Do small swarms have an advantage when house hunting? The effect of swarm size on nest-site selection by Apis mellifera.

Reproductive swarms of honeybees are faced with the problem of finding a good site to establish a new colony. We examined the potential effects of swarm size on the quality of nest-site choice through a combination of modelling and field experiments. We used an individual-based model to examine the effects of swarm size on decision accuracy under the assumption that the number of bees actively involved in the decision-making process (scouts) is an increasing function of swarm size. We found that the ability of a swarm to choose the best of two nest sites decreases as swarm size increases when there is some time-lag between discovering the sites, consistent with Janson & Beekman (Janson & Beekman 2007 Proceedings of European Conference on Complex Systems, pp. 204-211.). However, when simulated swarms were faced with a realistic problem of choosing between many nest sites discoverable at all times, larger swarms were more accurate in their decisions than smaller swarms owing to their ability to discover nest sites more rapidly. Our experimental fieldwork showed that large swarms invest a larger number of scouts into the decision-making process than smaller swarms. Preliminary analysis of waggle dances from experimental swarms also suggested that large swarms could indeed discover and advertise nest sites at a faster rate than small swarms.

Self-organized criticality in ant brood tending.

A new stochastic lattice gas model of ant brood tending is formulated to examine the role played by repulsive ant-ant interactions in the even distribution of care among brood members. The deterministic limit of the model is known to be self-organized critical. Numerical simulations of the model show that the ant-ant repulsion facilitates an even distribution of brood care in the middle of the brood. This provides a possible explanation for the fact that ants sort their brood so that the youngest brood (which are most in need of care) are placed in the middle. Simulations show that the uniformity of brood care distribution is optimal when ants operate in a regime intermediate between completely random and completely deterministic. A certain degree of randomness helps ants to avoid becoming trapped in suboptimal configurations but does not destroy the long-range correlations that are inherent to self-organized critical systems.

Self-organized criticality and emergent oscillations in models of termite architecture with crowding.

The termite architecture model of O'Toole et'al. (1999) is extended to incorporate arbitrary halting time-scales. It is shown that this also means that the assumption of synchronous building must be relaxed. Numerical simulations show that ordered nest architecture emerges under a wide range of time-scales but also that there is an optimal region of halting times. This optimal region is explained by the emergence of synchronized periods of termite activity. The correlation length of the building distribution is shown to diverge providing strong evidence that the model is self-organized critical.

Studies in vitro on the relative efficacy of current acaricides for Sarcoptes scabiei var. hominis.

Resistance of Sarcoptes scabiei to various topical therapies has been described, but clinical assessment of treatment failure is problematic and in-vitro assays are generally not available. We describe a simple in-vitro analysis used to evaluate the relative efficacy of a range of topical, oral, and herbal treatments available in Australia for the treatment of scabies. S. scabiei var. hominis mites were collected from skin scrapings obtained from 7 crusted scabies patients over a period of 2 years (1997 and 1998). Larvae, nymphal instars, and adult mites were tested within 3 h of collection and continuously exposed to selected commercially available treatment products until death, with the elapsed time recorded. Neem was the only product to show little acaricidal activity. Survival curves indicated that, of the other agents, 5% permethrin (Lyclear) had the slowest killing time, with 35% of mites still alive after 3 h, and 4% still alive after 18-22 h of constant exposure. In contrast, no mites were alive after 3 h exposure to 25% benzyl benzoate (Ascabiol), 1% lindane (Quellada), 5% tea tree oil and 100-8000 ng/g of ivermectin (Equimec). Despite the slower killing time with 5% permethrin, there was no evidence of any mite tolerance in vivo or treatment failure in any patients or contact cases.

Pattern formation in a generalized chemotactic model.

Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development.

Spatio-temporal patterns generated by Salmonella typhimurium.

We present experimental results on the bacterium Salmonella typhimurium which show that cells of chemotactic strains aggregate in response to gradients of amino acids, attractants that they themselves excrete. Depending on the conditions under which cells are cultured, they form periodic arrays of continuous or perforated rings, which arise sequentially within a spreading bacterial lawn. Based on these experiments, we develop a biologically realistic cell-chemotaxis model to describe the self-organization of bacteria. Numerical and analytical investigations of the model mechanism show how the two types of observed geometric patterns can be generated by the interaction of the cells with chemoattractant they produce.

Analysis of propagating pattern in a chemotaxis system.

We consider a cell-chemotaxis model which can generate spatially heterogeneous patterns in cell density and chemoattractant. A local perturbation about the uniform steady state propagates across the domain leaving behind a steady state pattern of standing peaks and troughs. We investigate this patterning process analytically and obtain estimates for the pattern wavelength and speed of spread. We compare the analytical results with numerical simulation of the full model systems.

Pigmentation pattern formation on snakes.

We consider a cell-chemotaxis model mechanism for generating some of the common, simple and complex, patterns found on the skin of snakes. By investigating the pattern generation potential of the model we show that many of the more complex patterns might result from growth of the integument during the pattern formation process. We suggest that many of the diverse elaborate patterns on snakes, and other species, can be generated by a single mechanism if the time scale of the pattern process is commensurate with the time scale associated with significant embryonic growth.

Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation.

We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989, J. exp. Zool. 251, 186-202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.

A model for swimming unipolar spirilla.

A mathematical model employing slender body theory is constructed for a unipolar Spirillum volutans cell with the model cell allowed to move unconstrainedly in the fluid. The results are compared with observation and previous studies and the effects of varying cell dimensions are investigated.