A framework for estimating the fixation time of an advantageous allele in stepping-stone models

The active spread of adaptive variation for reef resilience

The speed at which species adapt depends partly on the rates of beneficial adaptation generation and how quickly they spread within and among populations. Natural rates of adaptation of corals may not be able to keep pace with climate warming. Several interventions have been proposed to fast-track thermal adaptation, including the intentional translocation of warm-adapted adults or their offspring (assisted gene flow, AGF) and the ex situ crossing of warm-adapted corals with conspecifics from cooler reefs (hybridization or selective breeding) and field deployment of those offspring. The introgression of temperature tolerance loci into the genomic background of cooler-environment corals aims to facilitate adaptation to warming while maintaining fitness under local conditions. Here we use research on selective sweeps and connectivity to understand the spread of adaptive variants as it applies to AGF on the Great Barrier Reef (GBR), focusing on the genus Acropora. Using larval biophysical dispersal modeling, we estimate levels of natural connectivity in warm-adapted northern corals. We then model the spread of adaptive variants from single and multiple reefs and assess if the natural and assisted spread of adaptive variants will occur fast enough to prepare receiving central and southern populations given current rates of warming. We also estimate fixation rates and spatial extent of fixation under multiple release scenarios to inform intervention design. Our results suggest that thermal tolerance is unlikely to spread beyond northern reefs to the central and southern GBR without intervention, and if it does, 30+ generations are needed for adaptive gene variants to reach fixation even under multiple release scenarios. We argue that if translocation, breeding, and reseeding risks are managed, AGF using multiple release reefs can be beneficial for the restoration of coral populations. These interventions should be considered in addition to conventional management and accompanied by strong mitigation of CO2 emissions.

Simulating the spread of selection-driven genotypes using landscape resistance models for desert bighorn sheep

Landscape genetic studies based on neutral genetic markers have contributed to our understanding of the influence of landscape composition and configuration on gene flow and genetic variation. However, the potential for species to adapt to changing landscapes will depend on how natural selection influences adaptive genetic variation. We demonstrate how landscape resistance models can be combined with genetic simulations incorporating natural selection to explore how the spread of adaptive variation is affected by landscape characteristics, using desert bighorn sheep (Ovis canadensis nelsoni) in three differing regions of the southwestern United States as an example. We conducted genetic sampling and least-cost path modeling to optimize landscape resistance models independently for each region, and then simulated the spread of an adaptive allele favored by selection across each region. Optimized landscape resistance models differed between regions with respect to landscape variables included and their relationships to resistance, but the slope of terrain and the presence of water barriers and major roads had the greatest impacts on gene flow. Genetic simulations showed that differences among landscapes strongly influenced spread of adaptive genetic variation, with faster spread (1) in landscapes with more continuously distributed habitat and (2) when a pre-existing allele (i.e., standing genetic variation) rather than a novel allele (i.e., mutation) served as the source of adaptive genetic variation. The combination of landscape resistance models and genetic simulations has broad conservation applications and can facilitate comparisons of adaptive potential within and between landscapes.

Gene drive through a landscape: Reaction-diffusion models of population suppression and elimination by a sex ratio distorter

Some genes or gene complexes are transmitted from parents to offspring at a greater-than-Mendelian rate, and can spread and persist in populations even if they cause some harm to the individuals carrying them. Such genes may be useful for controlling populations or species that are harmful. Driving-Y chromosomes may be particularly potent in this regard, as they produce a male-biased sex ratio that, if sufficiently extreme, can lead to population elimination. To better understand the potential of such genes to spread over a landscape, we have developed a series of reaction-diffusion models of a driving-Y chromosome in 1-D and radially-symmetric 2-D unbounded domains. The wild-type system at carrying capacity is found to be unstable to the introduction of driving-Y males for all models investigated. Numerical solutions exhibit travelling wave pulses and fronts, and analytical and semi-analytical solutions for the asymptotic wave speed under bounded initial conditions are derived. The driving-Y male invades the wild-type equilibrium state at the front of the wave and completely replaces the wild-type males, leaving behind, at the tail of the wave, a reduced- or zero-population state of females and driving-Y males only. In our simplest model of a population with one life stage and density-dependent mortality, wave speed depends on the strength of drive and the diffusion rate of Y-drive males, and is independent of the population dynamic consequences (suppression or elimination). Incorporating an immobile juvenile stage of fixed duration into the model reduces wave speed approximately in proportion to the relative time spent as a juvenile. If females mate just once in their life, storing sperm for subsequent reproduction, then wave speed depends on the movement of mated females as well as Y-drive males, and may be faster or slower than in the multiple-mating model, depending on the relative duration of juvenile and adult life stages. Numerical solutions are shown for parameter values that may in part be representative for Anopheles gambiae, the primary vector of malaria in sub-Saharan Africa.