Genetic correlations between temperature-induced plasticity of life-history traits in a soil arthropod.

Temperature is considered one of the most important mediators of phenotypic plasticity in ectotherms. However, the costs and benefits shaping the evolution of different thermal responses are poorly elucidated. One of the possible constraints to phenotypic plasticity is its intrinsic genetic cost, such as genetic linkage or pleiotropy. Genetic coupling of the thermal response curves for different life history traits may significantly affect the evolution of thermal sensitivity in thermally fluctuating environments. We used the collembolan Orchesella cincta to study if there is genetic variation in temperature-induced phenotypic plasticity in life history traits, and if the degree of temperature-induced plasticity is correlated across traits. Egg development rate, juvenile growth rate and egg size of 19 inbred isofemale lines were measured at two temperatures. Our results show that temperature was a highly significant factor for all three traits. Egg development rate and juvenile growth rate increased with increasing temperature, while egg size decreased. Line by temperature interaction was significant for all traits tested; indicating that genetic variation for temperature-induced plasticity existed. The degree of plasticity was significantly positively correlated between egg development rate and growth rate, but plasticity in egg size was not correlated to the other two plasticity traits. The findings suggest that the thermal plasticities of egg development rate and growth rate are partly under the control of the same genes or genetic regions. Hence, evolution of the thermal plasticity of traits cannot be understood in isolation of the response of other traits. If traits have similar and additive effects on fitness, genetic coupling between these traits may well facilitate the evolution of optimal phenotypes. However, for this we need to know the selective forces under field conditions. © 2010 Springer Science+Business Media B.V

Surjective word maps and Burnside's p^a q^b theorem

We prove surjectivity of certain word maps on finite non-abelian simple groups. More precisely, we prove the following: if N is a product of two prime powers, then the word map (x,y)↦xNyN is surjective on every finite non-abelian simple group; if N is an odd integer, then the word map (x,y,z)↦xNyNzN is surjective on every finite quasisimple group. These generalize classical theorems of Burnside and Feit–Thompson. We also prove asymptotic results about the surjectivity of the word map (x,y)↦xNyN that depend on the number of prime factors of the integer N