The selection mutation equation

Fisher's Fundamental Theorem of Natural Selection is extended to the selection mutation model with mutation rates _ij=_ii.e. depending only on the target gene, by constructing a simple Lyapunov function. For other mutation rates stable limit cycles are possible.     

颞部骨块形态形成模型极限环的唯一性

本文研究了颞部骨块形态形成的Gierer-Meinhardt模型,并得到该模型在大范围内极限环的唯一性．     

Strange limits of stability in host-parasitoid systems

The classical Nicholson-Bailey model for a two species host-parasitoid system with discrete generations assumes random distributions of both hosts and parasitoids, randomly searching parasitoids, and random encounters between the individuals of the two species. Although unstable, this model induced many investigations into more complex host-parasitoid systems. Local linearized stability analysis shows that equilibria of host parasitoid systems within the framework of a generalized Nicholson-Bailey model are generally unstable. Stability is only possible if host fertility does not exceede ⁴=54.5982 and if superparasitism is unsuccessful. This special situation has already been discovered by Hassell et al. (1983) in their study of the effects of variable sex ratios on host parasitoid dynamics. We discuss global behaviour of the Hassell-Waage-May model using KAM-theory and illustrate its sensitivity to small perturbations, which can give rise to radically different patterns of the population dynamics of interacting hosts and parasitoids.     

一类具有Holling功能性反应的生态系统的定性分析

本文讨论了一类具有Holling功能性反应的生态系统得到（1）的极限环存在和唯一的充分条件．     

一类一级饱和反应系统的极限环

本文对一类一级饱和反应系统进行定性分析,得到（1）存在一个唯一环和存在两个（内不稳外稳）环的条件。     

The strong-migration limit in geographically structured populations

Summary Some strong-migration limits are established for geographically structured populations. A diploid monoecious population is subdivided into a finite number of colonies, which exchange migrants. The migration pattern is fixed and ergodic, but otherwise arbitrary. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus. In all the limiting results, an effective population number N _e ( N _T ) appears instead of the actual total population number N _T . 1. If there is no selection, every allele mutates at rate u to types not preexisting in the population, and the (finite) subpopulation numbers N _i are very large, then the ultimate rate and pattern of convergence of the probabilities of allelic identity are approximately the same as for panmixia. If, in addition, the N _i are proportional to 1/u, as N _T 8, the equilibrium probabilities of identity converge to the panmictic value. 2. With a finite number of alleles, any mutation pattern, an arbitrary selection scheme for each colony, and the mutation rates and selection coefficients proportional to 1/N _T , let P _j be the frequency of the allele A _j in the entire population, averaged with respect to the stationary distribution of the backward migration matrix M. As N _T 8, the deviations of the allelic frequencies in each of the subpopulations from P _j converge to zero; the usual panmictic mutation-selection diffusion is obtained for P _j , with the selection intensities averaged with respect to the stationary distribution of M. In both models, N _e = N _T and all effects of population subdivision disappear in the limit if, and only if, migration does not alter the subpopulation numbers.Supported by the National Science Foundation (Grant No. DEB77-21494)     

Les échos de la phase aquitano-burdigalienne dans la coupe de Dellaca Bianca (Val Scrivia,bassin Liguro-piémontais,Italie)

The geologic section of the Torrente Scrivia in 061 the vicinity of Rigoroso is generally reported as an conformable sequence in Oligocene and Miocene strata.In fact, it has suffered important reworkingsduring Lower Miocene and this event is not only evident in sedimentology but also in paleontology. Locally, these events reflect tectonic motions more strongly marked in the north-eastern part of the ligurian piemontese basin.Consequently, the result is that the geologicsection concerned could not be satisfactory referring to Lower Miocene.