Fixation probabilities in populations under demographic fluctuations

We study the fixation probability of a mutant type when introduced into a resident population. As opposed to the usual assumption of constant pop- ulation size, we allow for stochastically varying population sizes. This is implemented by a stochastic competitive Lotka-Volterra model. The compe- tition coefficients are interpreted in terms of inverse payoffs emerging from an evolutionary game. Since our study focuses on the impact of the competition values, we assume the same birth and death rates for both types. In this gen- eral framework, we derive an approximate formula for the fixation probability {\phi} of the mutant type under weak selection. The qualitative behavior of {\phi} when compared to the neutral scenario is governed by the invasion dynamics of an initially rare type. Higher payoffs when competing with the resident type yield higher values of {\phi}. Additionally, we investigate the influence of the remaining parameters and find an explicit dependence of {\phi} on the mixed equilibrium value of the corresponding deterministic system (given that the parameter values allow for its existence).Comment: 31 pages, 7 figure

A spatial model for selection and cooperation

We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias $\alpha$ with respect to the other type (called cooperator). However, a cooperator helps a neighbor (either defector or cooperator) to reproduce at rate $\gamma$. We prove that the one-dimensional nearest-neighbor interacting dynamical system exhibits a phase transition at $\alpha=\gamma$. For $\alpha>\gamma$ cooperators always die out, but if $\gamma>\alpha$, cooperation is the winning strategy.Comment: 19 pages, 1 figur

Egy molekuláris Növénykórtani Vizsgálatok Céljára Javasolható Növény−Gomba Kölcsönhatás

Növénybiológiai kutatásaink egyik alapvetô modellszervezete a Nicotiana benthamiana. A faj molekuláris növénykórtani célokra történô felhasználását tovább erôsítené egy olyan növénypatogén gomba alkalmazása, mely a növényen specifi kus tüneteket okoz és laboratóriumi körülmények között könnyen és megbízhatóan használható. Munkánkban bemutatjuk, hogy a Cercospora nicotianae hemibiotróf dohánykórokozó gomba hatékonyan fertôzi a N. benthamiana egyedeit. A laboratóriumi vizsgálatok céljára eddig nem elterjedt N. benthamiana−C. nicotianae gazda−parazita kapcsolat a molekuláris növénykórtani és kórélettani kutatások kézenfekvô modellrendszere lehet

Актуальні проблеми застосування державних соціальних стандартів та гарантій в Україні

The 16.4Ma old Bogács Ignimbrite, located south of the Bükk Mountains, northern Hungary, was formed during a silicic ignimbrite flare-up in the Pannonian Basin that occurred from 20Ma to 13Ma. It comprises two main units, a lower, variably welded pumiceous and an upper, scoriaceous pyroclastic flow unit. Bulk chemistry of the juvenile clasts indicates a gradual change of geochemical character with an upward decreasing SiO 2 content through the stratigraphic section. A detailed in-situ major and trace element investigation of the main mineral phases and glasses combined with petrogenetic model calculations reveals complex magma reservoir processes. Based on the major and trace element variability, six juvenile clast types were distinguished and each contain fresh glass fractions with distinct compositions. The mineral assemblage consists of plagioclase, orthopyroxene, biotite with minor and variable amounts of quartz, amphibole, ilmenite, zircon and allanite. The anorthite content of the plagioclases varies from 20 to 90mol%, whilst the Enstatite content of orthopyroxenes covers also a wide range from 40 to 90mol%. This large compositional variation can be detected even in single crystals. This extreme geochemical variability can be explained by mixing of crystal mush bodies evolved from both basaltic and more silicic magmas. The calcic plagioclases (An=80-90mol%) and magnesian orthopyroxenes (En=70-90mol%) clearly indicate the role of primitive mafic magmas in the growth of the silicic magma reservoir, even though no basaltic volcanic activity was associated with the Miocene silicic volcanism in the Pannonian basin. The prolonged crystallization in the mushy sills resulted in compositionally different residual melt fractions that moved upwards and accumulated in separated melt pods at the roof of the magma reservoir. Intermittent intrusions of mafic and intermediate magmas into this silicic magma system could have resulted in thorough stirring of the crystal mush bodies and the melt pods, leading to eruptive products having compositionally heterogeneous glass and mineral assemblage