American Institute of Mathematical Sciences

Advanced
2008, 5(4): 813-830. doi: 10.3934/mbe.2008.5.813

Local resource competition and the skewness of the sex ratio: a demographic model

Lorenzo Mari 1, , Marino Gatto 1, and  Renato Casagrandi 1,

1. 

Dipartimento di Elettronica e Informazione, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy, Italy, Italy

Received  December 2007 Revised  April 2008 Published  October 2008

Most animal populations are characterized by balanced sex ratios, but there exist several exceptions in which the sex ratio at birth is skewed. An interesting hypothesis proposed by Clark (1978) to explain male-biased sex ratios is the local resource competition theory: the bias may be expected in those species in which males disperse more than females, which are thus more prone to local competition for resources. Here we discuss some of the ideas underlying Clark's theory using a spatially explicit approach. In particular, we focus on the role of spatiotemporal heterogeneity as a possible determinant of biased sex ratios. We model spatially structured semelparous populations where either Ricker density dependence or environmental stochasticity can generate irregular spatiotemporal patterns. The proposed discrete-time model describes both genetic and complex population dynamics assuming that (1) sex ratio is genetically determined, (2) only young males can disperse, and (3) individuals locally compete for resources. The analysis of the model shows that no skewed sex ratios can arise in homogeneous habitats. Temporal asynchronized fluctuations between two distinct patches coupled with dispersal of young males is the minimum requirement for obtaining skewed sex ratios of demographic nature in local adult populations. However, the establishment of a male-biased sex ratio at birth in the long run is possible if dispersal is genetically determined and there is genetic linkage between sex ratio determination and dispersal.
Keywords: Sex ratio evolution, dispersal, spatially explicit models, population genetics, local resource competition.
Mathematics Subject Classification: 92Dxx.
Citation: Lorenzo Mari, Marino Gatto, Renato Casagrandi. Local resource competition and the skewness of the sex ratio: a demographic model. Mathematical Biosciences & Engineering, 2008, 5 (4) : 813-830. doi: 10.3934/mbe.2008.5.813
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