Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24×10(6) simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.

Broad-scale patterns of sex ratios in Patella spp.: a comparison of range edge and central range populations in the British Isles and Portugal

Sex change, or sequential hermaphroditism, occurs in the plant and animal kingdoms and often determines a predominance of the first sex. Our aim was to explore changes in sex ratios within the range of the species studied: Patella vulgata and Patella depressa. The broad-scale survey of sex with size of limpets covered a range of latitudes from Zambujeira do Mar (southern Portugal) to the English Channel. Indirect evidence was found for the occurrence of protandry in P. vulgata populations from the south of England, with females predominating in larger size-classes; cumulative frequency distributions of males and females were different; sex ratios were biased towards males and smallest sizes of males were smaller than the smallest sizes of females. In contrast in Portugal females were found in most size-classes of P. vulgata. In P. depressa populations from the south coast of England and Portugal females were interspersed across most size-classes; size distributions of males and females and size at first maturity of males and females did not differ. P. depressa did, however, show some indications of the possibility of slight protandry occurring in Portugal. The test of sex ratio variation with latitude indicated that P. vulgata sex ratios might be involved in determining the species range limit, particularly at the equatorward limit since the likelihood of being male decreased from the south coast of England to southern Portugal. Thus at the southern range limit, sperm could be in short supply due to scarcity of males contributing to an Allee effect.

Broad-scale patterns of sex ratios in Patella spp.: a comparison of range edge and central range populations in the British Isles and Portugal

Sex change, or sequential hermaphroditism, occurs in the plant and animal kingdoms and often determines a predominance of the first sex. Our aim was to explore changes in sex ratios within the range of the species studied: Patella vulgata and Patella depressa. The broad-scale survey of sex with size of limpets covered a range of latitudes from Zambujeira do Mar (southern Portugal) to the English Channel. Indirect evidence was found for the occurrence of protandry in P. vulgata populations from the south of England, with females predominating in larger size-classes; cumulative frequency distributions of males and females were different; sex ratios were biased towards males and smallest sizes of males were smaller than the smallest sizes of females. In contrast in Portugal females were found in most size-classes of P. vulgata. In P. depressa populations from the south coast of England and Portugal females were interspersed across most size-classes; size distributions of males and females and size at first maturity of males and females did not differ. P. depressa did, however, show some indications of the possibility of slight protandry occurring in Portugal. The test of sex ratio variation with latitude indicated that P. vulgata sex ratios might be involved in determining the species range limit, particularly at the equatorward limit since the likelihood of being male decreased from the south coast of England to southern Portugal. Thus at the southern range limit, sperm could be in short supply due to scarcity of males contributing to an Allee effect.