Competition between near and far dispersers in spatially structured habitats

Competitive interactions and invasibility between short- and long-distance dispersal was investigated in a population on a heterogeneous landscape with spatial correlations in habitat types, and where the driving interaction between individuals is competition for space. Stochastic spatially explicit simulations were used, along with differential equation models based on pair approximations. Conditions under which either dispersal strategy can successfully invade the other were determined, as a function of the amount and clustering of suitable habitat and the relative costs involved in the two dispersal strategies. Long-distance dispersal, which reduces intraspecific competition, is sometimes advantageous even where aggregation of suitable habitat would otherwise favor short-distance dispersal, although certain habitat distributions can lead to either strategy being dominant. Coexistence is also possible on some landscapes, where the spatial structure of the populations partitions suitable sites according to the number of suitable neighboring sites. Mutual competitive exclusion, where whichever strategy is established first cannot be invaded, is also possible. All of these results are observed even when there is no intrinsic difference in the two strategies' costs, such as mortality or competitive abilities.     

Forecasting spatially structured populations: the role of dispersal and scale

We forecasted spatially structured population models with complex dynamics, focusing on the effect of dispersal and spatial scale on the predictive capability of nonlinear forecasting (NLF). Dispersal influences NLF ability by its influence on population dynamics. For simple 2-cell models, when dispersal is small, our ability to predict abundance in subpopulations decreased and then increased with increasing dispersal. Spatial heterogeneity, dispersal manner, and environmental noise did not qualitatively change this result. But results are not clear for complex spatial configurations because of complicated dispersal interactions across subpopulations. Populations undergoing periodic fluctuations could be forecasted perfectly for all deterministic cases that we studied, but less reliably when environmental noise was incorporated. More importantly, for all models that we have examined, NLF was much worse at larger spatial scales as a consequence of the asynchronous dynamics of subpopulations when the dispersal rate was below some critical value. The only difference among models was the critical value of dispersal rate, which varied with growth rate, carrying capacity, mode of dispersal, and spatial configuration. These results were robust even when environmental noise was incorporated. Intermittency, common in the dynamics of spatially structured populations, lowered the predictive capability of NLF. Forecasting population behaviour is of obvious value in resource exploitation and conservation. We suggest that forecasting at local scales holds promise, whereas forecasting abundance at regional scales may yield poor results. Improved understanding of dispersal can enhance the management and conservation of natural resources, and may help us to understand resource-exploitation strategies employed by local indigenous humans.     

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.     

The effect of static and dynamic spatially structured disturbances on a locally dispersing population

Previous models of locally dispersing populations have shown that in the presence of spatially structured fixed habitat heterogeneity, increasing local spatial autocorrelation in habitat generally has a beneficial effect on such populations, increasing equilibrium population density. It has also been shown that with large-scale disturbance events which simultaneously affect contiguous blocks of sites, increasing spatial autocorrelation in the disturbances has a harmful effect, decreasing equilibrium population density. Here, spatial population models are developed which include both of these spatially structured exogenous influences, to determine how they interact with each other and with the endogenously generated spatial structure produced by the population dynamics. The models show that when habitat is fragmented and disturbance occurs at large spatial scales, the population cannot persist no matter how large its birth rate, an effect not seen in previous simpler models of this type. The behavior of the model is also explored when the local autocorrelation of habitat heterogeneity and disturbance events are equal, i.e. the two effects occur at the same spatial scale. When this scale parameter is very small, habitat fragmentation prevents the population from persisting because sites attempting to reproduce will drop most of their offspring on unsuitable sites; when the parameter is very large, large-scale disturbance events drive the population to extinction. Population levels reach their maximum at intermediate values of the scale parameter, and the critical values in the model show that the population will persist most easily at these intermediate scales of spatial influences. The models are investigated via spatially explicit stochastic simulations, traditional (infinite-dispersal) and improved (local-dispersal) mean-field approximations, and pair approximations.     

Relatedness in spatially structured populations with empty sites: An approach based on spatial moment equations

Taking into account the interplay between spatial ecological dynamics and selection is a major challenge in evolutionary ecology. Although inclusive fitness theory has proven to be a very useful tool to unravel the interactions between spatial genetic structuring and selection, applications of the theory usually rely on simplifying demographic assumptions. In this paper, I attempt to bridge the gap between spatial demographic models and kin selection models by providing a method to compute approximations for relatedness coefficients in a spatial model with empty sites. Using spatial moment equations, I provide an approximation of nearest-neighbour relatedness on random regular networks, and show that this approximation performs much better than the ordinary pair approximation. I discuss the connection between the relatedness coefficients I define and those used in population genetics, and sketch some potential extensions of the theory.     

Conservation biological control and enemy diversity on a landscape scale

Conservation biological control in agroecosystems requires a landscape management perspective, because most arthropod species experience their habitat at spatial scales beyond the plot level, and there is spillover of natural enemies across the crop–noncrop interface. The species pool in the surrounding landscape and the distance of crop from natural habitat are important for the conservation of enemy diversity and, in particular, the conservation of poorly-dispersing and specialized enemies. Hence, structurally complex landscapes with high habitat connectivity may enhance the probability of pest regulation. In contrast, generalist and highly vagile enemies may even profit from the high primary productivity of crops at a landscape scale and their abundance may partly compensate for losses in enemy diversity. Conservation biological control also needs a multitrophic perspective. For example, entomopathogenic fungi, plant pathogens and endophytes as well as below- and above-ground microorganisms are known to influence pest-enemy interactions in ways that vary across spatiotemporal scales. Enemy distribution in agricultural landscapes is determined by beta diversity among patches. The diversity needed for conservation biological control may occur where patch heterogeneity at larger spatial scales is high. However, enemy communities in managed systems are more similar across space and time than those in natural systems, emphasizing the importance of natural habitat for a spillover of diverse enemies. According to the insurance hypothesis, species richness can buffer against spatiotemporal disturbances, thereby insuring functioning in changing environments. Seemingly redundant enemy species may become important under global change. Complex landscapes characterized by highly connected crop–noncrop mosaics may be best for long-term conservation biological control and sustainable crop production, but experimental evidence for detailed recommendations to design the composition and configuration of agricultural landscapes that maintain a diversity of generalist and specialist natural enemies is still needed.