A Guide for Developing Demo-Genetic Models to Simulate Genetic Rescue

Abstract

Genetic rescue is a conservation management strategy that reduces the negative effects of genetic drift and inbreeding in small and isolated populations. However, such populations might already be vulnerable to random fluctuations in growth rates (demographic stochasticity). Therefore, the success of genetic rescue depends not only on the genetic composition of the source and target populations but also on the emergent outcome of interacting demographic processes and other stochastic events. Developing predictive models that account for feedback between demographic and genetic processes ('demo-genetic feedback') is therefore necessary to guide the implementation of genetic rescue to minimize the risk of extinction of threatened populations. Here, we explain how the mutual reinforcement of genetic drift, inbreeding, and demographic stochasticity increases extinction risk in small populations. We then describe how these processes can be modelled by parameterizing underlying mechanisms, including deleterious mutations with partial dominance and demographic rates with variances that increase as abundance declines. We combine our suggestions of model parameterization with a comparison of the relevant capability and flexibility of five open-source programs designed for building genetically explicit, individual-based simulations. Using one of the programs, we provide a heuristic model to demonstrate that simulated genetic rescue can delay extinction of small virtual populations that would otherwise be exposed to greater extinction risk due to demo-genetic feedback. We then use a case study of threatened Australian marsupials to demonstrate that published genetic data can be used in one or all stages of model development and application, including parameterization, calibration, and validation. We highlight that genetic rescue can be simulated with either virtual or empirical sequence variation (or a hybrid approach) and suggest that model-based decision-making should be informed by ranking the sensitivity of predicted probability/time to extinction to variation in model parameters (e.g., translocation size, frequency, source populations) among different genetic-rescue scenarios.

Keywords: SLiM; conservation genetics; demography; density feedback; inbreeding depression; marsupials; software.

FIGURE 1

An example of demo‐genetic feedback in genetic rescue. (a, and inset b) Populations below a threshold abundance (N) often exhibit decreasing per‐capita population growth rates (r) at lower N, which is a type of density dependence known as depensation. This contrasts with the compensation that is typical of density feedback at larger population sizes (represented by the Ricker logistic model of linear decline in r with increasing N). The dotted vertical line denoted by K represents the population size at carrying capacity, which is mathematically defined as the long‐term mean population density (or size, N) where r = 0. (b, c) Several mechanisms cause depensation, including (c) demographic stochasticity (random fluctuations in population growth rate or abundance) due to increased variance in demographic rates (e.g., survival, fertility) at small population sizes, and (d) genetic effects due to increased genetic drift and inbreeding at small population sizes, which increase the realized genetic load and reduce mean fitness. The mutually reinforcing interaction between demographic and genetic effects increases extinction probability in small populations (i.e., the extinction vortex). Ecological and behavioral mechanisms of depensation (e.g., mate limitation, social structure disruptions) that give rise to what is also referred to as the Allee effect (Courchamp et al. 1999) are not shown to retain a focus on demo‐genetic‐feedback mechanisms. Genetic drift and inbreeding can also be considered akin to genetic mechanisms of the Allee effect (Luque et al. 2016). It is these genetic mechanisms of population depensation that genetic rescue specifically seeks to reduce.

FIGURE 2

Individual‐based models of demo‐genetic feedback and simulations of applied genetic‐rescue scenarios. Left panel: The discrete and random nature of individual‐level and genetic mechanisms causing demographic and genetic stochasticity to emerge at the population scale (blue‐shaded box). Stochastic processes cause fluctuations in per‐capita population growth rate and the frequency and expression of deleterious alleles. Mutual reinforcement of demographic and genetic processes is driven by the effect of mean fitness on per‐capita growth rate and density feedback, as well as the strength of demographic and genetic processes (within the blue‐shaded box) on per‐capita growth rate and realized genetic load. We suggest how to link individual‐level and genetic mechanisms to model parameters in Table 2. We provide the capability and flexibility of available software for specifying parameters in Table 3. Right panel: Once the individual‐based, demo‐genetic model is parameterized and calibrated, it can be used to simulate the outcome of alternative scenarios of (virtual) genetic‐rescue interventions. Scenarios can be compared and ranked according to their relative success in decreasing mean time to extinction (T _ext ) and the probability of extinction (Pr(extinct)), at time t (‘outcome’ metrics). We provide a guide to the application of model simulations to inform genetic rescue in section Using simulations to inform applied genetic rescue.

FIGURE 3

Fluctuations in population abundance. Example simulations of different models that demonstrate the influence of (a) demographic stochasticity, (b) genetic effects, (c) demo‐genetic feedback, and (d) genetic rescue (scenario 4; see description in text) on abundance (N) over time. Each panel (a–d) shows two time series that were both run in parallel for a burn‐in of 10,000 simulation cycles (≈ years) and both reach an equilibrium N that fluctuated around the carrying capacity K ₁ of 2000 individuals. In each panel, the time series at the top represents the control population with N maintained at K ₁. The time series at the bottom of each panel represents the focal population that experienced an abrupt crash in N at cycle 10,001 to a new K ₂ = 500. Each panel shows a representative sample of up to 17 iterations of the simulation scenario (n = 120 per scenario in model results in main text). Each iteration shows a different trajectory of population abundance over time until extinction (at which point we stopped both control and focal population iterations and restarted them in the next iteration). The effect of demo‐genetic feedback on extinction probability is illustrated by comparing the bottom time series of (c) to that of (a) and (b). The effect of genetic rescue is illustrated by comparing the bottom time series of (c) with that of (d). Scale of the y axes differs between upper and lower plots in each panel.

FIGURE 4

Comparing the outcomes of (a) models that incorporate different component effects, and (b) four genetic‐rescue scenarios (see description in text) based on the demo‐genetic model on population viability. Grey‐shaded violin plots (with black dots indicating individual simulations) show time to extinction (T _ext, left y axis) measured in simulation cycles (≈ years) starting from the abrupt demographic decline of the focal population from a carrying capacity (K ₁) = 2000 during the burn‐in period to K ₂ = 500 individuals. Solid horizontal blue lines show median T _ext, and dashed blue lines show quartiles. Red dots show extinction probability (right y axis), Pr(ext) = 1 minus the proportion of iterations where the focal population was extant at 1500 years (simulation cycles) after the abundance decline. The control populations (K ₁ ) in all scenarios had no extinctions and 100% persistence probability. ∞ = no extinction. The main outcomes to note are: (i) simulations of the demo‐genetic base model (a) had higher extinction probability (red dots) and shorter time to extinction (violin plots) than base models that only incorporated demographic or genetic components, respectively; and (ii) simulated genetic rescue reduced extinction probability by 3%–9% relative to the demo‐genetic base model, with scenario 4 having the greatest reduction.