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 stellar population structure of the Galactic disk

The spatial structure of stellar populations with different chemical abundances in the Milky Way contains a wealth of information on Galactic evolution over cosmic time. We use data on 14,699 red-clump stars from the APOGEE survey, covering 4 kpc <~ R <~ 15 kpc, to determine the structure of mono-abundance populations (MAPs)---stars in narrow bins in [a/Fe] and [Fe/H]---accounting for the complex effects of the APOGEE selection function and the spatially-variable dust obscuration. We determine that all MAPs with enhanced [a/Fe] are centrally concentrated and are well-described as exponentials with a scale length of 2.2+/-0.2 kpc over the whole radial range of the disk. We discover that the surface-density profiles of low-[a/Fe] MAPs are complex: they do not monotonically decrease outwards, but rather display a peak radius ranging from ~5 kpc to ~13 kpc at low [Fe/H]. The extensive radial coverage of the data allows us to measure radial trends in the thickness of each MAP. While high-[a/Fe] MAPs have constant scale heights, low-[a/Fe] MAPs flare. We confirm, now with high-precision abundances, previous results that each MAP contains only a single vertical scale height and that low-[Fe/H], low-[a/Fe] and high-[Fe/H], high-[a/Fe] MAPs have intermediate (h_Z~300 to 600 pc) scale heights that smoothly bridge the traditional thin- and thick-disk divide. That the high-[a/Fe], thick disk components do not flare is strong evidence against their thickness being caused by radial migration. The correspondence between the radial structure and chemical-enrichment age of stellar populations is clear confirmation of the inside-out growth of galactic disks. The details of these relations will constrain the variety of physical conditions under which stars form throughout the MW disk.Comment: Code available at https://github.com/jobovy/apogee-map

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

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

Determination of population structure and stock composition of chum salmon (Oncorhynchus keta) in Russia determined with microsatellites

Variation at 14 microsatellite loci was examined in 34 chum salmon (Oncorhynchus keta) populations from Russia and evaluated for its use in the determination of population structure and stock composition in simulated mixed-stock fishery samples. The genetic differentiation index (Fst) over all populations and loci was 0.017, and individual locus values ranged from 0.003 to 0.054. Regional population structure was observed, and populations from Primorye, Sakhalin Island, and northeast Russia were the most distinct. Microsatellite variation provided evidence of a more fine-scale population structure than those that had previously been demonstrated with other genetic-based markers. Analysis of simulated mixed-stock samples indicated that accurate and precise regional estimates of stock composition were produced when the microsatellites were used to estimate stock compositions. Microsatellites can be used to determine stock composition in geographically separate Russian coastal chum salmon fisheries and provide a greater resolution of stock composition and population structure than that previously provided with other techniques