We consider two dimensional Lotka-Volterra systems in a fluctuating environment. Relying on recent results on stochastic persistence and piecewise deterministic Markov processes, we show that random switching between two environments that are both favorable to the same species can lead to the extinction of this species or coexistence of the two competing species.MSC: 60J99; 34A60

The exact extent of microbial diversity remains unknowable. Nevertheless, fingerprinting patterns [denaturing gradient electrophoresis (DGE), single-strand conformation polymorphism (SSCP)] provide an image of a microbial ecosystem and contain diversity data. We generated numerical simulation fingerprinting patterns based on three types of distribution (uniform, geometric and lognormal) with a range of units from 10 to 500,000. First, simulated patterns containing a diversity of around 1000 units or more gave patterns similar to those obtained in experiments. Second, the number of bands or peaks saturated quickly to about 35 and were unrelated to the degree of diversity. Finally, assuming lognormal distribution, we used an estimator of diversity on in silico and experimental fingerprinting patterns. Results on in silico patterns corresponded to the simulation inputs. Diversity results in experimental patterns were in the same range as those obtained from the same DNA sample in molecular inventories. Thus, fingerprinting patterns contain extractable data about diversity although not on the basis of a number of bands or peaks, as is generally assumed to be the case.

The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been completely analysed. Here, we complete this analysis and we delineate the conditions under which fragmentation associated to dispersal is either beneficial or detrimental to total population abundance. Therefore, this is a contribution to the SLOSS question. Importantly, we also show that, depending on the underlying mechanism, there is no unique way to generalize the logistic model to a patchy situation. In many cases, the standard model is not the correct generalization. We analyse several alternative models and compare their predictions. Finally, we emphasize the shortcomings of the logistic model when written in the r-K parameterization and we explain why Verhulst's original polynomial expression is to be preferred.