Male dimorphism of a neotropical arachnid: harem size, sneaker opportunities, and gonadal investment

Serracutisoma proximum is a harvestman with alternative male morphs. Large males use sexually dimorphic second legs in fights for the possession of territories on the vegetation, where females oviposit. Small males have short second legs and do not fight but rather sneak into the territories and copulate with egg-guarding females. We investigated the presence of male dimorphism across 10 populations of S. proximum, compared gonadal investment between male morphs, and assessed if the distribution of the sneakers is influenced by harem size. In all populations, there was male dimorphism, indicated by the bimodal distribution of the leg II length/body length. Gonadal investment did not differ between morphs and was not affected by male size, second leg length, and morph relative frequency in the populations. We found 361 territories, 90.0% containing 1 male, 9.7% containing 2 males (dyads), and 0.3% containing 3 males. The probability of encountering dyads increased with the number of females present in the territories. Moreover, the proportion of sneakers in territories containing dyads was higher than would be expected by chance. One possible reason for the ubiquity of alternative morphs in S. proximum could be the high mating opportunities experienced by sneakers in spatially structured populations with a resource defense polygyny system. Additionally, the high frequency of successful invasions by sneakers and hence the high sperm competition risk for both morphs may explain the similarity in gonadal investment between male morphs.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.