Sharp habitat shifts, evolutionary tipping points and rescue: Quantifying the perilous path of a specialist species toward a refugium in a changing environment.

Specialist species thriving under specific environmental conditions in narrow geographic ranges are widely recognised as heavily threatened by climate deregulation. Many might rely on both their potential to adapt and to disperse toward a refugium to avoid extinction. It is thus crucial to understand the influence of environmental conditions on the unfolding process of adaptation. Here, I study the eco-evolutionary dynamics of a sexually reproducing specialist species in a two-patch quantitative genetic model with moving optima. Thanks to a separation of ecological and evolutionary time scales and the phase-line study of the selection gradient, I derive the critical environmental speed for persistence, which reflects how the existence of a refugium impacts extinction patterns and how it relates to the cost of dispersal. Moreover, the analysis provides key insights about the dynamics that arise on the path towards this refugium. I show that after an initial increase of population size, there exists a critical environmental speed above which the species crosses a tipping point, resulting into an abrupt habitat switch. In addition, when selection for local adaptation is strong, this habitat switch passes through an evolutionary "death valley", leading to a phenomenon related to evolutionary rescue, which can promote extinction for lower environmental speeds than the critical one.

The Fisher process of sexual selection with the coevolution of preference strength.

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.

Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal?

When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to close the resulting system of equations, they often assume the local trait distributions are Gaussian [see for instance Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 )]. The aim of this paper is to introduce a mathematical framework that follows the whole trait distribution (without prior assumption) to study evolutionary dynamics of sexually reproducing populations. Specifically, it focuses on complex traits, whose inheritance can be encoded by the infinitesimal model of segregation (Fisher in Trans R Soc Edinb 52(2):399-433, 1919. https://doi.org/10.1017/S0080456800012163 ). We show that it allows us to derive a regime in which our model gives the same dynamics as when assuming Gaussian local trait distributions. To support that, we compare the stationary problems of the system of moments derived from our model with the one given in Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 ) and show that they are equivalent under this regime and do not need to be otherwise. Moreover, under this regime of equivalence, we show that a separation bewteen ecological and evolutionary time scales arises. A fast relaxation toward monomorphism allows us to reduce the complexity of the system of moments, using a slow-fast analysis. This reduction leads us to complete, still in this regime, the analytical description of the bistable asymmetrical equilibria numerically found in Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 ). More globally, we provide explicit modelling hypotheses that allow for such local adaptation patterns to occur.

Orthogonal contrast based models for quantitative genetic analysis in autotetraploid species.

Dissecting the genetic architecture of quantitative traits is a crucial goal for efficient breeding of polyploid plants, including autotetraploid crop species, such as potato and coffee, and ornamentals such as rose. To meet this goal, a quantitative genetic model is needed to link the genetic effects of genes or genotypes at quantitative trait loci (QTL) to the phenotype of quantitative traits. We present a statistically tractable quantitative genetic model for autotetraploids based on orthogonal contrast comparisons in the general linear model. The new methods are suitable for autotetraploid species with any population genetic structure and take full account of the essential features of autotetrasomic inheritance. The statistical properties of the new methods are explored and compared to an alternative method in the literature by simulation studies. We have shown how these methods can be applied for quantitative genetic analysis in autotetraploids by analysing trait phenotype data from an autotetraploid potato segregating population. Using trait segregation analysis, we showed that both highly heritable traits of flowering time and plant height were under the control of major QTL. The orthogonal model directly dissects genetic variance into independent components and gives consistent estimates of genetic effects provided that tetrasomic gene segregation is considered.

Integrating Genetic and Demographic Effects of Connectivity on Population Stability: The Case of Hatchery Trucking in Salmon.

Connectivity among populations can have counteracting effects on population stability. Demographically, connectivity can rescue local populations but increase the synchrony across populations. Genetically, connectivity can counteract drift locally but homogenize genotypes across populations. Population independence and diversity underlies system-level buffering against environmental variability, termed the portfolio effect. The portfolio effect has declined in California fall-run Chinook salmon, possibly in part because of the trucking of juvenile hatchery-reared fish for downstream release, which reduces juvenile mortality but increases the connectivity between rivers. We use a dynamical population model to test whether this increased connectivity can explain the loss of the portfolio effect and quantify the relative demographic and genetic contributions to portfolio effect erosion. In the model, populations experience different within-population environmental conditions and the same time-variable ocean conditions, the response to which can depend on a quantitative genetic trait. We find that increased trucking for one population's hatchery can lead to a loss of the portfolio effect, with a system-level trade-off between increased average abundance and increased variability in abundance. This trade-off is much stronger when we include the effects of genetic homogenization than when we consider demographic synchronization alone. Therefore, genetic homogenization can outweigh demographic synchrony in determining the system-level effect of connectivity.

Incorporating an ontogenetic perspective into evolutionary theory of sexual size dimorphism.

Sexual size dimorphism (SSD) describes divergent body sizes of adult males and females. While SSD has traditionally been explained by sexual and fecundity selection, recent advances in physiology and developmental biology emphasize that SSD would occur proximately because of sexual differences in ontogenetic growth trajectories (i.e., growth rate and duration). Notably, these ontogenetic traits are subject to energetic or time constraints and thus traded off with fitness components (e.g., survival and reproduction). To elucidate the importance of such ontogenetic trade-offs in the evolution of SSD, we developed a new theoretical framework by extending quantitative genetic models for the evolution of sexual dimorphism in which we reinterpret the trait as body size and reformulate sex-specific fitness in size-dependent manners. More specifically, we assume that higher growth rate or longer growth duration leads to larger body size and higher reproductive success but incurs the cost of lower survivorship or shorter reproduction period. We illustrate how two sexes would optimize ontogenetic growth trajectories in sex-specific ways and exhibit divergent body sizes. The present framework provides new insights into the evolutionary theory of SSD and predictions for empirical testing.

A statistical model for QTL mapping in polysomic autotetraploids underlying double reduction.

As a group of economically important species, linkage mapping of polysomic autotetraploids, including potato, sugarcane and rose, is difficult to conduct due to their unique meiotic property of double reduction that allows sister chromatids to enter into the same gamete. We describe and assess a statistical model for mapping quantitative trait loci (QTLs) in polysomic autotetraploids. The model incorporates double reduction, built in the mixture model-based framework and implemented with the expectation-maximization algorithm. It allows the simultaneous estimation of QTL positions, QTL effects and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We performed computer simulation to examine the statistical properties of the method and validate its use through analyzing real data in tetraploid switchgrass.

Assessing strategies to minimize unintended fitness consequences of aquaculture on wild populations.

Artificial propagation programs focused on production, such as commercial aquaculture or forestry, entail strong domestication selection. Spillover from such programs can cause unintended fitness and demographic consequences for wild conspecifics. The range of possible management practices to minimize such consequences vary in their control of genetic and demographic processes. Here, we use a model of coupled genetic and demographic dynamics to evaluate alternative management approaches to minimizing unintended consequences of aquaculture escapees. We find that, if strong natural selection occurs between escape and reproduction, an extremely maladapted (i.e., nonlocal-origin, highly domesticated) stock could have fitness consequences analogous to a weakly diverged cultured stock; otherwise, wild population fitness declines with increasing maladaptation in the cultured stock. Reducing escapees through low-level leakage is more effective than reducing an analogous number of escapees from large, rare pulses. This result arises because low-level leakage leads to the continual lowering of wild population fitness and subsequent increased proportional contribution of maladapted cultured escapees to the total population. Increased sterilization efficacy can cause rapid, nonlinear reductions in unintended fitness consequences. Finally, sensitivity to the stage of escape indicates a need for improved monitoring data on how the number of escapees varies across life cycle stages.

A QUANTITATIVE-GENETIC MODEL FOR SELECTION ON DEVELOPMENTAL NOISE.

We propose a simple model for analyzing the effects of microenvironmental variation in quantitative genetics. Our model assumes that the sensitivity of the phenotype to fluctuations in microenvironment has a genetic basis and allows for genetic correlation between trait value and microenvironmental sensitivity. We analyze the effects of short-term stabilizing and directional selection on the genotypic and microenvironmental components of phenotypic variance. Our model predicts that stabilizing selection on a quantitative trait increases developmental canalization. We show that stabilizing selection can result in an increase in the heritability. Our findings may provide an explanation for the results of selection experiments in which artificial stabilizing selection did not change the heritability coefficient or increased it.