Evolutionary dynamics on any population structure

Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been absent for a long time, but have recently emerged for special structures where all individuals have the same number of neighbors. But the problem of determining which trait is favored by selection in the natural case where the number of neighbors can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class which suggests there is no efficient algorithm. Whether there exists a simple solution for weak selection was unanswered. Here we provide, surprisingly, a general formula for weak selection that applies to any graph or social network. Our method uses coalescent theory and relies on calculating the meeting times of random walks. We can now evaluate large numbers of diverse and heterogeneous population structures for their propensity to favor cooperation. We can also study how small changes in population structure---graph surgery---affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.Comment: 68 pages, 10 figure

Customer population modelling with residence time structure

In many service industries, companies offer a variety of customer packages, with differing levels of service and associated charges. For example, in the case of cable companies, customers may choose to subscribe to different bundles of channels and may also buy phone and internet services. From time to time, customers will upgrade to a more expensive package, or possibly downgrade or discontinue their contract altogether. Numbercraft asked the Study Group to consider models for how the number of customers on each type of contract will change over time. Such models could be used to forecast companies' future income and also to ensure that marketing campaigns have maximum impact

Potential and Spatial Structure of Population

The goal of this work is to suggest a mechanism explaining different spatial patterns of residential locations. The basic idea is counterbalance of centripetal and centrifugal forces. This paper complements the previous author's works in this area. This article addresses the following questions: a) agglomeration potential, b) optimal city size, c) equilibrium agricultural density, d) influence of agglomeration on land rent. Both relative location and size distribution of cities and residential patterns in agricultural areas represent interesting objects of study. There exist two main forces, centripetal (agglomeration) and centrifugal (congestion) that shape urban areas. The origin of agglomeration forces is in scale economies, while congestion forces represent a cumulative negative externality from such agglomeration. Following the stylized facts about different production technologies, it is assumed that agricultural technology creates dispersion force (through intensive land use), while industrial technology creates agglomeration force. It is possible to find the optimal city size assuming some scale economies in production counterbalanced by commuting costs. Location heterogeneity is balanced across residents via location rent to bring identical utility. There might be two possibilities: finite optimal size (for low scale economies) and infinitely large city (for high scale economies). The rural community of farmers is also considered. Here the average distance to neighbor (as a proxy to market access) is balanced with the benefits from land ownership. The optimal rural population density is the point maximizing this potential. Finally, the spatial equilibrium is constructed. It consists of discrete cities of optimal size attracting certain fraction of the population and the continuous farmland between them. The concept of potential for agro-industrial cluster is also introduced. It is assumed that rural resident has an access to scale economies in production of a city via commuting, and also has land slot for agricultural activity. There exists equilibrium land rent giving agents identical utility.

The scale of population structure in Arabidopsis thaliana

The population structure of an organism reflects its evolutionary history and influences its evolutionary trajectory. It constrains the combination of genetic diversity and reveals patterns of past gene flow. Understanding it is a prerequisite for detecting genomic regions under selection, predicting the effect of population disturbances, or modeling gene flow. This paper examines the detailed global population structure of Arabidopsis thaliana. Using a set of 5,707 plants collected from around the globe and genotyped at 149 SNPs, we show that while A. thaliana as a species self-fertilizes 97% of the time, there is considerable variation among local groups. This level of outcrossing greatly limits observed heterozygosity but is sufficient to generate considerable local haplotypic diversity. We also find that in its native Eurasian range A. thaliana exhibits continuous isolation by distance at every geographic scale without natural breaks corresponding to classical notions of populations. By contrast, in North America, where it exists as an exotic species, A. thaliana exhibits little or no population structure at a continental scale but local isolation by distance that extends hundreds of km. This suggests a pattern for the development of isolation by distance that can establish itself shortly after an organism fills a new habitat range. It also raises questions about the general applicability of many standard population genetics models. Any model based on discrete clusters of interchangeable individuals will be an uneasy fit to organisms like A. thaliana which exhibit continuous isolation by distance on many scales

Fluctuations and correlations in population models with age structure

We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent death probability, as well as a variable reproduction probability for each individual as a function of age. We first solve for the steady-state of the model in mean field theory, before developing analytic techniques to compute Gaussian fluctuation corrections around the mean field fixed point. Our computations are found to be in good agreement with Monte-Carlo simulations. Finally we discuss how similar methods may be applied to fluctuations in continuous time population models.Comment: 4 page

Population structure of graptolite assemblages

Graptolite rhabdosomes display a diverse suite of morphologies. The range of morphotypes present within most moderate to high diversity assemblages from the Ordovician and Silurian is similar, despite the different taxonomic composition of the faunas at different times. Survivorship analyses of graptolite faunas from the Ordovician and Silurian demonstrate strong similarities in the mortality rates of unrelated graptolites of similar functional morphology. It also shows a strong correlation of decreasing mortality rates amongst more mature colonies with increasing rhabdosome complexity. This similarity in both functional morphology and life history of graptolites suggests that they lived within a very stable planktic community structure

Population Structure and Cryptic Relatedness in Genetic Association Studies

We review the problem of confounding in genetic association studies, which arises principally because of population structure and cryptic relatedness. Many treatments of the problem consider only a simple ``island'' model of population structure. We take a broader approach, which views population structure and cryptic relatedness as different aspects of a single confounder: the unobserved pedigree defining the (often distant) relationships among the study subjects. Kinship is therefore a central concept, and we review methods of defining and estimating kinship coefficients, both pedigree-based and marker-based. In this unified framework we review solutions to the problem of population structure, including family-based study designs, genomic control, structured association, regression control, principal components adjustment and linear mixed models. The last solution makes the most explicit use of the kinships among the study subjects, and has an established role in the analysis of animal and plant breeding studies. Recent computational developments mean that analyses of human genetic association data are beginning to benefit from its powerful tests for association, which protect against population structure and cryptic kinship, as well as intermediate levels of confounding by the pedigree.Comment: Published in at http://dx.doi.org/10.1214/09-STS307 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fine-scale population structure and asymmetrical dispersal in an obligate salt-marsh passerine, the Saltmarsh Sparrow (Ammodramus Caudacutus)

Understanding the spatial scale of gene flow can yield valuable insight into the ecology of an organism and guide conservation strategies. Fine-scale genetic structure is uncommon in migratory passerines because of their high vagility and presumed high dispersal abilities. Aspects of the behavior and ecology of some migratory species, however, may promote structure on a finer scale in comparison to their mobility. We investigated population genetic structure in the Saltmarsh Sparrow (Ammodramus caudacutus), a migratory passerine that breeds along the northeastern coast of the United States, where it is restricted exclusively to a narrow strip of patchily distributed tidal marsh habitat. Using genotyping with 10 microsatellite loci, we detected weak but significant population structure among Saltmarsh Sparrows from nine marshes on the breeding grounds between Scarborough, Maine, and Oceanside, New York. Genetic variation among marshes was largely consistent with a pattern of isolation by distance, with some exceptions. One inland marsh was genetically divergent despite its proximity to other sampled marshes, which suggests that mechanisms besides geographic distance influence population genetic structure. Bayesian clustering, multivariate analyses, and assignment tests supported a population structure consisting of five groups. Estimates of migration rates indicated variation in gene flow among marshes, which suggests asymmetrical dispersal and possible source-sink population dynamics. The genetic structure that we found in Saltmarsh Sparrows may result from natal philopatry and breeding-site fidelity, combined with restricted dispersal due to obligate dependence on a patchy habitat. Our findings suggest that fine-scale population structure may be important in some migratory passerines. Received 12 July 2011, accepted 1 February 2012