Jonathan W. Pitchford

Scaling laws of marine predator search behaviour

Many free-ranging predators have to make foraging decisions with little, if any, knowledge of present resource distribution and availability. The optimal search strategy they should use to maximize encounter rates with prey in heterogeneous natural environments remains a largely unresolved issue in ecology. Lévy walks are specialized random walks giving rise to fractal movement trajectories that may represent an optimal solution for searching complex landscapes. However, the adaptive significance of this putative strategy in response to natural prey distributions remains untested. Here we analyse over a million movement displacements recorded from animal-attached electronic tags to show that diverse marine predators—sharks, bony fishes, sea turtles and penguins—exhibit Lévy-walk-like behaviour close to a theoretical optimum. Prey density distributions also display Lévy-like fractal patterns, suggesting response movements by predators to prey distributions. Simulations show that predators have higher encounter rates when adopting Lévy-type foraging in natural-like prey fields compared with purely random landscapes. This is consistent with the hypothesis that observed search patterns are adapted to observed statistical patterns of the landscape. This may explain why Lévy-like behaviour seems to be widespread among diverse organisms, from microbes to humans, as a ‘rule’ that evolved in response to patchy resource distributions.

Disentangling nestedness from models of ecological complexity

Complex networks of interactions are ubiquitous and are particularly important in ecological communities, in which large numbers of species exhibit negative (for example, competition or predation) and positive (for example, mutualism) interactions with one another. Nestedness in mutualistic ecological networks is the tendency for ecological specialists to interact with a subset of species that also interact with more generalist species. Recent mathematical and computational analysis has suggested that such nestedness increases species richness. By examining previous results and applying computational approaches to 59 empirical data sets representing mutualistic plant–pollinator networks, we show that this statement is incorrect. A simpler metric—the number of mutualistic partners a species has—is a much better predictor of individual species survival and hence, community persistence. Nestedness is, at best, a secondary covariate rather than a causative factor for biodiversity in mutualistic communities. Analysis of complex networks should be accompanied by analysis of simpler, underpinning mechanisms that drive multiple higher-order network properties.

Exact Results for the Evolution of Stochastic Switching in Variable Asymmetric Environments

The ability of bacteria to spontaneously switch their expressed phenotype from an identical underlying genotype is now widely acknowledged. Mechanisms behind these switches have been shown to be evolvable. Important questions thus arise: In a fluctuating environment, under what conditions can stochastic switching evolve and how is the evolutionarily optimal switching rate related to the environmental changes? Here we derive exact analytical results for the long-term exponential population growth rate in a two-state periodically changing environment, where the environmental states vary in both their duration and in their impact on the fitness of each phenotype. Using methods from statistical physics we derive conditions under which nonswitching is evolutionarily optimal, and we furthermore demonstrate that the transition between the nonswitching and switching regimes is discontinuous (a first-order phase transition). Our general analytical method allows the evolutionary effects of asymmetries in selection pressures and environmental growth rates to be quantified. The evolutionary implications of our findings are discussed in relation to their to real-world applications in the light of recent experimental evidence.

The relationship between plankton blooms, the hatching of fish larvae, and recruitment

Models of fish recruitment must include a realistic description of the underlying prey population dynamics. In the example presented here a model for the growth of haddock larvae (Melanogrammus aeglefinus) and recruitment to the population of juvenile fish is coupled to an excitable medium representation of the planktonic ecosystem. The results elucidate and quantify non-trivial interactions between the larval and planktonic populations. Fish spawning can act to influence the date of onset of the spring phytoplankton bloom, and to increase bloom duration. Simulations show the effects of different reproductive strategies in a stochastic and evolving environment.

An event-based model of superspreading in epidemics.

Many recent disease outbreaks (e.g. SARS, foot-and-mouth disease) exhibit superspreading, where relatively few individuals cause a large number of secondary cases. Epidemic models have previously treated this as a demographic phenomenon where each individual has an infectivity allocated at random from some distribution. Here, it is shown that superspreading can also be regarded as being caused by environmental variability, where superspreading events (SSEs) occur as a stochastic consequence of the complex network of interactions made by individuals. This interpretation based on SSEs is compared with data and its efficacy in evaluating epidemic control strategies is discussed.

Variability of the mechanical properties of bone, and its evolutionary consequences

The relative variabilities (coefficient of variation (CV)) of 10 different mechanical properties of compact bone were determined from 2166 measurements. All measures of variability were made on a minimum of four specimens from any bone. Three pre-yield properties had a CV of about 12%. Six post-yield properties had CVs varying from 24 to 46%. Pre-yield properties increase as a function of mineral content, whereas post-yield properties decrease. These differences give insight into mechanical phenomena occurring at different stages during loading. Furthermore, the fact that some properties are more tightly determined than others has implications for the optimum values set by natural selection. This assertion is made more rigorous using a simple mathematical model for the evolutionarily optimal allocation in a trade-off where one property is imprecisely determined. It is argued that in general the optimum will be biased in favour of the more tightly determined properties than would be the case if all properties had the same CV.

Efficient or Inaccurate? Analytical and Numerical Modelling of Random Search Strategies

A large number of observational and theoretical studies have investigated animal movement strategies for finding randomly located food items. Many of these studies have claimed that a particular strategy is advantageous over other strategies or that the spatial distribution of the food items affects the search efficiency. Here, we study a deliberately idealised problem, in which a blind forager searches for re-visitable food items. We show analytically that the forager’s efficiency is completely independent of both its movement strategy and the spatial pattern of the food items and depends only on the density of food in the environment. However, in some cases, apparent optima in search strategies can arise as artefacts of inappropriate and inaccurate numerical simulations. We discuss modifications to the idealised foraging problem that can confer an advantage on certain strategies, including when the forager has some memory or knowledge of the environment; when the food items are non-revisitable; and when the problem is viewed in an evolutionary context.

Evolutionary optimality in stochastic search problems

‘Optimal’ behaviour in a biological system is not simply that which maximizes a mean, or temporally and spatially averaged, fitness function. Rather, population dynamics and demographic and environmental stochasticity are fundamental evolutionary ingredients. Here, we revisit the problem of optimal foraging, where some recent studies claim that organisms should forage according to Lévy walks. We show that, in an ecological scenario dominated by uncertainty and high mortality, Lévy walks can indeed be evolutionarily favourable. However, this conclusion is dependent on the definition of efficiency and the details of the simulations. We analyse measures of efficiency that incorporate population-level characteristics, such as variance, superdiffusivity and heavy tails, and compare the results with those generated by simple maximizing of the average encounter rate. These results have implications on stochastic search problems in general, and also on computational models of evolutionary optima.

Optimal root proliferation strategies: the roles of nutrient heterogeneity, competition and mycorrhizal networks

AbstractBackground and Aims Plants proliferate roots in order to acquire nutrients, typically contending with heterogeneous resources and competing neighbours. A mathematical model was developed to identify optimal root proliferation strategies in patchy nutrient environments. The impact of joining mycorrhizal networks was also assessed. Methods A simple model of growth and competition in one spatial dimension was implemented within a genetic algorithm to obtain optimal proliferation strategies under different scenarios of resource distribution, and in the presence or absence of local competition and large-scale mycorrhizal networks. Results A strong proliferation response emerged for isolated plants in heterogeneous environments with low resources, and also for plants growing in competition. Even in statistically homogeneous environments, the presence of competition conferred a selective advantage to plants proliferating in the direction of the most recently acquired patch. In the presence of mycorrhizal networks, the optimal strategy switched from symbiosis to proliferation driven growth as the relative cost of acquiring resources through the networks increased. Conclusions The optimal proliferation response in a given scenario was governed by a hierarchy of factors: resource levels and distribution; the presence or absence of competition; and the marginal benefit of obtaining resources via symbiotic relationships with mycorrhizas.

Constructing Random Matrices to Represent Real Ecosystems

Models of complex systems with n components typically have order n2 parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species’ trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.