce mathematically equivalent models with subtly different biological details. These scenarios differ in the way that information becomes available to individuals because the parents often have information on mating partners while they are making sex allocation decisions, but must make these decisions before brood mortality takes place. This makes it possible to test which mechanism, stochastic mortality or variation in mating partners, is responsible for observed sex ratios. Alternatively, asymmetric variance between sexual functions can cause skewed sex allocation, even in the absence of local mate competition. This allows the evolution of either female- or male-biased sex ratios depending on which sexual function is more variable.     

Compositional divergence and convergence in local communities and spatially structured landscapes

Community structure depends on both deterministic and stochastic processes. However, patterns of community dissimilarity (e.g. difference in species composition) are difficult to interpret in terms of the relative roles of these processes. Local communities can be more dissimilar (divergence) than, less dissimilar (convergence) than, or as dissimilar as a hypothetical control based on either null or neutral models. However, several mechanisms may result in the same pattern, or act concurrently to generate a pattern, and much research has recently been focusing on unravelling these mechanisms and their relative contributions. Using a simulation approach, we addressed the effect of a complex but realistic spatial structure in the distribution of the niche axis and we analysed patterns of species co-occurrence and beta diversity as measured by dissimilarity indices (e.g. Jaccard index) using either expectations under a null model or neutral dynamics (i.e., based on switching off the niche effect). The strength of niche processes, dispersal, and environmental noise strongly interacted so that niche-driven dynamics may result in local communities that either diverge or converge depending on the combination of these factors. Thus, a fundamental result is that, in real systems, interacting processes of community assembly can be disentangled only by measuring traits such as niche breadth and dispersal. The ability to detect the signal of the niche was also dependent on the spatial resolution of the sampling strategy, which must account for the multiple scale spatial patterns in the niche axis. Notably, some of the patterns we observed correspond to patterns of community dissimilarities previously observed in the field and suggest mechanistic explanations for them or the data required to solve them. Our framework offers a synthesis of the patterns of community dissimilarity produced by the interaction of deterministic and stochastic determinants of community assembly in a spatially explicit and complex context.     

Habitat selection reduces extinction of populations subject to Allee effects

Theoretical studies indicate that a single population under an Allee effect will decline to extinction if reduced below a particular threshold, but the existence of multiple local populations connected by random dispersal improves persistence of the global population. An additional process that can facilitate persistence is the existence of habitat selection by dispersers. Using analytic and simulation models of population change, I found that when habitat patches exhibiting Allee effects are connected by dispersing individuals, habitat selection by these dispersers increases the likelihood that patches persist at high densities, relative to results expected by random settlement. Populations exhibiting habitat selection also attain equilibrium more quickly than randomly dispersing populations. These effects are particularly important when Allee effects are large and more than two patches exist. Integrating habitat selection into population dynamics may help address why some studies have failed to find extinction thresholds in populations, despite well-known Allee effects in many species.     

On indirect genetic effects in structured populations

Indirect genetic effects (IGEs) occur when the phenotype of an individual, and possibly its fitness, depends, at least in part, on the genes of its social partners. The effective result is that environmental sources of phenotypic variance can themselves evolve. Simple models have shown that IGEs can alter the rate and direction of evolution for traits involved in interactions. Here we expand the applicability of the theory of IGEs to evolution in metapopulations by including nonlinear interactions between individuals and population genetic structure. Although population subdivision alone generates some dramatic and nonintuitive evolutionary dynamics for interacting phenotypes, the combination of nonlinear interactions with subdivision reveals an even greater importance of IGEs. The presence of genetic structure links the evolution of interacting phenotypes and the traits that influence their expression ("effector traits") even in the absence of genetic correlations. When nonlinear social effects occur in subdivided populations, evolutionary response is altered and can even oppose the direction expected due to direct selection. Because population genetic structure allows for multilevel selection, we also investigate the role of IGEs in determining the response to individual and group selection. We find that nonlinear social effects can cause interference between levels of selection even when they act in the same direction. In some cases, interference can be so extreme that the actual evolutionary response to multilevel selection is opposite in direction to that predicted by summing selection at each level. This theoretical result confirms empirical data that show higher levels of selection cannot be ignored even when selection acts in the same direction at all levels.     

The spread of infectious diseases in spatially structured populations: an invasory pair approximation

The invasion of new species and the spread of emergent infectious diseases in spatially structured populations has stimulated the study of explicit spatial models such as cellular automata, network models and lattice models. However, the analytic intractability of these models calls for the development of tractable mathematical approximations that can capture the dynamics of discrete, spatially-structured populations. Here we explore moment closure approximations for the invasion of an SIS epidemic on a regular lattice. We use moment closure methods to derive an expression for the basic reproductive number, R(0), in a lattice population. On lattices, R(0) should be bounded above by the number of neighbors per individual. However, we show that conventional pair approximations actually predict unbounded growth in R(0) with increasing transmission rates. To correct this problem, we propose an 'invasory' pair approximation which yields a relatively simple expression for R(0) that remains bounded above, and also predicts R(0) values from lattice model simulations more accurately than conventional pair and triple approximations. The invasory pair approximation is applicable to any spatial model, since it takes into account characteristics of invasions that are common to all spatially structured populations.     

Personality-dependent dispersal: characterization, ontogeny and consequences for spatially structured populations

Dispersal is one of the most fundamental components of ecology, and affects processes as diverse as population growth, metapopulation dynamics, gene flow and adaptation. Although the act of moving from one habitat to another entails major costs to the disperser, empirical and theoretical studies suggest that these costs can be reduced by having morphological, physiological or behavioural specializations for dispersal. A few recent studies on different systems showed that individuals exhibit personality-dependent dispersal, meaning that dispersal tendency is associated with boldness, sociability or aggressiveness. Indeed, in several species, dispersers not only develop behavioural differences at the onset of dispersal, but display these behavioural characteristics through their life cycle. While personality-dependent dispersal has been demonstrated in only a few species, we believe that it is a widespread phenomenon with important ecological consequences. Here, we review the evidence for behavioural differences between dispersers and residents, to what extent they constitute personalities. We also examine how a link between personality traits and dispersal behaviours can be produced and how personality-dependent dispersal affects the dynamics of metapopulations and biological invasions. Finally, we suggest future research directions for population biologists, behavioural ecologists and conservation biologists such as how the direction and the strength of the relationship between personality traits and dispersal vary with ecological contexts.     

Evolution of dispersal polymorphism and local adaptation of dispersal distance in spatially structured landscapes

Many organisms show polymorphism in dispersal distance strategies. This variation is particularly ecological relevant if it encompasses a functional separation of short‐ (SDD) and long‐distance dispersal (LDD). It remains, however, an open question whether both parts of the dispersal kernel are similarly affected by landscape related selection pressures. We implemented an individual‐based model to analyze the evolution of dispersal traits in fractal landscapes that vary in the proportion of habitat and its spatial configuration. Individuals are parthenogenetic with dispersal distance determined by two alleles on each individual's genome: one allele coding for the probability of global dispersal and one allele coding for the variance σ of a Gaussian local dispersal with mean value zero. Simulations show that mean distances of local dispersal and the probability of global dispersal, increase with increasing habitat availability, but that changes in the habitat's spatial autocorrelation impose opposing selective pressure: local dispersal distances decrease and global dispersal probabilities increase with decreasing spatial autocorrelation of the available habitat. Local adaptation of local dispersal distance emerges in landscapes with less than 70% of clumped habitat. These results demonstrate that long and short distance dispersal evolve separately according to different properties of the landscape. The landscape structure may consequently largely affect the evolution of dispersal distance strategies and the level of dispersal polymorphism.     

The genetic structure of populations of Metrioptera bicolor in a spatially structured landscape: effects of dispersal barriers and geographic distance

The stability and long-term survival of animal populations in fragmented landscapes largely depends on the colonisation of habitat patches and the exchange of individuals between patches. The degree of inter-patch dispersal, in turn, depends on the dispersal abilities of species and the landscape structure (i.e. the nature of the landscape matrix and habitat distribution). Here, we investigated the genetic structure of populations of Metrioptera bicolor, a wing-dimorphic bush cricket, in a spatially structured landscape with patches of suitable habitat distributed within a diverse matrix of different habitat types. Using six microsatellite markers, we assessed the effects of geographic distance and different matrix types on the extent of genetic differentiation among 24 sampling sites. We found that forest and a river running through the study area both impede inter-patch dispersal. The presence of these two matrix types was positively correlated with the extent of genetic differentiation between sites. In addition, we found a significant positive correlation between pairwise genetic and geographic distances for a subsample of sites which were separated only by arable land or settlements. For the complete data set, this correlation could not be found. This is most probably because the adverse effect of forest and river on gene flow dominates the effect of geographic distance in our limited set of patches. Our analyses clearly emphasize the differential resistance of different habitat types on dispersal and the importance of a more detailed view on matrix “quality” in metapopulation studies.     

Ascertainment bias in spatially structured populations: a case study in the eastern fence lizard

Despite increased interest in applying single nucleotide polymorphism (SNP) data to questions in natural systems, one unresolved issue is to what extent the ascertainment bias induced during the SNP discovery phase will impact available analysis methods. Although most studies addressing ascertainment bias have focused on human populations, it is not clear whether existing methods will work when applied to other species with more complex demographic histories and more significant levels of population structure. Here we present findings from an empirical approach to exploring the effect of population structure on issues of ascertainment bias in the Eastern Fence Lizard, Sceloporus undulatus. We find that frequency spectra and summary statistics were highly sensitive to SNP discovery strategy, necessitating careful selection of the initial ascertainment panel. Randomly selected ascertainment panels performed equally well as ascertainment panels chosen to jointly sample geographic, phenotypic, and genetic diversity. Geographically restricted panels resulted in larger biases. Additionally, we found existing ascertainment bias correction methods, which were not developed for geographically structured data sets, were largely effective at reducing the impact of ascertainment bias. Because bias correction methods performed well even when underlying assumptions were violated, our results suggest tools are currently available to analyze SNP data in structured populations.