skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Stationary frequencies and mixing times for neutral drift processes with spatial structure
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types (``traits"), which can be discrete or continuous. Under minimal assumptions, we show that the marginal trait distributions of the evolutionary process, which specify the probability that any given individual has a certain trait, all converge to the stationary distribution of the mutation process. In particular, the stationary frequencies of traits in the population are independent of its size, spatial structure, and evolutionary update rule, and these frequencies can be calculated by evaluating a simple stochastic process describing a population of size one (i.e. the mutation process itself). We conclude by analyzing mixing times, which characterize rates of convergence of the mutation process along the lineages, in terms of demographic variables of the evolutionary process.  more » « less
Award ID(s):
1715315
PAR ID:
10101472
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences
Volume:
474
ISSN:
0080-4630
Page Range / eLocation ID:
20180238
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; (, Trends in Ecology & Evolution)
    We develop a conceptual framework for geo-evolutionary feedbacks which de- scribes the mutual interplay between landscape change and the evolution of traits of organisms residing on the landscape, with an emphasis on contempo- rary timeframes. Geo-evolutionary feedbacks can be realized via the direct evo- lution of geomorphic engineering traits or can be mediated by the evolution of trait variation that affects the population size and distribution of the specific geo- morphic engineering organisms involved. Organisms that modify their local envi- ronments provide the basis for patch-scale geo-evolutionary feedbacks, whereas spatial self-organization provides a mechanism for geo-evolutionary feedbacks at the landscape scale. Understanding these likely prevalent geo- evolutionary feedbacks, that occur at timescales similar to anthropogenic cli- mate change, will be essential to better predict landscape adaptive capacity and change. 
    more » « less
  2. ; ; (, Journal of Evolutionary Biology)
    Abstract Allometric scaling describes the relationship of trait size to body size within and among taxa. The slope of the population‐level regression of trait size against body size (i.e. static allometry) is typically invariant among closely related populations and species. Such invariance is commonly interpreted to reflect a combination of developmental and selective constraints that delimit a phenotypic space into which evolution could proceed most easily. Thus, understanding how allometric relationships do eventually evolve is important to understanding phenotypic diversification. In a lineage of fossil Threespine Stickleback (Gasterosteus doryssus), we investigated the evolvability of static allometric slopes for nine traits (five armour and four non‐armour) that evolved significant trait differences across 10 samples over 8500 years. The armour traits showed weak static allometric relationships and a mismatch between those slopes and observed evolution. This suggests that observed evolution in these traits was not constrained by relationships with body size, perhaps because prior, repeated adaptation to freshwater habitats by Threespine Stickleback had generated strong selection to break constraint. In contrast, for non‐armour traits, we found stronger allometric relationships. Those allometric slopes did evolve on short time scales. However, those changes were small and fluctuating and the slopes remained strong predictors of the evolutionary trajectory of trait means over time (i.e. evolutionary allometry), supporting the hypothesis of allometry as constraint. 
    more » « less
  3. ; ; ; ; ; (, Journal of Ecology)
    Abstract Evolutionary change begins at the population scale. Therefore, understanding adaptive variation requires the identification of the factors maintaining and shaping standing genetic variation at the within‐population level. Spatial and temporal environmental heterogeneity represent ecological drivers of within‐population genetic variation, determining the evolutionary trajectory of populations along with random processes. Here, we focused on the effects of spatiotemporal heterogeneity on quantitative and molecular variation in a natural population of the annual plant Arabidopsis thaliana . We sampled 1093 individuals from a Spanish A. thaliana population across an area of 7.4 ha for 10 years (2012–2021). Based on a sample of 279 maternal lines, we estimated spatiotemporal variation in life‐history traits and fitness from a common garden experiment. We genotyped 884 individuals with nuclear microsatellites to estimate spatiotemporal variation in genetic diversity. We assessed spatial patterns by estimating spatial autocorrelation of traits and fine‐scale genetic structure. We analysed the relationships between phenotypic variation, geographical location and genetic relatedness, as well as the effects of environmental suitability and genetic rarity on phenotypic variation. The common garden experiment indicated that there was more temporal than spatial variation in life‐history traits and fitness. Despite the differences among years, genetic distance in ecologically relevant traits (e.g. flowering time) tended to be positively correlated to genetic distance among maternal lines, while isolation by distance was less important. Genetic diversity exhibited significant spatial structure at short distances, which were consistent among years. Finally, genetic rarity, and not environmental suitability, accounted for genetic variation in life‐history traits. Synthesis . Our study highlighted the importance of repeated sampling to detect the large amount of genetic diversity at the quantitative and molecular levels that a single A. thaliana population can harbour. Overall, population genetic attributes estimated from our long‐term monitoring scheme (genetic relatedness and genetic rarity), rather than biological (dispersal) or ecological (vegetation types and environmental suitability) factors, emerged as the most important drivers of within‐population structure of phenotypic variation in A. thaliana . 
    more » « less
  4. ; ; (, Evolution)
    Abstract Sexual selection has a rich history of mathematical models that consider why preferences favor one trait phenotype over another (for population genetic models) or what specific trait value is preferred (for quantitative genetic models). Less common is exploration of the evolution of choosiness or preference strength: i.e., by how much a trait is preferred. We examine both population and quantitative genetic models of the evolution of preferences, specifically developing “baseline models” of the evolution of preference strength during the Fisher process. Using a population genetic approach, we find selection for stronger and stronger preferences when trait variation is maintained by mutation. However, this force is quite weak and likely to be swamped by drift in moderately-sized populations. In a quantitative genetic model, unimodal preferences will generally not evolve to be increasingly strong without bounds when male traits are under stabilizing viability selection, but evolve to extreme values when viability selection is directional. Our results highlight that different shapes of fitness and preference functions lead to qualitatively different trajectories for preference strength evolution ranging from no evolution to extreme evolution of preference strength. 
    more » « less
  5. ; ; ; ; (, Annual Review of Ecology, Evolution, and Systematics)
    Density-dependent selection, which promotes contrasting patterns of trait means at different population densities, has a long history in population genetics and ecology. The unifying principle from theory is that density-dependent selection operates on phenotypic traits whose values counter the effects of whatever ecological agent is limiting population growth, be it resource competition, predators, or pathogens. However, the complexity inherent in density dependence means that the same selective process can generate multiple outcomes, depending upon the details of how population density affects vital rates and the age or size structure of a population. Failure to appreciate the potential for multiple outcomes confounded many early studies of the process. Nonetheless, careful empirical work in laboratory studies, long-term field studies, and studies of sexual selection demonstrates the wide reach of density-dependent selection. The inconsistent outcomes observed in these studies call for renewed research into how the details of density dependence channel adaptive responses. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email