Introduction

Widespread and rapid environmental change is forcing many species to drastically alter how they interact with and respond to the environment (Hoffman & Sgro 2011). As these changes become harder to mitigate and manage, imperilled populations may survive by shifting their geographic range, through phenotypic plasticity, or via genetic adaptation (Nunney 2015). It is, however, increasingly difficult for populations to shift their range because many plant and animal species are now in fragmented habitat and do not possess the dispersal ability to navigate between suitable patches (Tingley et al . 2009). It is also unclear how often plasticity will provide a long term advantage since plasticity may or may not be aligned in an adaptive direction, and may also reduce the effectiveness of natural selection in driving adaptation to changing conditions (Ghalambor et al. 2007; Chevin & Hoffman 2017; Nobleet al . 2019). Genetic adaptation is clearly the most robust solution to directional environmental change, and for populations with suitable standing genetic variation, rapid adaptation may forestall extinction through evolutionary rescue (Bell et al. 2019; Harriset al. 2019). But for many species, necessary traits are either locally absent or at low frequencies, slowing the evolutionary response and priming populations for extinction (Lacey 1997; Hoffman et al. 2017).
One way to increase the chance of evolutionary rescue is to provide populations with the genetic variation necessary for adaptation. Some strategies advocate simply increasing genetic variation, in a non-directional manner. Such “genetic rescue” is particularly powerful when populations have low diversity and are suffering inbreeding depression (Lande & Shannon 1996; Hedrick & Fredrickson 2010). Other strategies take a more targeted approach, seeking to increase genetic variation in the direction needed to adapt. This idea of introducing individuals with pre-adapted traits into a population was first proposed as a possible response to the impact of climate change, where the idea was termed “assisted gene flow”. It is, however, a strategy that can be applied to broad suite of conservation problems, and in recognition of this broader application we refer to it here as “targeted gene flow”. Conservation managers have already begun to employ targeted gene flow (hereafter TGF) with the aim of increasing the frequency of pre-adapted traits in threatened populations (Aitken et al. 2013; Kelly & Phillips 2016, 2018; Weeks et al. 2017; Indigo et al. 2018).
As with any conservation action, TGF carries both risk and cost. Relative to other conservation actions, TGF will tend to be very cost effective, but it is not without risk: outbreeding depression (Frankhamet al. 2011), genetic swamping, and disease transmission (Cunningham 1996; Sainsbury & Vaughan-Higgins 2012) are all possibilities to be considered. Because of risks and costs, any conservation action needs to be characterized to allow scenario-testing, cost-benefit analysis, and to provide managers with realistic expectations (Knight et al. 2006a; Weeks et al. 2011) While conservation managers regularly use population models to assess alternative scenarios, adaptive evolutionary processes are rarely included in models of population viability (Lacey 2019) or in cost-benefit exercises (Klein et al. 2009). By its nature, TGF requires models that incorporate evolution into population viability and cost-benefit analyses.
The stated aims of conservation translocations are usually to create or maintain viable populations of a single, focal species, with measures of success based on abundance, extent, resilience, persistence, or any combination of the above (Pavlik 1996; Vallee et al. 2004). With TGF we also want a viable population, but we want to avoid swamping the local genome in the process. Swamping the local genome is akin to extinction and reintroduction, and one of the great promises of TGF is that we might both prevent extinction and conserve local genetic diversity in the process: the aim being to manipulate populations so that they are not only locally adapted but carry genes that allow them to survive under future environmental shifts (Harris et al.2019). Given the complexity of prioritizing management actions across multiple measures of success, we need a clear statement of our management objective (Regan et al. 2005). Here we propose a robust objective: to keep the recipient population extant and to achieve this whilst maintaining the genetic diversity currently present. While extinction is straightforward, diversity is a rich concept that admits a wide range of possible definitions (see Morris et al. (2014)). We focus here on the maintenance of genetic diversity through maintaining, as far as possible, the set of alleles that are initially present in the recipient population. This provides an objective that considers not only the richness of genetic material remaining but the evenness at which this material occurs. Aside from the total number of alleles present in a population the distribution of their abundances is also an important component of diversity. If an allele is represented in only a tiny percentage of individuals, it should be clear that it contributes less to the population’s diversity than an allele represented in 50% of the population. The importance of allelic evenness has received less attention than that of richness but its value seems inarguable.
We equate our management objective to a gambler’s return on investment: the probability of winning (avoiding extinction) multiplied by the payout (the remaining allelic diversity). To achieve this, we incorporate our probability of ‘winning’ (1 – x ), where xis the extinction probability, with a common measure of genetic diversity, the Gini-Simpson Index . The Gini-Simpson Index of diversity (D ) is equivalent to the expected heterozygosity under Hardy-Weinberg equilibrium and is a common measure of diversity (Guiasu & Guiasu 2012; Morris et al. 2014), where 1 represents maximum diversity, and 0, no diversity. Thus our objective is to maximise the expected return:
Where we calculate D using only alleles initially present in the recipient population. The problem we address is a general one: how does varying key management levers (the timing and size of the introduced cohort) influence the expected return of a TGF action? We explore this question across a range of scenarios of environmental change ranging from near step changes to a much more gradual environmental shift. We explore the influence of a continuous gradual shift in the environment, similar to climate change projections (IPCC ARC6 Climate Change 2018), as well as threats that constitute a shorter, more drastic change in environmental suitability, such as the introduction of a wildlife disease or the invasion of a pest species.
We utilize a discrete-time individual-based population model with the goal of exploring the optimal timing and size of a TGF action across various scenarios of environmental change. Our model is structured such that it is flexible across study species and various projections of environmental change. Against our new management objective, we explore the sensitivity of the optimal choice of management strategy across a wide range of demographic, evolutionary and environmental parameter values.