Linking quantitative genetics with community-level performance: Are there operational models for plant breeding?

Plant breeding is focused on the genotype and population levels while targeting effects at higher levels of biodiversity, from crop covers to agroecosystems. Making predictions across nested levels of biodiversity is therefore a major challenge for the development of intercropping practices. New prediction tools and concepts are required to design breeding strategies with desirable outcomes at the crop community level. We reviewed theoretical advances in the field of evolutionary ecology to identify potentially operational ways of predicting the effects of artificial selection on community-level performances. We identified three main types of approaches differing in the way they model interspecific indirect genetic effects (IIGEs) at the community level: (1) The community heritability approach estimates the variance for IIGE induced by a focal species at the community level; (2) the joint phenotype approach quantifies genetic constraints between direct genetic effects and IIGE for a set of interacting species; (3) the community-trait genetic gradient approach decomposes the IIGE for a focal species across a multivariate set of its functional traits. We discuss the potential operational capacities of these approaches and stress that each is a special case of a general multitrait and multispecies selection index. Choosing one therefore involves assumptions and goals regarding the breeding target and strategy. Obtaining reliable quantitative, community-level predictions at the genetic level is constrained by the size and complexity of the experimental designs usually required. Breeding strategies should instead be compared using theoretically informed qualitative predictions. The need to estimate genetic covariances between traits measured both within and among species (for IIGE) is another obstacle, as the two are not determined by the exact same biological processes. We suggest future research directions and strategies to overcome these limits. Our synthesis offers an integrative theoretical framework for breeders interested in the genetic improvement of crop communities but also for scientists interested in the genetic bases of plant community functioning.

A method to predict the response to directional selection using a Kalman filter

Predicting evolution remains challenging. The field of quantitative genetics provides predictions for the response to directional selection through the breeder's equation, but these predictions can have errors. The sources of these errors include omission of traits under selection, inaccurate estimates of genetic variance, and nonlinearities in the relationship between genetic and phenotypic variation. Previous research showed that the expected value of these prediction errors is often not zero, so predictions are systematically biased. Here, we propose that this bias, rather than being a nuisance, can be used to improve the predictions. We use this to develop a method to predict evolution, which is built on three key innovations. First, the method predicts change as the breeder's equation plus a bias term. Second, the method combines information from the breeder's equation and from the record of past changes in the mean to predict change using a Kalman filter. Third, the parameters of the filter are fitted in each generation using a learning algorithm on the record of past changes. We compare the method to the breeder's equation in two artificial selection experiments, one using the wing of the fruit fly and another using simulations that include a complex mapping of genotypes to phenotypes. The proposed method outperforms the breeder's equation, particularly when traits under selection are omitted from the analysis, when data are noisy, and when additive genetic variance is estimated inaccurately or not estimated at all. The proposed method is easy to apply, requiring only the trait means over past generations.

Why and How to Switch to Genomic Selection: Lessons From Plant and Animal Breeding Experience

The present study is a transversal analysis of the interest in genomic selection for plant and animal species. It focuses on the arguments that may convince breeders to switch to genomic selection. The arguments are classified into three different “bricks.” The first brick considers the addition of genotyping to improve the accuracy of the prediction of breeding values. The second consists of saving costs and/or shortening the breeding cycle by replacing all or a portion of the phenotyping effort with genotyping. The third concerns population management to improve the choice of parents to either optimize crossbreeding or maintain genetic diversity. We analyse the relevance of these different bricks for a wide range of animal and plant species and sought to explain the differences between species according to their biological specificities and the organization of breeding programs.

Environmental Change, If Unaccounted, Prevents Detection of Cryptic Evolution in a Wild Population

AbstractDetecting contemporary evolution requires demonstrating that genetic change has occurred. Mixed effects models allow estimation of quantitative genetic parameters and are widely used to study evolution in wild populations. However, predictions of evolution based on these parameters frequently fail to match observations. Here, we applied three commonly used quantitative genetic approaches to predict the evolution of size at maturity in a wild population of Trinidadian guppies. Crucially, we tested our predictions against evolutionary change observed in common-garden experiments performed on samples from the same population. We show that standard quantitative genetic models underestimated or failed to detect the cryptic evolution of this trait as demonstrated by the common-garden experiments. The models failed because (1) size at maturity and fitness both decreased with increases in population density, (2) offspring experienced higher population densities than their parents, and (3) selection on size was strongest at high densities. When we accounted for environmental change, predictions better matched observations in the common-garden experiments, although substantial uncertainty remained. Our results demonstrate that predictions of evolution are unreliable if environmental change is not appropriately captured in models.

Predicting Thermal Adaptation by Looking Into Populations' Genomic Past

Molecular evolution offers an insightful theory to interpret the genomic consequences of thermal adaptation to previous events of climate change beyond range shifts. However, disentangling often mixed footprints of selective and demographic processes from those due to lineage sorting, recombination rate variation, and genomic constrains is not trivial. Therefore, here we condense current and historical population genomic tools to study thermal adaptation and outline key developments (genomic prediction, machine learning) that might assist their utilization for improving forecasts of populations' responses to thermal variation. We start by summarizing how recent thermal-driven selective and demographic responses can be inferred by coalescent methods and in turn how quantitative genetic theory offers suitable multi-trait predictions over a few generations via the breeder's equation. We later assume that enough generations have passed as to display genomic signatures of divergent selection to thermal variation and describe how these footprints can be reconstructed using genome-wide association and selection scans or, alternatively, may be used for forward prediction over multiple generations under an infinitesimal genomic prediction model. Finally, we move deeper in time to comprehend the genomic consequences of thermal shifts at an evolutionary time scale by relying on phylogeographic approaches that allow for reticulate evolution and ecological parapatric speciation, and end by envisioning the potential of modern machine learning techniques to better inform long-term predictions. We conclude that foreseeing future thermal adaptive responses requires bridging the multiple spatial scales of historical and predictive environmental change research under modern cohesive approaches such as genomic prediction and machine learning frameworks.

Fundamental Theorems of Evolution

Evolutionary biology is undergirded by an extensive and impressive set of mathematical models. Yet only one result, Fisher's theorem about selection and fitness, is generally accorded the status of a fundamental theorem. I argue that although its fundamental status is justified by its simplicity and scope, there are additional results that seem similarly fundamental. I suggest that the most fundamental theorem of evolution is the Price equation, both because of its simplicity and broad scope and because it can be used to derive four other familiar results that are similarly fundamental: Fisher's average-excess equation, Robertson's secondary theorem of natural selection, the breeder's equation, and Fisher's fundamental theorem. These derivations clarify both the relationships behind these results and their assumptions. Slightly less fundamental results include those for multivariate evolution and social selection. A key feature of fundamental theorems is that they have great simplicity and scope, which are often achieved by sacrificing perfect accuracy. Quantitative genetics has been more productive of fundamental theorems than population genetics, probably because its empirical focus on unknown genotypes freed it from the tyranny of detail and allowed it to focus on general issues.

Quantitative genetics of genomic imprinting: a comparison of simple variance derivations, the effects of inbreeding, and response to selection

The level of expression of an imprinted gene is dependent on the sex of the parent from which it was inherited. As a result, reciprocal heterozygotes in a population may have different mean phenotypes for quantitative traits. Using standard quantitative genetic methods for deriving breeding values, population variances, and covariances between relatives, we demonstrate that although these approaches are equivalent under Mendelian expression, this equivalence is lost when genomic imprinting is acting. Imprinting introduces both parent-of-origin-dependent and generation-dependent effects that result in differences in the way additive and dominance effects are defined for the various approaches. Further, imprinting creates a covariance between additive and dominance terms absent under Mendelian expression, but the expression for this covariance cannot be derived using a number of the standard approaches for defining additive and dominance terms. Inbreeding also generates such a covariance, and we demonstrate that a modified method for partitioning variances can easily accommodate both inbreeding and imprinting. As with inbreeding, the concept of breeding values has no useful meaning for an imprinted trait. Finally, we derive the expression for the response to selection under imprinting, and conclude that the response to selection for an imprinted trait cannot be predicted from the breeder's equation, even when there is no dominance.