Joint statistical distribution of surface elevation and water velocity for irregular waves propagating over a shoal

<p>In Trulsen et al. (2020) we reported that when irregular waves propagate over a shoal the extreme wave statistics of surface elevation and water velocity can be dramatically different:  The surface elevation can have a local maximum of kurtosis some distance into the shallower part of the shoal, while it relaxes to normality after the shoal.  The velocity field can have a local maximum of kurtosis after the shoal, while it is close to normality over the shallower part of the shoal.  These two fields clearly do not coincide regarding the location of increased probability of extreme waves.</p><p>Here we consider the evolution of the irregular waves over the shoal as a multivariate stochastic process, with a view to reveal the evolution of the joint statistical distribution of surface elevation and water velocity.  Higher order multivariate moments, coskewness and cokurtosis, more commonly seen in mathematical finance theory, are employed to describe the joint extreme wave statistical distribution of the elevation and the velocity.</p><p>Trulsen, K., Raustøl, A., Jorde, S. & Rye, L. B. (2020) Extreme wave statistics of longcrested irregular waves over a shoal. <em> J. Fluid Mech.</em><strong> 882</strong>, R2.</p>

Analysis of Genetic Structure and Dispersal Patterns in a Population of Sea Beet

A model of the migration pattern in a metapopulation of sea beet (Beta vulgaris L. ssp. maritima), based on the continuous distributions of seed and pollen movements, is fitted to gene frequency data at 12 isozyme and RFLP loci by maximum likelihood by using an approximation of the simultaneous equilibrium distribution of the gene frequencies generated by the underlying multivariate stochastic process of genetic drift in the population. Several alternative restrictions of the general model are fitted to the data, including the island model, a model of complete isolation, and a model in which the seed and pollen dispersal variances are equal. Several likelihood ratio tests between these alternatives are performed, and median bias in the estimated parameters is corrected by using parametric bootstrapping. To assess the fit of the selected model, the predicted covariances are compared with covariances computed from the data directly. The dependency of estimated parameters on the ratio between effective and absolute subpopulation sizes, which is treated as a known parameter in the analysis, is also examined. Finally, we note that the data also appear to contain some information about this ratio.