Two-Loop Crossover Scaling Functions of the O(N) Model

Using Environmentally Friendly Renormalization, we present an analytic calculation of the series for the renormalization constants that describe the equation of state for the $O(N)$ model in the whole critical region. The solution of the beta-function equation, for the running coupling to order two loops, exhibits crossover between the strong coupling fixed point, associated with the Goldstone modes, and the Wilson-Fisher fixed point. The Wilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$, and thus the effective critical exponents associated with renormalization of the transverse vertex functions, also exhibit non-trivial crossover between these fixed points.Comment: 21 pages, 4 figures, version to appears in IJMPL

Mating Patterns and Post-Mating Isolation in Three Cryptic Species of the Engystomops Petersi Species Complex

Determining the extent of reproductive isolation in cryptic species with dynamic geographic ranges can yield important insights into the processes that generate and maintain genetic divergence in the absence of severe geographic barriers. We studied mating patterns, propensity to hybridize in nature and subsequent fertilization rates, as well as survival and development of hybrid F1 offspring for three nominal species of the Engystomops petersi species complex in Yasuní National Park, Ecuador. We found at least two species in four out of six locations sampled, and 14.3% of the wild pairs genotyped were mixed-species (heterospecific) crosses. We also found reduced fertilization rates in hybrid crosses between E. petersi females and E. “magnus” males, and between E. “magnus” females and E. “selva” males but not in the reciprocal crosses, suggesting asymmetric reproductive isolation for these species. Larval development times decreased in F1 hybrid crosses compared to same species (conspecific) crosses, but we did not find significant reduction in larval survival or early metamorph survival. Our results show evidence of post-mating isolation for at least two hybrid crosses of the cryptic species we studied. The general decrease in fertilization rates in heterospecific crosses suggests that sexual selection and reinforcement might have not only contributed to the pattern of call variation and behavioral isolation we see between species today, but they may also contribute to further signal divergence and behavioral evolution, especially in locations where hybridization is common and fertilization success is diminished

Mating Patterns and Post-Mating Isolation in Three Cryptic Species of the Engystomops Petersi Species Complex

Determining the extent of reproductive isolation in cryptic species with dynamic geographic ranges can yield important insights into the processes that generate and maintain genetic divergence in the absence of severe geographic barriers. We studied mating patterns, propensity to hybridize in nature and subsequent fertilization rates, as well as survival and development of hybrid F1 offspring for three nominal species of the Engystomops petersi species complex in Yasuní National Park, Ecuador. We found at least two species in four out of six locations sampled, and 14.3% of the wild pairs genotyped were mixed-species (heterospecific) crosses. We also found reduced fertilization rates in hybrid crosses between E. petersi females and E. “magnus” males, and between E. “magnus” females and E. “selva” males but not in the reciprocal crosses, suggesting asymmetric reproductive isolation for these species. Larval development times decreased in F1 hybrid crosses compared to same species (conspecific) crosses, but we did not find significant reduction in larval survival or early metamorph survival. Our results show evidence of post-mating isolation for at least two hybrid crosses of the cryptic species we studied. The general decrease in fertilization rates in heterospecific crosses suggests that sexual selection and reinforcement might have not only contributed to the pattern of call variation and behavioral isolation we see between species today, but they may also contribute to further signal divergence and behavioral evolution, especially in locations where hybridization is common and fertilization success is diminished