Scale-free olfactory-driven foraging

Scent plumes form when the wind disperses scent molecules from their source. Many species of insects can follow scent plumes to their sources to find mates or distant resources. The pheromones of many important pest species and semiochemicals that mediate such insect behaviour have now been identified, synthesized, and formulated for use in pest-management schemes and are used widely in traps for population monitoring. However, despite considerable research semiochemicals have not been universally successful in these applications. This is, in part, because the detailed understanding of scent dispersal which underlies the inter-play between sources and distributions of scent, atmospheric conditions and pest behaviour responses remains largely unknown. This proposal will address this shortcoming by formulating and validate new mathematical models for the scent concentration experienced by insects flying within scent plumes. This is a considerable challenege because scent concentrations exhibit a complex, chaotically evolving structure over a broad range of spatial and temporal scales. Indeed, fluctuations in scent concentrations are amongst the most extreme form of flcutuations found in Nature. These new mathematical models of scent concentration will be combined with models of insect response and used to predict insect movement patterns. It is hypothesised that the observed complexity of insect foraging patterns arises from naive insect responses to the complex patterns in scent concentrations. This constrasts with the widely held notion that the complex behaviour of insects has, through the process of evolution, resulted in optimal or advantageous searching strategies. The model will then be used in parallel with future experimentation to provide a better understanding of other aspects of chemical ecology and pest-management. The model could, for example, be used to assess the extent to which the individual components of attractive pheromones and other semiochemicals can mediate the earliest behaviours in source location, such as locking onto a plume, and later behaviours, such as landing or courtship. The model could also be used to determine the effective extent of traps and relate trap counts to densities of airborne population--a problem of considerable practical importance for population monitoring because trap counts often do not corelate well densities.

The pheromones of many important pest species and semiochemicals that mediate pest behaviour have been identified, synthesized, and formulated for use in pest-management schemes and are used widely in traps for population monitoring. The neural computations used to represent olfactory information in the brain have also been investigated extensively. Much less progress has been made in understanding and predicting accurately histories of scent concentration experienced by insects along their trajectories. As a consequence, the inter-play between sources and distributions of semiochemicals, atmospheric conditions and pest behaviour responses remains largely unknown. This proposal will address this shortcoming. Predictive models of pest behaviour will be formulated by combining a new type of stochastic model for scent fluctuations with models of olfactory-response. The new stochastic models will reproduce accurately key aspects of scent signals including: distributions of concentration, intermittency factors and threshold up-crossing rates. The movement patterns of some other foragers exhibit a scale-free characteristic. Heinrich's [1979] data for the flight lengths (distance between consecutive landing sites on previously unvisited florets) of foraging bumble-bees is, for example, characterized by a Levy distribution. The nocturnal foraging characteristics of a species of African jackal (Canis adustus) are also consistent with this Levy distribution [Atkinson et al. 2002], as are the flight characteristics of the wandering albatross [Viswanathan et al., 1996]. These scale-free (fractal) patterns have aroused considerable excitement because they are known to optimize the success of random searches when target sites are randomly and sparsely distributed [Viswanathan et al., 1999.]. Levy walks are also advantageous because the probability of returning to a previously visited site is smaller than for a Gaussian [M. Levandowsky et al. 1988; F.L. Schuster and M. Levandowsky, 1996.]. It has even been suggested that the fractal properties of the set of sites visited by a Levy walker are related to scale invariant properties of the underlying ecosystem [Viswanathan et al., 1996]. The association of Levy walks with optimum or advantageous behaviour does, however, fail to acknowledge that foragers tend to move within a scent plume undergoing turbulent dispersion within the atmospheric boundary-layer. Indeed, the results of preliminary numerical studies undertaken by the PI, using a simple stochastic model [T. L. Hilderman and D.J. Wilson, 1999], suggest the a naive response to the complex structure of scent plumes may account for observed scale-free foraging patterns. The approach reproduces the distribution of observed scale-free flight-lengths of foraging bumble-bees [Hienrich, 1979] and the observed scale-free growth of the displacement variance of the Canis adustus [Atkinson et al., 2002]. This intriguing development leaves open the issue of robustness of the finding with respect to improved representations of the scent fluctuations experienced by foragers that can be captured by the new class of stochastic model being advocated by the PI.The new models are particularly advantageous in the context of insect-response modelling because they account explicitly temporal gradients in scent concentrations which are central to the determination of scent-concentration recurrence statistics (distributions of durations between threshold concentrations being exceeded, concentration threshold up-crossing rates etc.) [27]. These recurrence statistics underlie the statistical properties of olfactory-driven foraging. In all current models, temporal gradients in scent concentration are non-physical divergent quantities!