Panmixia in Pocillopora verrucosa from South Africa

The genetic structure of six local collections of Pocillopora verrrucosa from six coral reefs in KwaZulu-Natal, South Africa, was examined using allozyme electrophoresis. The six separate reefs lie within two different reef complexes. Twenty-two enzymes were screened on five buffer systems, but only five polymorphic loci (Gpi-1, Gdh-1, Lgg-2, Lpp-1, Est-1) could be consistently resolved. No significant differences in allelic frequencies were detected among the six sites. All local collections were genotypically diverse, with evidence of only very limited clonal replication at each site. Indeed, the ratio of observed to expected genotypic diversity (mean Go:Ge=0.64 +/-0.05 SD), the ratio of observed number of genotypes to the number of individuals (mean Ng:N = 0.65 +/-0.04 SE), and deviations from the Hardy-Weinberg equilibrium indicate that sexual reproduction plays a major role in the maintenance of the populations. No genetic differentiation was found either within (FSR = 0.026 +/-0.003 SE) or between (FRT = 0.000 +/-0.001 SE) reef complexes. The homogeneity of the gene frequencies across the six reefs strongly supports the assumption that the KwaZulu-Natal reef complexes are highly connected by gene flow (Nem=44). The reefs in the southern and central reef complexes along the northern Maputaland coastline can therefore be considered part of a single population.

Carapace dentition patterns, morphometrics and allozyme differentiation amongst two toothed freshwater crab species (Potamonautes warreni and P-unispinus) (Decapoda : Brachyura : Potamonautidae) from river systems in South Africa

The taxonomic relationship between two toothed South African river crabs, Potamonautes warreni and P. unispinus, is unclear. The problem stems from the widespread variation in carapace dentition patterns amongst P. warreni individuals over its biogeographic range, where single toothed individuals may appear similar in carapace morphology to P. unispinus. Ten populations of P. warreni and 18 populations of P. unispinus were collected and the morphometric and genetic differentiation between the two taxa quantified. Patterns of morphometric and genetic variation were examined using multivariate statistics and protein gel electrophoresis, respectively. Principal component analyses of carapace characters showed that the two species are morphologically indistinguishable. However, discriminate functions analyses and additional statistical results corroborate the morphological distinction between the two taxa. Allozyme electrophoresis of 17 protein coding loci, indicated a close genetic similarity between the two species (I = 0.92). A fixed allelic difference at one locus (LT-2) and extensive genetic variability at another locus (PGM-1) indicate that two gene pools are present and that the two taxa are genetically isolated. Intraspecific genetic I values for both species were > 0.97 and indicated no apparent genetic structuring on a micro or macro-geographic scale. The variation in carapace dentition among P. warreni populations possesses no genetic basis and may possibly toe the product of ecogenesis. The value of dentition patterns in the systematics of river crabs is discussed. Dentition patterns among river crab species appear to be conserved and reliable as species specific diagnostic markers, but should ideally be used in combination with other morphological data sets and genetic evidence.

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.