Bet‐hedging as a complex interaction among developmental instability,environmental heterogeneity,dispersal, and life‐history strategy

One potential evolutionary response to environmental heterogeneity is the production of randomly variable offspring through developmental instability, a type of bet‐hedging. I used an individual‐based, genetically explicit model to examine the evolution of developmental instability. The model considered both temporal and spatial heterogeneity alone and in combination, the effect of migration pattern (stepping stone vs. island), and life‐history strategy. I confirmed that temporal heterogeneity alone requires a threshold amount of variation to select for a substantial amount of developmental instability. For spatial heterogeneity only, the response to selection on developmental instability depended on the life‐history strategy and the form and pattern of dispersal with the greatest response for island migration when selection occurred before dispersal. Both spatial and temporal variation alone select for similar amounts of instability, but in combination resulted in substantially more instability than either alone. Local adaptation traded off against bet‐hedging, but not in a simple linear fashion. I found higher‐order interactions between life‐history patterns, dispersal rates, dispersal patterns, and environmental heterogeneity that are not explainable by simple intuition. We need additional modeling efforts to understand these interactions and empirical tests that explicitly account for all of these factors.     

On a population pathogen model incorporating species dispersal with temporal variation in dispersal rate

In the present paper, we consider a mathematical model of ecosystem population interaction where the population suffers from a susceptible–infectious–susceptible disease. Dispersal of both the susceptible and the infective is incorporated using reaction–diffusion equations. We first study the stability criteria of the basic (non-spatial) model around the disease-free and the infected steady states. We find that the loss rate of the infective species controls disease prevalence. Also without predation pressure, the disease will continue to exist among the population. Then we analyze the spatial model with species dispersal in constant as well as in time-varying form. It is observed that though constant dispersal is unable to generate diffusion-driven instability, dispersal with sinusoidal variation in dispersion rate can generate diffusive instability when the wave number of the perturbation lies within a given range. Numerical simulations are performed to illustrate analytical studies.     

Effects of branching spatial structure and life history on the asymptotic growth rate of a population

The dendritic structure of a river network creates directional dispersal and a hierarchical arrangement of habitats. These two features have important consequences for the ecological dynamics of species living within the network. We apply matrix population models to a stage-structured population in a network of habitat patches connected in a dendritic arrangement. By considering a range of life histories and dispersal patterns, both constant in time and seasonal, we illustrate how spatial structure, directional dispersal, survival, and reproduction interact to determine population growth rate and distribution. We investigate the sensitivity of the asymptotic growth rate to the demographic parameters of the model, the system size, and the connections between the patches. Although some general patterns emerge, we find that a species’ modes of reproduction and dispersal are quite important in its response to changes in its life history parameters or in the spatial structure. The framework we use here can be customized to incorporate a wide range of demographic and dispersal scenarios.     

Evolutionarily stable consumer home range size in relation to resource demography and consumer spatial organization

There is a large variation in home range size within species, yet few models relate that variation to demographic and life-history traits. We derive an approximate deterministic population dynamics model keeping track of spatial structure, via spatial moment equations, from an individual-based spatial consumer-resource model; where space-use of consumers resembles that of central place foragers. Using invasion analyses, we investigate how the evolutionarily stable home range size of the consumer depends on a number of ecological and behavioral traits of both the resource and the consumer. We show that any trait variation leading to a decreased overall resource production or an increased spatial segregation between consumer and resource acts to increase consumer home range size. In this way, we extend theoretical predictions on optimal territory size to a larger range of ecological scenarios where home ranges overlap and population dynamics feedbacks are possible. Consideration of spatial traits such as dispersal distances also generates new results: (1) consumer home range size decreases with increased resource dispersal distance, and (2) when consumer agonistic behavior is weak, more philopatric consumers have larger home ranges. Finally, our results emphasize the role of the spatial correlation between consumer and resource distributions in determining home range size, and suggest resource dispersion is less important.     

Process from pattern in the distribution of an endangered leaf beetle

We investigated whether signals of known dispersal processes and habitat patch turnover could be detected in a snapshot of the distribution of the tansy leaf beetle Chrysolina graminis among patches of its host plant tansy Tanacetum vulgare . Beetle occupancy in 1305 patches was analysed using autologistic generalised additive models (GAMs). These model spatial autocorrelation with an autocovariate calculated as the distance-weighted rate of occupancy among neighbouring patches. The autocovariate that best explained beetle occupancy was one which represented the active search for patches during beetle dispersal, included a distance weight that closely matched a previously fitted dispersal kernel and had neighbourhood sizes encompassing ∼95% of known dispersal distances. Autocovariates distinguishing between neighbours on the same and opposite riverbanks outperformed those that did not, revealing the river as a barrier to dispersal. Differentiating between up and downstream autocorrelation did not improve model fit, as is consistent with the beetle's lack of directional bias in dispersal. Habitat connectivity (the extent to which it was surrounded by other patches) did not appear to affect beetle occupancy in the field, while positive effects were found for distributions simulated from the GAM. We argue that this reflects a non-equilibrium distribution driven by slow responses to high rates of habitat patch turnover due to limited dispersal ability. Our findings suggest that presence/absence snapshots can reveal patterns of dispersal and be used to test whether species' ranges are at equilibrium. Such information is important for effective conservation so the possibility of inferring these patterns from distribution data is an appealing one.     

Phase Transitions in a Logistic Metapopulation Model with Nonlocal Interactions

The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms causing such a phenomenon. We propose a single-species, continuous time metapopulation model taking nonlocal interactions into account. Discrete probability kernels are used to model these interactions in a patchy environment. A linear stability analysis of the model shows that solutions to this equation exhibit pattern formation if the dispersal rate of the species is sufficiently small and the discrete interaction kernel satisfies certain conditions. We numerically observe that traveling and stationary wave-type patterns arise near critical dispersal rate. We use weakly nonlinear analysis to better understand the behavior of formed patterns. We show that observed patterns arise through both supercritical and subcritical bifurcations from spatially homogeneous steady state. Moreover, we observe that as the dispersal rate decreases, amplitude of the patterns increases. For discontinuous transitions to instability, we also show that there exists a threshold for the amplitude of the initial condition, above which pattern formation is observed.     

General relationships between consumer dispersal,resource dispersal and metacommunity diversity

One of the central questions of metacommunity theory is how dispersal of organisms affects species diversity. Here, we show that the diversity–dispersal relationship should not be studied in isolation of other abiotic and biotic flows in the metacommunity. We study a mechanistic metacommunity model in which consumer species compete for an abiotic or biotic resource. We consider both consumer species specialised to a habitat patch, and generalist species capable of using the resource throughout the metacommunity. We present analytical results for different limiting values of consumer dispersal and resource dispersal, and complement these results with simulations for intermediate dispersal values. Our analysis reveals generic patterns for the combined effects of consumer and resource dispersal on the metacommunity diversity of consumer species, and shows that hump‐shaped relationships between local diversity and dispersal are not universal. Diversity–dispersal relationships can also be monotonically increasing or multimodal. Our work is a new step towards a general theory of metacommunity diversity integrating dispersal at multiple trophic levels.     

Linking rates of diffusion and consumption in relation to resources

The functional response is a fundamental model of the relationship between consumer intake rate and resource abundance. The random walk is a fundamental model of animal movement and is well approximated by simple diffusion. Both models are central to our understanding of numerous ecological processes but are rarely linked in ecological theory. To derive a synthetic model, we draw on the common logical premise underlying these models and show how the diffusion and consumption rates of consumers depend on elementary attributes of naturally occurring consumer-resource interactions: the abundance, spatial aggregation, and traveling speed of resources as well as consumer handling time and directional persistence. We show that resource aggregation may lead to increased consumer diffusion and, in the case of mobile resources, reduced consumption rate. Resource-dependent movement patterns have traditionally been attributed to area-restricted search, reflecting adaptive decision making by the consumer. Our synthesis provides a simple alternative hypothesis that such patterns could also arise as a by-product of statistical movement mechanics.     

Inferring Processes from Spatial Patterns: The Role of Directional and Non–Directional Forces in Shaping Fish Larvae Distribution in a Freshwater Lake System

Larval dispersal is a crucial factor for fish recruitment. For fishes with relatively small-bodied larvae, drift has the potential to play a more important role than active habitat selection in determining larval dispersal; therefore, we expect small-bodied fish larvae to be poorly associated with habitat characteristics. To test this hypothesis, we used as model yellow perch (Perca flavescens), whose larvae are among the smallest among freshwater temperate fishes. Thus, we analysed the habitat association of yellow perch larvae at multiple spatial scales in a large shallow fluvial lake by explicitly modelling directional (e.g. due to water currents) and non-directional (e.g. due to aggregation) spatial patterns. This allowed us to indirectly assess the relative roles of drift (directional process) and potential habitat choice on larval dispersal. Our results give weak support to the drift hypothesis, whereas yellow perch show a strong habitat association at unexpectedly small sizes, when compared to other systems. We found consistent non-directional patterns in larvae distributions at both broad and medium spatial scales but only few significant directional components. The environmental variables alone (e.g. vegetation) generally explained a significant and biologically relevant fraction of the variation in fish larvae distribution data. These results suggest that (i) drift plays a minor role in this shallow system, (ii) larvae display spatial patterns that only partially covary with environmental variables, and (iii) larvae are associated to specific habitats. By suggesting that habitat association potentially includes an active choice component for yellow perch larvae, our results shed new light on the ecology of freshwater fish larvae and should help in building more realistic recruitment models.     

Pattern analysis of eastern spruce budworm Choristoneura fumiferana dispersal

Dispersal has been proposed as an important mechanism in the broad‐scale synchronisation of insect outbreaks by linking spatially disjunct populations. Evidence suggests that dispersal is influenced by landscape structure, phenology, temperature, and air currents; however, the details remain unclear due to the difficulty of quantifying dispersal. In this study, we used data on the abundance and distribution of spruce budworm Choristoneura fumiferana larvae (potential dispersers) and adult male moths (dispersers) to make inference on the effects of air currents and host‐species abundance on dispersal. Hierarchical‐Bayesian and inverse modeling was used to explore 4 dispersal models: 1) isotropic dispersal; 2) directional‐dispersal; 3) directional‐and‐host‐species dispersal; and 4) host‐species dispersal. Despite their strong dependence on balsam fir Abies balsamea and spruce species Picea spp., the mapped basal area of these host species did not influence the pattern of dispersed moths. The model that best fit the data was the directional‐dispersal model, which showed that the prevailing dispersal direction was from the northwest (328°). We infer that the strong pattern of directional dispersal was due to a prevailing wind from the same direction. Our interpretation was corroborated by independent wind data during the period of active adult male budworm flight, particularly in the region with high larval abundance. Our results indicate that there was a relatively high probability of individuals flying at least 48 km with the wind where larvae abundance at source locations was also high. Such findings emphasize the importance of long‐distance dispersal on spatial distribution of adult male spruce budworms. Insight into the population‐level consequences of such dispersal patterns requires additional research.     

Nonrandom larval dispersal can steepen marine clines

Sharp and stable clinal variation is enigmatic when found in species with high gene flow. Classical population genetic models treat gene flow as a random homogenizing force countering local adaptation across habitat discontinuities. Under this view, dispersal over large spatial scales will lower the effectiveness of adaptation by natural selection at finer spatial scales. Thus, random gene flow will create a shallow phenotypic cline across an ecotone in response to a steep selection gradient. In sedentary marine species that disperse primarily as larvae, nonrandom dispersal patterns are expected due to coastal hydrodynamics. Surprisingly sharp phenotypic and genotypic clines have been documented in marine species with high gene flow. We are interested in the extent to which nonrandom dispersal could accentuate such clines. We model a linear species range in which populations have stable and uniform densities along a selection gradient; in contrast to random dispersal, convergent advection of larvae can amplify phenotypic differentiation if coupled with a semipermeable dispersal barrier in the convergence zone. The migration load caused by directional dispersal pushes the phenotypic mean away from the local trait optimum in downstream populations, that is, near the convergence zone. A dispersal barrier is possible as a result of colliding currents if the water and larvae are mostly displaced offshore, away from suitable settlement habitat. Disjunctions in a quantitative trait were enlarged in the convergence zone by faster current flows or a more complete dispersal barrier. With advection of larvae per generation one-third as far as the average dispersal distance by diffusion, convergence on a dispersal barrier with 40% permeability generated a trait disjunction across the convergence zone of two phenotypic standard deviations. Without directional dispersal, similar clines also developed across a habitat gap, where population density was low, or across dispersal barriers with less than 1% permeability. These findings suggest that the types of hydrographic phenomena often associated with marine transition zones can strongly affect the balance between gene flow and selection and generate surprisingly steep clines given the large-scale gene flow expected from larvae.     

Spatial patterns and coexistence mechanisms in systems with unidirectional flow

River ecosystems are the prime example of environments where unidirectional flow influences the dispersal of individuals. Spatial patterns of community composition and species replacement emerge from complex interplays of hydrological, geochemical, biological, and ecological factors. Local processes affecting algal dynamics are well understood, but a mechanistic basis for large scale emerging patterns is lacking. To understand how these patterns could emerge in rivers, we analyze a reaction-advection-diffusion model for two competitors in heterogeneous environments. The model supports waves that invade upstream up to a well-defined "upstream invasion limit". We discuss how these waves are produced and present their key properties. We suggest that patterns of species replacement and coexistence along spatial axes reflect stalled waves, produced from diffusion, advection, and species interactions. Emergent spatial scales are plausible given parameter estimates for periphyton. Our results apply to other systems with unidirectional flow such as prevailing winds or climate-change scenarios.     

Synchronization in ecological systems by weak dispersal coupling with time delay

One of the most salient spatiotemporal patterns in population ecology is the synchronization of fluctuating local populations across vast spatial extent. Synchronization of abundance has been widely observed across a range of spatial scales in relation to the rate of dispersal among discrete populations. However, the dependence of synchrony on patterns of among-patch movement across heterogeneous landscapes has been largely ignored. Here, we consider the duration of movement between two predator–prey communities connected by weak dispersal and its effect on population synchrony. More specifically, we introduce time-delayed dispersal to incorporate the finite transmission time between discrete populations across a continuous landscape. Reducing the system to a phase model using weakly connected network theory, it is found that the time delay is an important factor determining the nature and stability of phase-locked states. Our analysis predicts enhanced convergence to stable synchronous fluctuations in general and a decreased ability of systems to produce in-phase synchronization dynamics in the presence of delayed dispersal. These results introduce delayed dispersal as a tool for understanding the importance of dispersal time across a landscape matrix in affecting metacommunity dynamics. They further highlight the importance of landscape and dispersal patterns for predicting the onset of synchrony between weakly coupled populations.     

Wind dispersal results in a gradient of dispersal limitation and environmental match among discrete aquatic habitats

Directional dispersal by wind and other dispersal agents may generate spatial patterns in passively dispersing metacommunities which cannot be detected by classical eigenvector methods based on Euclidean distances. We analysed zooplankton communities (Rotifera, Cladocera, Copepoda) in a cluster of soda pans distributed over a short spatial scale of 18 km and tested explicitly for directional signals in their spatial configuration. The study area is exposed to a prevailing northwestern wind direction. By applying asymmetric eigenvector maps (AEM), we were able to identify corresponding directionality in the spatial structure of communities. Furthermore, the match between community composition and environmental conditions exhibited a spatial pattern consistent with the prevailing wind corridor, with best match found downwind the dominant wind direction. We also found that classical eigenvector methods based on Euclidean distances underestimated the role of spatial processes in our data. Our study furthermore shows that dispersal limitation may constrain community assembly in highly mobile organisms even at spatial scales below 5 km.     

Does spatial heterogeneity blur the signature of dispersal syndromes on spatial patterns of woody species? A test in a tropical dry forest

Spatial patterns of adult plants are a consequence of several ecological processes related to seed dispersal and recruitment. Dispersal limitation, mediated by dispersal syndrome, is considered a key factor in the formation of adult plant spatial patterns. Although this initial pattern determined by dispersal has been thoroughly studied, the subsequently modification by the effect of additional ecological factors, such as habitat heterogeneity is less understood. We explored the relative importance of dispersal syndrome and spatial heterogeneity on the realization of spatial patterns of adult trees in an Ecuadorian tropical dry forest. The spatial distribution of 28 species was modeled with four different spatial point processes each: homogeneous Poisson (HPP), inhomogeneous Poisson (IPP), homogeneous Poisson cluster (HPCP), and inhomogeneous Poisson cluster process (IPCP). These models allowed us to discern between effects of random processes, habitat heterogeneity, limited dispersal, and joint effects of habitat heterogeneity and limited dispersal. We employed Akaike's information criterion (AIC) to select the model which best fit the spatial pattern of each species. The best model of each species was used to analyze differences in cluster size and degree of aggregation, between dispersal syndromes. Seventy‐five percent of the species showed inhomogeneous patterns. IPCP yielded the best fit for the spatial distribution of 50% of species in the studied forest and was the prevalent model for the three dispersal syndromes. Thus, the effect of spatial heterogeneity was prevalent in the distribution of most species in this dry tropical forest. Only 21% of species had spatial patterns compatible with random mechanisms associated to limited dispersal around parent sources. Clearly, ignoring habitat heterogeneity could bias the analysis of relationships between dispersal syndrome and species patterns.     

Evolution of dispersal in a multi‐trophic community context

Much is known about the evolution of dispersal when species interact with their resources or natural enemies, but very little is known about dispersal evolution when species interact with both resources and natural enemies. Here I investigate how the dispersal of an intermediate consumer evolves in response to its interactions with a basal resource and top predator. I find that dispersal evolution is possible even when the consumer species is not directly affected by environmental variability, but rather experiences the consequences that such variability has on its resource and predator. Spatial variation in the consumer's fitness is driven by spatial heterogeneity in resource productivity, which determines whether a predator can colonize a resource‐consumer community. Temporal variation in the consumer's fitness is driven by random disturbances that cause periodic local extinctions of the predator, followed by recolonizations that lead to transient fluctuations in consumer abundance. When spatial variation in resource productivity is low and the predator can colonize all patches in the landscape, there is no spatial variation in consumer fitness but temporal variation in fitness favors the evolution of a dispersal monomorphism. When spatial variation in resource productivity is high and the predator cannot colonize many patches in the landscape, spatial variation in fitness selects against dispersal. In this case, temporal variation can promote the evolution of a dispersal polymorphism with sedentary and mobile phenotypes, but only for certain types of tri‐trophic interactions. This finding underscores the importance of indirect interactions in shaping the evolution of dispersal. While the ecological community can provide a strong selective environment for the evolution of dispersal, the nature of interactions between trophic levels can also impose constraints on evolution.     

Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity

Abstract In the presence of permanent spatial heterogeneity, local dispersal, especially short‐range dispersal, can facilitate coexistence by concentrating low‐density species in the areas where their rates of increase are higher. We present a framework for predicting the effects of local dispersal on coexistence for arbitrary forms of dispersal and arbitrary spatial patterns of environmental variation. Using the lottery model as an example, we find that local dispersal contributes to coexistence by enhancing the effects of environmental variation on scales longer than typical dispersal distances, which can be characterized solely by the variance of the dispersal kernel. Higher moments of the dispersal kernel are not important.     

Spatial processes and evolutionary models: a critical review

Evolution is a fundamentally population level process in which variation, drift and selection produce both temporal and spatial patterns of change. Statistical model fitting is now commonly used to estimate which kind of evolutionary process best explains patterns of change through time using models like Brownian motion, stabilizing selection (Ornstein–Uhlenbeck) and directional selection on traits measured from stratigraphic sequences or on phylogenetic trees. But these models assume that the traits possessed by a species are homogeneous. Spatial processes such as dispersal, gene flow and geographical range changes can produce patterns of trait evolution that do not fit the expectations of standard models, even when evolution at the local‐population level is governed by drift or a typical OU model of selection. The basic properties of population level processes (variation, drift, selection and population size) are reviewed and the relationship between their spatial and temporal dynamics is discussed. Typical evolutionary models used in palaeontology incorporate the temporal component of these dynamics, but not the spatial. Range expansions and contractions introduce rate variability into drift processes, range expansion under a drift model can drive directional change in trait evolution, and spatial selection gradients can create spatial variation in traits that can produce long‐term directional trends and punctuation events depending on the balance between selection strength, gene flow, extirpation probability and model of speciation. Using computational modelling that spatial processes can create evolutionary outcomes that depart from basic population‐level notions from these standard macroevolutionary models.     

The role of environmental and spatial processes in structuring native and non‐native fish communities across thousands of lakes

Quantifying the role of spatial patterns is an important goal in ecology to further understand patterns of community composition. We quantified the relative role of environmental conditions and regional spatial patterns that could be produced by environmental filtering and dispersal limitation on fish community composition for thousands of lakes. A database was assembled on fish community composition, lake morphology, water quality, climatic conditions, and hydrological connectivity for 9885 lakes in Ontario, Canada. We utilized a variation partitioning approach in conjunction with Moran's Eigenvector Maps (MEM) and Asymmetric Eigenvector Maps (AEM) to model spatial patterns that could be produced by human‐mediated and natural modes of dispersal. Across 9885 lakes and 100 fish species, environmental factors and spatial structure explained approximately 19% of the variation in fish community composition. Examining the proportional role of spatial structure and environmental conditions revealed that as much as 90% of the explained variation in native species assemblage composition is governed by environmental conditions. Conversely on average, 67% of the explained variation in non‐native assemblage composition can be related to human‐mediated dispersal. This study highlights the importance of including spatial structure and environmental conditions when explaining patterns of community composition to better discriminate between the ecological processes that underlie biogeographical patterns of communities composed of native and non‐native fish species.