Exact results for fixation probability of bithermal evolutionary graphs

One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats exchanging individuals among each other and can be modeled by an evolutionary graph (EG), where directed links weight the probability for the offspring of one individual to replace another individual in the community. Very few exact analytical results are known for EGs. We show here how by using the techniques of the fixed point of Probability Generating Function, we can uncover a large class of of graphs, which we term bithermal, for which the exact fixation probability can be simply computed

Fisher Waves: an individual based stochastic model

The propagation of a beneficial mutation in a spatially extended population is usually studied using the phenomenological stochastic Fisher-Kolmogorov (SFKPP) equation. We derive here an individual based, stochastic model founded on the spatial Moran process where fluctuations are treated exactly. At high selection pressure, the results of this model are different from the classical FKPP. At small selection pressure, the front behavior can be mapped into a Brownian motion with drift, the properties of which can be derived from microscopic parameters of the Moran model. Finally, we show that the diffusion coefficient and the noise amplitude of SFKPP are not independent parameters but are both determined by the dispersal kernel of individuals

Exact results for a noise-induced bistable system

A stochastic system where bistability is caused by noise has been recently investigated by Biancalani et al. (PRL 112:038101, 2014). They have computed the mean switching time for such a system using a continuous Fokker-Planck equation derived from the Taylor expansion of the Master equation to estimate the parameter of such a system from experiment. In this article, we provide the exact solution for the full discrete system without resorting to continuous approximation and obtain the expression for the mean switching time. We further extend this investigation by solving exactly the Master equation and obtaining the expression of other quantities of interests such as the dynamics of the moments and the equilibrium time

Extradyadic Communication with Friends about Negative Relational Events in Romantic Relationships: Development of a Measure and Implications for Friendship and Romantic Relationship Functioning

Interpersonal relationships, and the communication that takes place within them, do not exist in a vacuum (Milardo, 1982). Extant research provides much useful information about the importance of perceived network support and interference for romantic relationships, yet there is limited information regarding why and how people engage in extradyadic communication with network members when they experience negative relational events in their romantic relationships. The purpose of the current dissertation was to (a) develop and validate measures of the motives and content of romantic partners\u27 and friends\u27 extradyadic communication about negative relational events in romantic relationships, (b) investigate relational and partner characteristics as predictors of extradyadic communication, and (c) examine the implications of extradyadic communication for communication behavior and relational outcomes in both friendships and romantic relationships. Three studies were designed to accomplish these goals. Results of focus groups conducted in Study One provided several dominant themes related to romantic partners\u27 and friends\u27 respective motives for and message content within extradyadic interactions about negative relational events in romantic relationships. These themes provided the basis for scale item development for Study Two, in which the results of exploratory factor analyses revealed the initial underlying factor structure of the motives and content scales for both romantic partners and friends. Results also indicated that romantic partners\u27 perceived relational quality, as defined by the Investment Model (Rusbult, 1980), significantly and negatively predicted romantic partners\u27 use of negative extradyadic messages, but not friends\u27 extradyadic messages. In addition, romantic partners\u27 perceived partner uniqueness negatively predicted the use of their own negative messages and friends\u27 interference messages. Further, romantic partners\u27 satisfaction with their friendship negatively predicted their use of negative extradyadic messages, and friends\u27 perceptions of friendship closeness negatively predicted their use of support messages. In Study Three, additional scale modifications and confirmatory factor analyses were undertaken, validating the final factor structure of romantic partners\u27 and friends\u27 motives and content scales, respectively. Study Three also used observed conversations to examine the interactions of romantic partners\u27 and friends\u27 message content. Overwhelmingly, results indicated that the interaction of romantic partners\u27 and friends\u27 extradyadic messages (in terms of content) did not have a significant impact on immediate relational outcomes. Although there were some limitations to be considered, results provide a foundation for several areas of future research and continued investigation into reasons for and patterns of extradyadic communication and both romantic relationship and friendship functioning

Analytical solution of a neutral model of biodiversity.

International audienceThe unified neutral model of biodiversity proposed by S. Hubbell is solved analytically: The distributions of species abundance in the metacommunity and in a local community are calculated exactly as a function of speciation and migration rates and of the size of the community. In the limit of large population sizes the densities of species of given relative abundance are found to be given by universal functions depending only on two parameters

Securing the Right Skills: A Longitudinal Assessment of College Students’ Writing and Public Speaking Self-Efficacy

This research investigated the developmental patterns of students’ writing and public-speaking self-efficacy throughout their experience in the basic communication course (BCC). Questions were posed regarding (a) whether students grew in their reported writing and public speaking self-efficacy over two semesters, (b) whether growth differed based on biological sex, and (c) whether affinity and apprehension (as sources of performance self-efficacy) played a role in student growth. Two multilevel models revealed significant differences in students’ initial status and rate of growth for each outcome. Specifically, sex, affinity, and apprehension influenced students’ starting positions in the course, while only apprehension had a significant impact on growth. Analyses also revealed a contextual effect of the winter break on growth patterns. The results paint an important picture of the factors influencing students’ personal development in the BCC, while also highlighting the use of multilevel modeling as a potential and relevant tool for contextualizing communicative development over time

A simple, general result for the variance of substitution number in molecular evolution.

International audienceThe number of substitutions (of nucleotides, amino acids, ...) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of substitutions during molecular evolution of a sequence can be estimated for a given substitution model, no simple solution exists for the variance of this random variable. We show in this article that the computation of the variance is as simple as that of the mean number of substitutions for both short and long times. Apart from its fundamental importance, this result can be used to investigate the dispersion index R , i.e. the ratio of the variance to the mean substitution number, which is of prime importance in the neutral theory of molecular evolution. By investigating large classes of substitution models, we demonstrate that although R\ge1 , to obtain R significantly larger than unity necessitates in general additional hypotheses on the structure of the substitution model