A mathematical model for the population dynamics of army ants

Reduced foraging investment as an adaptation to patchy food sources: A phasic army ant simulation

Colonies of several ant species within the subfamily Dorylinae alternate stereotypical discrete phases of foraging and reproduction. Such phasic cycles are thought to be adaptive because they minimize the amount of foraging and the related costs, and at the same time enhance the colony-level ability to rely on patchily distributed food sources. In order to investigate these hypotheses, we use here a simple computational approach to study the population dynamics of two species of virtual ant colonies that differ quantitatively in their foraging investment. One species, which we refer to as "phasic", forages only half of the time, mirroring the phasic activity of some army ants; the other "non-phasic" species forages instead all the time. We show that, when foraging costs are relatively high, populations of phasic colonies grow on average faster than non-phasic populations, outcompeting them in mixed populations. Interestingly, such tendency becomes more consistent as food becomes more difficult to find but locally abundant. According to our results, reducing the foraging investment, for example by adopting a phasic lifestyle, can result in a reproductive advantage, but only in specific conditions. We thus suggest phasic colony cycles to have emerged together with the doryline specialization in feeding on the brood of other eusocial insects, a resource that is hard to obtain but highly abundant if available.

A persistence criterion for metapopulations

Simple conditions to evaluate the persistence of populations living in fragmented habitats are of primary importance in ecology. We address this need here using a spatially implicit approach that accounts for discrete individuals in a metapopulation. Demographic stochasticity is incorporated into a Markovian model in a natural way, as local extinction is characterized by the death or the dispersal of the last individual inhabiting a patch. The variables of the model are the probabilities p(i) (i=0, 1, 2...) that a patch be occupied by a finite, integer number i of individuals at a given time. We compare the stationary distributions predicted by the model with field data and discuss the role of dispersal in determining different distributions of local abundances. The analysis of the model leads to a persistence criterion which is equivalent to a condition formerly proved by Chesson (Z. Wahrscheinlichkeitstheor. 66, 97-107, 1984) namely that E(0)>1, where E(0) is the expected number of successful dispersers from a patch begun with one individual and to which immigration is excluded. We provide an analytic way of computing E(0) as a function of the main biological characteristics of the species (natality, mortality and dispersal rates, and colonizing ability). We can thus obtain persistence-extinction boundaries in the space of model parameters.

Arms races and the evolution of big fierce societies

The causes of biological gigantism have received much attention, but only for individual organisms. What selection pressures might favour the evolution of gigantic societies? Here we consider the largest single-queen insect societies, those of the Old World army ant Dorylus, single colonies of which can have 20 million workers. We propose that colony gigantism in Dorylus arises as a result of an arms race and test this prediction by developing a size-structured mathematical model. We use this model for exploring and potentially explaining differences in colony size, colony aggression and colony propagation strategies in populations of New World army ants Eciton and Old World army ants Dorylus. The model shows that, by determining evolutionarily stable strategies (ESSs), differences in the trophic levels at which these army ants live feed forwards into differences in their densities and collision rates and, hence, into different strategies of growth, aggression and propagation. The model predicts large colony size and the occurrence of battles and a colony-propagation strategy involving highly asymmetrical divisions in Dorylus and that Eciton colonies should be smaller, non-combative and exhibit equitable binary fission. These ESSs are in excellent agreement with field observations and demonstrate that gargantuan societies can arise through arms races.

Habitat fragmentation, percolation theory and the conservation of a keystone species

Many species survive in specialized habitats. When these habitats are destroyed or fragmented the threat of extinction looms. In this paper, we use percolation theory to consider how an environment may fragment. We then develop a stochastic, spatially explicit, individual-based model to consider the effect of habitat fragmentation on a keystone species (the army ant Eciton burchelli ) in a neo tropical rainforest. The results suggest that species may become extinct even in huge reserves before their habitat is fully fragmented; this has important implications for conservation. We show that sustainable forest-harvesting strategies may not be as successful as is currently thought. We also suggest that habitat corridors, once thought of as the saviour for fragmented environments, may have a detrimental effect on population persistence.