David J. Murrell

The evolution of density-dependent dispersal

Despite a large body of empirical evidence suggesting that the dispersal rates of many species depend on population density, most metapopulation models assume a density–independent rate of dispersal. Similarly, studies investigating the evolution of dispersal have concentrated almost exclusively on density–independent rates of dispersal. We develop a model that allows density–dependent dispersal strategies to evolve. Our results demonstrate that a density–dependent dispersal strategy almost always evolves and that the form of the relationship depends on reproductive rate, type of competition, size of subpopulation equilibrium densities and cost of dispersal. We suggest that future metapopulation models should account for density–dependent dispersal

POPULATION GROWTH IN SPACE AND TIME: SPATIAL LOGISTIC EQUATIONS

How great an effect does self-generated spatial structure have on logistic population growth? Results are described from an individual-based model (IBM) with spatially localized dispersal and competition, and from a deterministic approximation to the IBM describing the dynamics of the first and second spatial moments. The dynamical system incorporates a novel closure that gives a close approximation to the IBM in the presence of strong spatial structure. Population growth given by the spatial logistic model can differ greatly from that of the nonspatial logistic equation. Numerical simulations show that populations may grow more slowly or more rapidly than would be expected from the nonspatial model, and may reach their maximum rate of increase at densities other than half of the carrying capacity. Populations can achieve asymptotic densities substantially greater than or less than the carrying capacity of the nonspatial logistic model, and can even tend towards extinction. These properties of the spatial logistic model are caused by local dispersal and competition that affect spatial structure, which in turn affects population growth. Accounting for these local spatial processes brings the theory of single-species population growth a step closer to the growth of real spatially structured populations.

Local Spatial Structure and Predator-Prey Dynamics: Counterintuitive Effects of Prey Enrichment

The Lotka‐Volterra predator‐prey model with prey density dependence shows the final prey density to be independent of its vital rates. This result assumes the community to be well mixed so that encounters between predators and prey occur as a product of the landscape densities, yet empirical evidence suggests that over small spatial scales this may not be the normal pattern. Starting from an individual‐based model with neighborhood interactions and movements, a deterministic approximation is derived, and the effect of local spatial structure on equilibrium densities is investigated. Incorporating local movements and local interactions has important consequences for the community dynamics. Now the final prey density is very much dependent on its birth, death, and movement rates and in ways that seem counterintuitive. Increasing prey fecundity or mobility and decreasing the coefficient of competition can all lead to decreases in the final density of prey if the predator is also relatively immobile. However, analysis of the deterministic approximation makes the mechanism for these results clear; each of these changes subtly alters the emergent spatial structure, leading to an increase in the predator‐prey spatial covariance at short distances and hence to a higher predation pressure on the prey.

Frequency-dependent advantages of plasmid carriage by Pseudomonas in homogeneous and spatially structured environments

The conditions promoting the persistence of a plasmid carrying a trait that may be mutually beneficial to other cells in its vicinity were studied in structured and unstructured environments. A large plasmid encoding mercury resistance in Pseudomonas fluorescens was used, and the mercury concentration allowing invasion from rare for both plasmid-bearing and plasmid-free cells was determined for different initial inoculum densities in batch-culture structured (filter surface) and unstructured (mixed broth) environments. A range of mercury concentrations were found where both cell types could coexist, the regions being relatively similar in the two types of environment although density-dependent in the unstructured environment. The coexistence is explained in terms of frequency-dependent selection of the mutually beneficial mercury resistance trait, and the dynamics of bacterial growth under batch culture conditions. However, the region of coexistence was complicated by conjugation which increased plasmid spread in the mixed broth culture but not the structured environment.

Testing Spatial Theories of Plant Coexistence: No Consistent Differences in Intra- and Interspecific Interaction Distances

Plants stand still and interact with their immediate neighbors. Theory has shown that the distances over which these interactions occur may have important consequences for population and community dynamics. In particular, if intraspecific competition occurs over longer distances than interspecific competition (heteromyopia), coexistence can be promoted. We examined how intraspecific and interspecific competition scales with neighbor distance in a target‐neighbor greenhouse competition experiment. Individuals from co‐occurring forbs from calcareous grasslands were grown in isolation and with single conspecific or heterospecific neighbors at distances of 5, 10, or 15 cm (Plantago lanceolata vs. Plantago media and Hieracium pilosella vs. Prunella grandiflora). Neighbor effects were strong and declined with distance. Interaction distances varied greatly within and between species, but we found no evidence for heteromyopia. Instead, neighbor identity effects were mostly explained by relative size differences between target and neighbor. We found a complex interaction between final neighbor size and identity such that neighbor identity may become important only as the neighbor becomes very large compared with the target individual. Our results suggest that species‐specific size differences between neighboring individuals determine both the strength of competitive interactions and the distance over which these interactions occur.

Scaling up predator–prey dynamics using spatial moment equations

Summary Classical models of predator–prey dynamics, commonly used in community and evolutionary ecology to explain population cycles, species coexistence, the effects of enrichment, or predict the evolution of behavioural traits, are often based on the mass-action assumption. This means encounter rates between predators and prey are expressed as a product of predator and prey landscape densities; as if the system was well-mixed. While mass-action may occur at small spatial scales, spatial variances and covariances in prey and predator densities affect encounter rates at large spatial scales. In the context of host–parasitoid interactions, this has been incorporated into theory for some time, but for predators, well-mixed or other ad hoc models are often used despite empirical evidence for intricate spatial variation in predator and prey numbers. We review the classical models and concepts, their strengths and weaknesses, and we present two recent spatial moment approaches that scale up predator–prey population dynamics from the individual or patch level to large spatial scales. Both methods include descriptors of spatial structure as corrections to encounter rates, but differ in whether or not these descriptors have dynamics that are explicit functions of movements, births and deaths. We describe how these spatial moment techniques work, what new results they have so far produced, and provide some suggestions to improve the connection of predator–prey theoretical models to empirical studies.

Intraspecific aggregation and species coexistence

Our recent article in TREE [1xUniting pattern and process in plant ecology. Murrell, D.J. et al. Trends Ecol. Evol. 2001; 16: 529–530Abstract | Full Text | Full Text PDF | Scopus (69)See all References[1] was motivated by the lack of empirical information on the effect of spatial structure on competition. We thank Rejmanek [2xSee all References[2] for drawing attention to several further empirical studies.Chesson and Neuhauser [3xSee all References[3] create the impression that, in the absence of life-history tradeoffs, coexistence of competing species becomes less likely when spatial structure is considered. The basis for this is an analysis by Neuhauser and Pacala [4xAn explicitly spatial version of the Lotka–Volterra model with interspecific competition. Neuhauser, C. and Pacala, S.W. Ann. Appl. Prob. 1999; 9: 1226–1259CrossrefSee all References[4] that concluded that local interactions in a spatial version of the Lotka–Volterra competition model would reduce the parameter space of coexistence. We offer the following counterexample (model from [4xAn explicitly spatial version of the Lotka–Volterra model with interspecific competition. Neuhauser, C. and Pacala, S.W. Ann. Appl. Prob. 1999; 9: 1226–1259CrossrefSee all References[4] with small modifications) in which the spatial extension causes the coexistence of two species (Fig. 1Fig. 1).Fig. 1In the non-spatial Lotka–Volterra model (heavy solid and dashed lines), the strong competitor (red) drives the weak one (blue) to extinction. In the spatial model, by allowing interspecific interactions to occur over a shorter range than do the intraspecific interactions, the weaker competitor is able to coexist with its rival. This is shown both in a stochastic model (uneven lines) averaged over 40 realizations and also in a deterministic approximation based on moment dynamics (light solid and dashed lines). Apart from the weak and strong competition, the two species have the same parameter values.View Large Image | Download PowerPoint SlideIn this example, the first species is a stronger competitor and leads to extinction of the second in the nonspatial Lotka–Volterra system. But the distance over which interactions between species occur is shorter than that within species. This, together with the spatial segregation of the species, reduces the strength of interspecific competition sufficiently to permit either species to invade the other. We have not invoked a life-history tradeoff (e.g. the familiar competition–colonization tradeoff) to achieve coexistence here. Moreover, there is nothing intrinsic to coexistence here that says that it has to be due to niche differentiation. But, this is not to say that, if competition extends to conspecific neighbors that are more distant than heterospecifics, niche differentation is not a potential mechanism; different distances could, for instance, be caused by host-specific enemies that aggregate around parents (the Janzen–Connell hypothesis).That we get dynamics different from [4xAn explicitly spatial version of the Lotka–Volterra model with interspecific competition. Neuhauser, C. and Pacala, S.W. Ann. Appl. Prob. 1999; 9: 1226–1259CrossrefSee all References[4] is not surprising – the models have several different assumptions. Six extra functions are needed in the spatial version of the two-species Lotka–Volterra competition model to deal fully with local interactions and local dispersal, and each function has at least one parameter [5xA dynamical system for neighborhoods in plant communities. Law, R. and Dieckmann, U. Ecology. 2000; 81: 2137–2148See all References[5]. To make analysis tractable, theoreticians have had to use simplifying symmetries in the interactions; investigation of how the extended parameter space affects asymptotic and transient coexistence has barely begun.Coupling of spatial structure to population dynamics is intricate and it would be unwise to assume either that aggregation always leads to exclusion or the reverse. It is most likely that there are some conditions under which spatial structure promotes coexistence and others under which it does not: the former obviously deserve special attention.

The memory of spatial patterns: changes in local abundance and aggregation in a tropical forest

The current spatial pattern of a population is the result of previous individual birth, death, and dispersal events. We present a simple model followed by a comparative analysis for a species-rich plant community to show how the current spatial aggregation of a population may hold information about recent population dynamics. Previous research has shown how locally restricted seed dispersal often leads to stronger aggregation in less abundant populations than it does in more abundant populations. In contrast, little is known about how changes in the local abundance of a species may affect the spatial distribution of individuals. If the level of aggregation within a species depends to some extent on the abundance of the species, then changes in abundance should lead to subsequent changes in aggregation. However, an overall change of spatial pattern relies on many individual birth and death events, and a surplus of deaths or births may have short-term effects on aggregation that are opposite to the long-term change predicted by the change in abundance. The change in aggregation may therefore lag behind the change in abundance, and consequently, the current aggregation may hold information about recent population dynamics. Using an individual-based simulation model with local dispersal and density-dependent competition, we show that, on average, recently growing populations should be more aggregated than shrinking populations of the same current local abundance. We tested this hypothesis using spatial data on individuals from a long-term tropical rain forest plot, and find support for this relationship in canopy trees, but not in understory and shrub species. On this basis we argue that current spatial aggregation is an important characteristic that contains information on recent changes in local abundance, and may be applied to taxonomic groups where dispersal is limited and within-species aggregation is observed.

A SIMPLE EXPLANATION FOR UNIVERSAL SCALING RELATIONS IN FOOD WEBS

Much of the interest in food webs has been driven by a search for universal patterns that could indicate common organizing principles. In an approach that treats food webs as transportation networks (represented by minimum spanning trees) it was recently shown that food webs exhibit universal scaling relations, analogous to those found in river networks and vascular systems. It was concluded that this pattern is due to an optimization process acting in ecological communities. Here we construct minimum spanning trees using Monte Carlo simulations of a simple model that has two parameters that control the pro- portion of basal species and limit food-chain length, respectively. We show that when the food-chain length is of a similar size to that reported for real food webs, the universal scaling relations readily emerge in the model. This result is robust in a wide range of values for the proportion of basal species. We therefore conclude that the processes that limit food-chain length in ecological communities are sufficient to explain the observed universal scaling relations in food webs, and that complicated adaptive explanations are not required.

Intense or spatially heterogeneous predation can select against prey dispersal

Dispersal theory generally predicts kin competition, inbreeding, and temporal variation in habitat quality should select for dispersal, whereas spatial variation in habitat quality should select against dispersal. The effect of predation on the evolution of dispersal is currently not well-known: because predation can be variable in both space and time, it is not clear whether or when predation will promote dispersal within prey. Moreover, the evolution of prey dispersal affects strongly the encounter rate of predator and prey individuals, which greatly determines the ecological dynamics, and in turn changes the selection pressures for prey dispersal, in an eco-evolutionary feedback loop. When taken all together the effect of predation on prey dispersal is rather difficult to predict. We analyze a spatially explicit, individual-based predator-prey model and its mathematical approximation to investigate the evolution of prey dispersal. Competition and predation depend on local, rather than landscape-scale densities, and the spatial pattern of predation corresponds well to that of predators using restricted home ranges (e.g. central-place foragers). Analyses show the balance between the level of competition and predation pressure an individual is expected to experience determines whether prey should disperse or stay close to their parents and siblings, and more predation selects for less prey dispersal. Predators with smaller home ranges also select for less prey dispersal; more prey dispersal is favoured if predators have large home ranges, are very mobile, and/or are evenly distributed across the landscape.