Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep.Comment: 29 page

Applying trait-based models to achieve functional targets for theory-driven ecological restoration

Manipulating community assemblages to achieve functional targets is a key component of restoring degraded ecosystems. The response-and-effect trait framework provides a conceptual foundation for translating restoration goals into functional trait targets, but a quantitative framework has been lacking for translating trait targets into assemblages of species that practitioners can actually manipulate. This study describes new trait-based models that can be used to generate ranges of species abundances to test theories about which traits, which trait values and which species assemblages are most effective for achieving functional outcomes. These models are generalisable, flexible tools that can be widely applied across many terrestrial ecosystems. Examples illustrate how the framework generates assemblages of indigenous species to (1) achieve desired community responses by applying the theories of environmental filtering, limiting similarity and competitive hierarchies, or (2) achieve desired effects on ecosystem functions by applying the theories of mass ratios and niche complementarity. Experimental applications of this framework will advance our understanding of how to set functional trait targets to achieve the desired restoration goals. A trait-based framework provides restoration ecology with a robust scaffold on which to apply fundamental ecological theory to maintain resilient and functioning ecosystems in a rapidly changing world

On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model

Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we cannot appeal to this result because trait values of different species are correlated due to shared evolutionary history. In this paper, we consider a $2$-state symmetric model for a single binary trait and investigate the theoretical properties of the MLE for the transition rate in the large-tree limit. Here, the large-tree limit is a theoretical scenario where the number of taxa increases to infinity and we can observe the trait values for all species. Specifically, we prove that the MLE converges to the true value under some regularity conditions. These conditions ensure that the tree shape is not too irregular, and holds for many practical scenarios such as trees with bounded edges, trees generated from the Yule (pure birth) process, and trees generated from the coalescent point process. Our result also provides an upper bound for the distance between the MLE and the true value

Controlling the Overfitting of Heritability in Genomic Selection through Cross Validation.

In genomic selection (GS), all the markers across the entire genome are used to conduct marker-assisted selection such that each quantitative trait locus of complex trait is in linkage disequilibrium with at least one marker. Although GS improves estimated breeding values and genetic gain, in most GS models genetic variance is estimated from training samples with many trait-irrelevant markers, which leads to severe overfitting in the calculation of trait heritability. In this study, we demonstrated overfitting heritability due to the inclusion of trait-irrelevant markers using a series of simulations, and such overfitting can be effectively controlled by cross validation experiment. In the proposed method, the genetic variance is simply the variance of the genetic values predicted through cross validation, the residual variance is the variance of the differences between the observed phenotypic values and the predicted genetic values, and these two resultant variance components are used for calculating the unbiased heritability. We also demonstrated that the heritability calculated through cross validation is equivalent to trait predictability, which objectively reflects the applicability of the GS models. The proposed method can be implemented with the Mixed Procedure in SAS or with our R package "GSMX" which is publically available at https://cran.r-project.org/web/packages/GSMX/index.html

Individualistic responses of forest herb traits to environmental change

Intraspecific trait variation (ITV; i.e. variability in mean and/or distribution of plant attribute values within species) can occur in response to multiple drivers. Environmental change and land-use legacies could directly alter trait values within species but could also affect them indirectly through changes in vegetation cover. Increasing variability in environmental conditions could lead to more ITV, but responses might differ among species. Disentangling these drivers on ITV is necessary to accurately predict plant community responses to global change. We planted herb communities into forest soils with and without a recent history of agriculture. Soils were collected across temperate European regions, while the 15 selected herb species had different colonizing abilities and affinities to forest habitat. These mesocosms (384) were exposed to two-level full-factorial treatments of warming, nitrogen addition and illumination. We measured plant height and specific leaf area (SLA). For the majority of species, mean plant height increased as vegetation cover increased in response to light addition, warming and agricultural legacy. The coefficient of variation (CV) for height was larger in fast-colonizing species. Mean SLA for vernal species increased with warming, while light addition generally decreased mean SLA for shade-tolerant species. Interactions between treatments were not important predictors. Environmental change treatments influenced ITV, either via increasing vegetation cover or by affecting trait values directly. Species' ITV was individualistic, i.e. species responded to different single resource and condition manipulations that benefited their growth in the short term. These individual responses could be important for altered community organization after a prolonged period

Symbolic Values, Value Formation and Interpersonal Relations

Interpersonal relations are shaped by the judgements associated with the social categories that individuals perceive in their social contacts. I develop a model of how those judgments form based on a theory of symbolic values. The model depicts the interaction between two values, one associated with an inherited ethnic trait ("nationality") and one with an endogenous achievement trait ("income"). Individuals who are less likely to achieve are predicted to invest more value on nationalism and to have hostile relations with immigrants. Multiple equilibria are possible and better schooling may eliminate equilibria with xenophobia. Econometric findings from three large surveys corroborate the predictions derived from the theoretical model.nationalism, immigration, interpersonal relations, value systems

Nationalism, cognitive ability, and interpersonal relations

Interpersonal relations are shaped by the judgements associated with the social categories that individuals perceive in their social contacts. I develop a model of how those judgments form based on a theory of symbolic values. The model depicts the interaction between two values, one associated with an inherited ethnic trait (nationality) and one with an endogenous achievement trait (income). Individuals with lower cognitive ability are predicted to invest more value on nationalism and to have hostile relations with immigrants. Multiple equilibria are possible and better schooling may eliminate equilibria with xenophobia. Econometric findings based on data from three large surveys corroborate the predictions derived from the theoretical model. --nationalism,xenophobia,interpersonal relations,value systems

Confidence intervals for test information and relative efficiency

In latent theory the measurement properties of a mental test can be expressed in the test information function. The relative merits of two tests for the same latent trait can be described by the relative efficiency function, i.e. the ratio of the test information functions. It is argued that these functions have to be estimated if the values of the item difficulties are unknown. Using conditional maximum likelihood estimation as indicated by Andersen (1973), pointwise asymptotic distributions of the test information and relative efficiency function are derived for the case of dichotomously scored Rasch homogeneous items. Formulas for confidence intervals are derived from the asymptotic distributions. An application to a mathematics test is given and extensions to other latent trait models are discussed