Amaïa Lamarins
email: amaia.lamarins@inrae.fr

Florèn Hugon

Cyril Piou

Julien Papaïx

Etienne Prévost

Stephanie M Carlson

Mathieu Buoro

Implications of dispersal in Atlantic salmon: lessons from a demo-genetic agent-based model

Keywords: Atlantic salmon, demo-genetic agent-based model, dispersal, eco-evolutionary dynamics, metapopulation, portfolio effect, synchrony

Despite growing evidence of spatial dispersal and gene flow between salmonid populations, the implications of connectivity for adaptation, conservation, and management are still poorly appreciated. Here, we explore the influence of a gradient of dispersal rates on portfolio strength and eco-evolutionary dynamics in a simulated population network of Atlantic salmon (Salmo salar) by extending a demo-genetic agent-based model to a spatially explicit framework. Our model results highlight a non-linear relationship between dispersal rates and the stability of the metapopulation, resulting in an optimal portfolio effect for dispersal rates around 20%. At local population scale, we also demonstrate phenotypic changes induced by density-dependent effects modulated by dispersal, and a dispersal-induced increase in genetic diversity. We conclude that it is critical to account for complex interactions between dispersal and ecoevolutionary processes and discuss future avenues of research that could be addressed by such modeling approaches to more fully appreciate responses of Atlantic salmon to environmental changes and investigate management actions accordingly.

INTRODUCTION

Rapid environmental changes and associated selection pressures are affecting the adaptive capacity and persistence of many species globally [START_REF] Ceballos | Accelerated modern human-induced species losses: Entering the sixth mass extinction[END_REF]. Consequently, there is considerable interest in understanding species responses to current and predicted global changes [START_REF] Urban | Improving the forecast for biodiversity under climate change[END_REF]. This ambitious goal requires not only a consideration of the different processes and mechanisms facilitating species adaptation, persistence, and stability but also their interactions. Ideally such processes and interactions would be studied in a single, integrative framework and the field of eco-evolutionary dynamics provides such a context [START_REF] Hendry | Eco-evolutionary Dynamics. Page Eco-evolutionary Dynamics[END_REF]. Ultimately, this framework should guide management and conservation practices to maintain adaptive capacity and persistence of natural resources.

The main eco-evolutionary processes underlying species adaptation and responses to environmental changes include phenotypic plasticity (or acclimatization) and genetic adaptation of traits in response to natural selection [START_REF] Reed | Interacting Effects of Phenotypic Plasticity and Evolution on Population Persistence in a Changing Climate[END_REF]). These processes shape a great diversity of life-history traits that can be phenotypic (e.g., growth, behavior) or phenological (e.g., reproduction timing). These life-history traits are not only influenced by environmental and genetic factors, but also by complex interactions between individuals (e.g., sexual selection) and demographic processes such as density-dependence effects. Accounting for relevant eco-evolutionary processes (e.g., sexual selection) and their underlying mechanisms (e.g., genetic architecture and transmission) in empirical and theoretical approaches is necessary to fully appreciate populations dynamics and responses to environmental changes.

Dispersal or the movement of individuals from their natal population to a different breeding population, is ubiquitous in nature and is also a process that promotes species responses to environmental change by spreading the risk of reproductive failure (Ronce 2007, Buoro andCarlson 2014). There is growing appreciation -from both theory and empirical studies -of the causes and consequences of dispersal [START_REF] Clobert | Informed dispersal, heterogeneity in animal dispersal syndromes and the dynamics of spatially structured populations[END_REF][START_REF] Clobert | Dispersal Ecology and Evolution[END_REF]. For example, dispersal and gene flow among interconnected populations can induce genotypic and demographic consequences on recipient populations [START_REF] Cayuela | Demographic and genetic approaches to study dispersal in wild animal populations: A methodological review[END_REF]. This may prevent the extirpation of local populations via rescue effects (see [START_REF] Carlson | Evolutionary rescue in a changing world[END_REF] for review) but also lead to "antirescue effects" [START_REF] Harding | A unifying framework for metapopulation dynamics[END_REF] and reduce metapopulation diversity through the homogenizing effect of dispersal [START_REF] Paradis | Dispersal and spatial scale affect synchrony in spatial population dynamics[END_REF][START_REF] Lenormand | Gene flow and the limits to natural selection[END_REF]. Within a metapopulation context [START_REF] Hanski | Metapopulation dynamics[END_REF], the connectivity among populations is critical because it has consequences for the dynamics of local populations and the whole metapopulation. Thus, we would expect eco-evolutionary dynamics of a metapopulation to differ from that of a single population taken in isolation, highlighting the need to consider eco-evolutionary processes, feedback loops, and the spatial structure of populations within a single, coherent framework.

More generally, the resilience of ecological systems, such as a metapopulation, relies on the connectivity and the diversity of responses of its components [START_REF] Elmqvist | Response diversity, ecosystem change, and resilience[END_REF][START_REF] Webster | Who Should Pick the Winners of Climate Change?[END_REF]. Indeed, there is growing recognition that a diverse network of populations can promote overall stability of population complexes and resource flows (e.g., fishery yields, [START_REF] Schindler | Population diversity and the portfolio effect in an exploited species[END_REF]. Ecological portfolio theory emphasizes the importance of biocomplexity, or life history diversity within and among populations [START_REF] Hilborn | Biocomplexity and fisheries sustainability[END_REF][START_REF] Abbott | Portfolio effects, climate change, and the persistence of small populations: analyses on the rare plant Saussurea weberi[END_REF], as well as asynchronous dynamics among populations as factors contributing to stability of population complexes [START_REF] Schindler | Population diversity and the portfolio effect in an exploited species[END_REF][START_REF] Schindler | The portfolio concept in ecology and evolution[END_REF]. The portfolio effect has been studied extensively in imperiled and exploited salmonid species, especially for Pacific salmonids (e.g., [START_REF] Moore | Synchronization and portfolio performance of threatened salmon[END_REF][START_REF] Carlson | Weakened portfolio effect in a collapsed salmon population complex[END_REF][START_REF] Anderson | Portfolio conservation of metapopulations under climate change[END_REF]). However, the potential influence of dispersal among salmon populations on portfolio strength has received less attention (but see [START_REF] Yeakel | Eco-evolutionary dynamics, density-dependent dispersal and collective behaviour: implications for salmon metapopulation robustness[END_REF].

Dispersal rates are often considered low in salmonids (Schtickzelle andQuinn 2007, Birnie-Gauvin et al. 2019), even though identification of dispersers (or "strayers") and dispersal rates remain difficult to assess in wild populations. For instance, Atlantic salmon (Salmo salar) is well known for its great diversity of life-history strategies linked to phenotypic plasticity (Mangel andSatterthwaite 2016, Erkinaro et al. 2019) and genetic basis of life history traits (e.g., age at maturation, [START_REF] Barson | Sex-dependent dominance at a single locus maintains variation in age at maturity in salmon[END_REF][START_REF] Lepais | Genetic architecture of threshold reaction norms for male alternative reproductive tactics in Atlantic salmon (Salmo salar L.)[END_REF]), but it is also commonly presented as a highly philopatric species [START_REF] Salmenkova | Mechanisms of homing in salmonids[END_REF]). Yet, evidence of dispersal behavior and gene flow have been reported between several populations of Atlantic salmon (e.g., [START_REF] Consuegra | Asymmetric gene flow and the evolutionary maintenance of genetic diversity in small, peripheral Atlantic salmon populations[END_REF], see Keefer and Caudill 2014 for review), allowing recolonization and expansion [START_REF] Makhrov | Atlantic salmon colonization of the Russian Arctic coast: pioneers from North America[END_REF][START_REF] Perrier | Natural recolonization of the Seine River by Atlantic salmon (Salmo salar) of multiple origins[END_REF][START_REF] Pess | Re-colonization of Atlantic and Pacific rivers by anadromous fishes: linkages between life history and the benefits of barrier removal[END_REF]. However, few studies have estimated dispersal rates between wild populations of Atlantic salmon (but see [START_REF] Jonsson | Differences in life history and migratory behaviour between wild and hatchery-reared Atlantic salmon in nature[END_REF], 2003[START_REF] Consuegra | Asymmetric gene flow and the evolutionary maintenance of genetic diversity in small, peripheral Atlantic salmon populations[END_REF][START_REF] Jonsson | Maternal inheritance influences homing and growth of hybrid offspring between wild and farmed Atlantic salmon[END_REF], and even fewer discuss or assess the potential consequences of metapopulation functioning on conservation and management of Atlantic salmon populations (but see Castellani et al. 2015, Bowlby and[START_REF] Bowlby | Evaluating whether metapopulation structure benefits endangered diadromous fishes[END_REF]. As suggested by [START_REF] Schtickzelle | A metapopulation perspective for salmon and other anadromous fish[END_REF], future work should strategically consider salmon dynamics from a metapopulation perspective.

Modeling approaches can overcome the difficulties associated with examining dispersal consequences in nature. Among them, classical metapopulation theory, demographic, patch occupancy models [START_REF] Hanski | Metapopulation dynamics[END_REF][START_REF] Hanski | Metapopulation Ecology[END_REF][START_REF] Sutherland | A demographic, spatially explicit patch occupancy model of metapopulation dynamics and persistence[END_REF][START_REF] Bowlby | Evaluating whether metapopulation structure benefits endangered diadromous fishes[END_REF] Gibson 2020 for salmonids), as well as evolutionary analytical models [START_REF] Berdahl | On the evolutionary interplay between dispersal and local adaptation in heterogeneous environments[END_REF][START_REF] Yeakel | Eco-evolutionary dynamics, density-dependent dispersal and collective behaviour: implications for salmon metapopulation robustness[END_REF], have advanced general concepts in metapopulation functioning and persistence. Mechanistic eco-evolutionary models such as Demo-Genetic Agent-Based Models (DG-ABMs, also called Eco-Genetic ABMs) provide a complementary and flexible approach for simulating the complexity of a species life cycle (DeAngelis and [START_REF] Deangelis | Individual-based models in ecology after four decades[END_REF][START_REF] Stillman | Making Predictions in a Changing World: The Benefits of Individual-Based Ecology[END_REF] and assessing the demo-genetic consequences of dispersal in a unified framework. By integrating variation and interactions between individuals, as well as explicit genetic basis of traits and their transmission, this approach allows life-history traits to evolve in interaction with demographic effects in response to environmental and anthropogenic pressures [START_REF] Dunlop | Eco-genetic modeling of contemporary life-history evolution[END_REF], Johnston et al. 2019). Recently, several generic metapopulation DG-ABMs have emerged such as Nemo [START_REF] Guillaume | Nemo: an evolutionary and population genetics programming framework[END_REF], SimAdapt [START_REF] Rebaudo | SimAdapt: an individual-based genetic model for simulating landscape management impacts on populations[END_REF], RangeShifter [START_REF] Bocedi | RangeShifter: a platform for modelling spatial eco-evolutionary dynamics and species' responses to environmental changes[END_REF][START_REF] Bocedi | RangeShifter 2.0: an extended and enhanced platform for modelling spatial eco-evolutionary dynamics and species' responses to environmental changes[END_REF] or CDMetaPOP [START_REF] Landguth | CDMetaPOP: an individualbased, eco-evolutionary model for spatially explicit simulation of landscape demogenetics[END_REF]. Several specific DG-ABMs represent the complex life cycle of salmonid species (e.g., [START_REF] Thériault | The impact of fishing-induced mortality on the evolution of alternative life-history tactics in brook charr[END_REF][START_REF] Ayllón | InSTREAM-Gen: Modelling eco-evolutionary dynamics of trout populations under anthropogenic environmental change[END_REF], but only two studies incorporate dispersal between populations to our knowledge. [START_REF] Landguth | CDMetaPOP: an individualbased, eco-evolutionary model for spatially explicit simulation of landscape demogenetics[END_REF] simulate a network of non-native Eastern Brook Trout (Salvelinus fontinalis) populations and evaluate efficiency of fish removal management strategies taking into account dispersal between patches. [START_REF] Lin | Modeling local adaptation and gene flow in sockeye salmon[END_REF] extended a single population model of sockeye salmon (Oncorhynchus nerka) to two populations to assess the consequences of dispersal on local adaptation and demography. We build on this general approach, but with a focus on Atlantic salmon, to explore dispersal implications within a realistic network of populations and an eco-evolutionary framework.

Our ultimate goal is to shed light on the potential implications of dispersal on the portfolio effect and eco-evolutionary dynamics in Atlantic salmon. To do so, we extended a demogenetic agent-based model of Atlantic salmon (IBASAM, Piou and Prévost 2012) to a metapopulation context. The original IBASAM model was developped to evaluate eco-evolutionary responses to climate change and selective exploitation (Piou andPrévost 2013, Piou et al. 2015). It includes most of the knowledge available today on the eco-evolutionary processes and mechanisms of this species. However, IBASAM was designed to mimic a single population with complete philopatry, so we incorporated a dispersal process to simulate a realistic network of fifteen Atlantic salmon populations [START_REF] Bouchard | Synchrony in population dynamics of juvenile Atlantic salmon: analyzing spatiotemporal variation and the influence of river flow and demography[END_REF]. By doing so, our model allows an investigation of the consequences of dispersal on local populations and network dynamics at the demographic, phenotypic, and genotypic levels. In this article, we first describe the main features of the model. Second, we test a gradient of dispersal rates and examine consequences for network stability, synchrony, local extinction risk, and life-history traits. Finally, we highlight pending questions that could be addressed with a more explicit consideration of dispersal, including basic studies related to eco-evolutionary dynamics of Atlantic salmon metapopulations and practical management questions relevant to connected populations of this exploited species.

MODEL DESCRIPTION: MetaIBASAM, A SPATIALLY STRUCTURED VERSION OF IBASAM

The model presented here is a simple extension of the Individual-Based Atlantic Salmon Model (IBASAM) proposed by [START_REF] Piou | A demo-genetic individual-based model for Atlantic salmon populations: Model structure, parameterization and sensitivity[END_REF] (winter and summer). A set of traits are genetically determined and can be transmitted to their offspring, including maturation tactics and growth capacity, using a bi-allelic multilocus system (see section 2.1.3.). 2.1.2. Density and environment effects on life-history traits

In the model, life-history traits of individuals are influenced both by density-dependent and density-independent processes (Fig. 1). For instance, survival from the egg stage to emergence and growth of juveniles in freshwater are impacted by water temperature and stream flow [START_REF] Baum | The effect of temperature on growth and early maturation in a wild population of Atlantic salmon parr[END_REF][START_REF] Jonsson | Does climate during embryonic development influence parr growth and age of seaward migration in Atlantic salmon (Salmo salar)?[END_REF], but also by negative density-dependence effects [START_REF] Imre | Density-Dependent Growth of Young-of-the-Year Atlantic Salmon Salmo salar in Catamaran Brook, New Brunswick[END_REF]. The seaward migration decision ("smoltification") is based on a probabilistic sizedependent reaction norm [START_REF] Buoro | Investigating evolutionary trade-offs in wild populations of atlantic salmon (salmo salar): incorporating detection probabilities and individual heterogeneity[END_REF]. Marine conditions also affect individual lifehistory traits through growth and size-dependent survival at sea.

Heritable traits and selective pressures

Life-history traits can also evolve in response to selective pressures in IBASAM. Maturation decision in river and sea has been implemented using the environmental threshold model [START_REF] Piché | Genetic variation in threshold reaction norms for alternative reproductive tactics in male Atlantic salmon, Salmo salar[END_REF][START_REF] Lepais | Genetic architecture of threshold reaction norms for male alternative reproductive tactics in Atlantic salmon (Salmo salar L.)[END_REF]. The maturation decision is based on a comparison between the individual value of the threshold (genetically determined) and the individual energetic reserves (growth-related and environmentally determined, Fig. 1). The maturation thresholds (varying between river and sea, as well as male and female) can thus evolve under natural selection, which then influences the age at maturation in the population (precocious males vs. time at sea). These traits are supported by a genetic architecture which is a combination of the quantitative genetics framework and the Mendelian inheritance system. Specifically, the phenotype expression of the traits above results from the additive effect of its genetic and environmental components based on heritability and the genetic value (so-called breeding value) controlled by a bi-allelic multilocus genotype with a variable number of loci.

Sexual selection is known as an important selective pressure in fish (Kodric-Brown 1990). In IBASAM, there is an advantage in reproductive success for larger females (higher fecundity and access to anadromous males), and a sexual selection for large anadromous males by females [START_REF] Fleming | Reproductive strategies of Atlantic salmon: ecology and evolution[END_REF][START_REF] Fleming | Pattern and variability in the breeding system of Atlantic salmon (Salmo salar), with comparisons to other salmonids[END_REF]. Though a fraction of the maturing parr can also reproduce based on observations of "sneaker" behavior [START_REF] Fleming | Reproductive strategies of Atlantic salmon: ecology and evolution[END_REF], there is no sexual selection by females.

Model improvements: a genetic basis of growth and a growth -survival trade-off

While growth depends mainly on environmental conditions encountered by individuals, we introduced a genetic basis for the growth potential parameter as suggested by [START_REF] Gjerde | Estimates of genetic and phenotypic parameters for body weight, growth rate and sexual maturity in Atlantic salmon[END_REF]. However, preliminary analysis showed that including a genetic basis to growth potential led to its evolution toward higher values, resulting in larger individuals over time (see Supporting information 1). Indeed, because sea survival and reproductive success depend positively on size and growth [START_REF] Piou | A demo-genetic individual-based model for Atlantic salmon populations: Model structure, parameterization and sensitivity[END_REF], natural and sexual selection tend to favor larger individuals with higher growth potential. To limit this directional selection and represent mortality costs of rapid growth as reported in experimental studies [START_REF] Bochdansky | Experimental evidence for selection against fish larvae with high metabolic rates in a food limited environment[END_REF][START_REF] Biro | Behavioural trade-offs between growth and mortality explain evolution of submaximal growth rates[END_REF], we implemented a growth-survival trade-off in river (Fig. 1, Supporting information 1; survival at sea is size-dependent). Combined with the sizedependent survival at sea and reproductive success, the growth-survival trade-off induces a stabilizing selection for growth and size and an optimal fitness value of growth potential (Fig. and [START_REF] Lin | Modeling local adaptation and gene flow in sockeye salmon[END_REF], we assume that (1) philopatry is constant over space and time, (2) dispersal is not phenotypically and genotypically determined. However, in our model the choice of recipient population is based on a dispersal kernel that depends on distance from the natal river and the attractiveness of the recipient population (see [START_REF] Nathan | Evidence for spatial coherence in time trends of marine life history traits of Atlantic salmon in the North Atlantic[END_REF] for review).

At the time of adult riverward migration, dispersing individuals are randomly selected from their population of origin j with a probability to disperse P j , independently from their individual characteristics (Equation 1). The probability P j is function of a constant philopatry rate (noted h), i.e., without variation between populations, fixed at initialization. Then, for the subset of dispersing individuals, the recipient population j' is determined by sampling into a multinomial distribution of parameter p j,j' , which is the probability to disperse from the population j to the population j'.

𝑃 𝑗 = 1 -ℎ 𝑗 = 𝑛 ∑ 𝑗 ′ = 1, 𝑗 ≠ 𝑗 ′ 𝑝 𝑗,𝑗 ′ (1)
With P j the total dispersal rate of the population j and h the philopatry rate.

This matrix of dispersal probabilities p represents the connectivity between populations and is derived from a dispersal kernel (Fig. 2 B). Here, we assume that dispersal probability p j,j'

between two populations j and j' is a function of the distance between their estuaries, D j,j' . We use the Laplace distribution, a leptokurtic distribution commonly used for fish [START_REF] Pépino | Fish dispersal in fragmented landscapes: a modeling framework for quantifying the permeability of structural barriers[END_REF], which maximizes the connectivity between close populations while still allowing some flow of individuals between distant rivers (long-distance dispersal, Equation 2). Because the attractiveness of rivers for anadromous salmonids can vary as a function of the population size, likely because of chemical attraction to congeners, collective behavior, and/or the influence of river discharge [START_REF] Jonsson | Atlantic salmon straying from the River Imsa[END_REF][START_REF] Berdahl | A collective navigation hypothesis for homeward migration in anadromous salmonids[END_REF]; see Keefer and Caudill 2014 for review), we weigh the distance kernel by a parameter g j' , the relative size of the destination population with other populations, to represent its attractiveness (Equation 3). The larger the populations, the more attractive they are to dispersing individuals.

𝑝 𝑗,𝑗 ′ (𝐷 𝑗,𝑗 ′ , 𝑏) = 𝑔 𝑗 ′ × 1 2𝑏 × 𝑒𝑥𝑝 ( - 𝐷 𝑗,𝑗′ 𝑏 ) (2) with 𝑔 𝑗 ′ = log10 (𝐴 𝑗 ′ ) ∑ 𝐴 𝑛𝑝𝑜𝑝 𝐴 1 log10 (𝐴 𝑗 ′ ) (3)
With b the mean dispersal distance in the metapopulation and A j' the production area of juveniles of river j', considered as a proxy of population size.

Altogether, the dispersal kernel assumes that a given migrant fish will tend to disperse to the nearest population from its natal river but this will be moderated by the "attractiveness" (i.e., the relative population size) of nearby rivers (Fig. 2 B). Even with a constant dispersal rate over space and time, the spatial structure of the population network, the demography of local populations, and the dispersal kernel lead to various immigration rates between populations.

Model parameterization and outputs

MetaIBASAM consists of a set of IBASAM sessions -with one session simulating one population -running in parallel and exchanging information about the dispersers (e.g., phenotypic, genetic values, and genotypes). Similar to IBASAM, MetaIBASAM was parameterized in a pattern-oriented modeling framework [START_REF] Grimm | Pattern-oriented modeling of agent-based complex systems: lessons from ecology[END_REF] survival rates at different life stages and a temperature-survival related parameter (dr) that have been adjusted (Supporting information 2) to updated environmental conditions (see section 3.1). The parameter b of dispersal kernel was adjusted to limit dispersal under 50km for at least 80% of dispersers individuals, as suggested by [START_REF] Jonsson | Atlantic salmon straying from the River Imsa[END_REF] and [START_REF] Keefer | Homing and straying by anadromous salmonids: a review of mechanisms and rates[END_REF]. Daily water temperature, water discharge, marine growth conditions, and exploitation are the main environmental and anthropogenic factors affecting individuals in the model (Fig. 1).

IBASAM is coded in C++ language, and an R package named MetaIBASAM has been developed (https://github.com/Ibasam/MetaIBASAM). Each IBASAM can be parametrized by users to represent a unique population with its own demographic (area, distance), phenotypic, genetic (initial distribution), environmental (water temperature, discharge), and anthropogenic (exploitation rate) characteristics. One simulation of MetaIBASAM returns all information on individuals (e.g., unique ID, population of origin, current population, body size, genetic values)

and nests (e.g., ID of parents, number of eggs) two times per year for each population.

APPLICATION: CONSEQUENCES OF A GRADIENT OF DISPERSAL RATES ON LOCAL POPULATIONS AND METAPOPULATION DYNAMICS

Scenario and parameterization

To investigate the consequences of dispersal on Atlantic salmon metapopulation dynamics and persistence, we ran the model for a gradient of dispersal rates P from 0% to 50%, corresponding to a large range of variation encompassing rates of straying that have been reported in the wild The network is composed of fifteen major populations (small coastal rivers) of different river sizes and distances between each pair. We gathered the area of juvenile production of each population (population area A j ), measured annually by the angling club federations, and the distance between their estuaries (Supporting information 2). Note that the objective was not to accurately mimic each population but to define a realistic spatial configuration and diversity of demographic characteristics to explore eco-evolutionary questions. Beyond population size and distance between pairs of populations, all other parameters are the same for all populations (e.g., environmental conditions, trait distributions at initialization, etc.) for all dispersal scenarios. In doing so, we can isolate the effect of dispersal on portfolio strength from the effects of biocomplexity and diversity of population responses.

We simulated a daily time series of water temperature and water discharge for each river, with the same regime (average and amplitude) but no spatial covariation to focus on the role of dispersal and spatial structure in populations dynamics. The different models and data used to simulate these series, as well as the parameters estimated, are detailed in Supporting information 3. The daily effects of marine growth conditions on the fish are drawn from a normal distribution of similar mean and standard deviation between the populations.

Exploitation rates (7% and 15% for 1SW and MSW individuals respectively, [START_REF] Lebot | Taking full advantage of the diverse assemblage of data at hand to produce time series of abundance: a case study on Atlantic salmon populations of Brittany[END_REF] were kept identical across populations.

Simulations were initialized for each population using a random draw of individuals corresponding to 25% of rivers production area A j only to limit the computing time without loss of generality. Phenotypic and genetic values were sampled using the same distributions implemented in IBASAM (see [START_REF] Piou | A demo-genetic individual-based model for Atlantic salmon populations: Model structure, parameterization and sensitivity[END_REF]. Since generation time for this species is approximately 2.5 years in French populations, we simulated each dispersal scenario and population network over 50 years, which is sufficient time to detect any changes in the population dynamics and evolution of life-history traits. For each dispersal scenario, we simulated 100 replicates with a 10-year burn-in period. We ran the simulation using R version 3.6.3 and the package MetaIbasam version 0.0.6. Code and R scripts are freely available at https://github.com/Ibasam/Portfolio. 3.2. Simulations outcomes analysis 3.2.1. Network spatial structure

In our application set up, each population was independently "stable", i.e., was not growing or declining. Thus, while source-sink populations are commonly determined based on demography (growth rate) and immigrants rates, we classified each population as sink, neutral, or source based on the ratio of incoming individuals (immigrants) to outgoing individuals (emigrants) in the sea-adult returns. We considered populations with a ratio above one as sinks, those with a ratio below one as sources, whereas the neutral populations have a ratio near one.

Regardless of the fixed dispersal rate, source-sink dynamics within a network of fifteen populations emerged from the model due to asymmetric dispersal that was driven by differences in population size and spatial structure (Fig. 3 A and B). For example, larger populations generated more emigrants, and more isolated populations received less immigrants but "sent" the same proportion of emigrants. The ratio between immigrants and emigrants was highly variable between populations, as well as the proportion of immigrants, which ranged from 4% to 27% for dispersal rates of 10%. But the source-sink dynamics among populations within the network remained similar between dispersal scenarios or over time (Fig. 3 A).

Demographic consequences of dispersal: population network stability, synchrony, and persistence

For each dispersal scenario and simulation, we measured the stability and diversity of the network using the portfolio effect and synchrony metrics. The portfolio effect (hereafter PE) is a metric measuring the stabilizing effect of population diversity on metapopulation dynamics [START_REF] Schindler | Population diversity and the portfolio effect in an exploited species[END_REF], by comparing the measured metapopulation variance over the time series to the theoretical variance expected if the metapopulation was considered as a unique population. To do so, we used the mean-variance method from the R package ecofolio [START_REF] Anderson | Ecological prophets: quantifying metapopulation portfolio effects[END_REF]. Using this approach, if this ratio equals 1, it means that the network is as stable as expected if it was a single population. If the ratio exceeds 1, it suggests evidence of a portfolio effect. For example, a ratio of 1.25 means that the variance of the metapopulation dynamic is reduced by 25% as compared to a scenario where the metapopulation acts as a single population, and so on.

The synchrony index ϕ x , reflecting the degree of population synchrony in their demographic evolution over time, was measured as the ratio between the detrended network variance σ x ² and the squared sum of populations detrended standard deviation σ xi (adapted from Loreau and de Mazancourt 2008, Equation 4). This index is expressed between 0 (asynchrony) and 1 (synchrony).

𝜑 𝑥 = 𝜎 2 𝑥 ( ∑ 𝑖 𝜎 𝑥 𝑖 )² (4)
For each dispersal scenario and simulation, a population's stability was measured through the coefficient of variation of adult returns number over the 40 last years. A population viability analysis was also performed for each scenario. In particular, we evaluated the quasi-extinction risk for each population as the proportion of simulations where the abundance was at least two consecutive years below an "at-risk" threshold (defined as 5% of the population carrying capacity Rmax, adjusted in Piou and Prévost 2012, Supporting information 2).

Our analyses revealed a non-linear relationship between dispersal and stability of the population network, resulting in an optimal portfolio effect for dispersal rates around 20%, i.e., 80% of a population returning to its natal site (Fig. 4 A). With strict philopatry (i.e., no dispersal), the PE was on average above 1, meaning that the population network was more stable than expected if it was the sum of the local populations. Indeed, the dynamics of all populations were stable and asynchronous (φ~0.1; Fig. 4 B). Between dispersal rates of 0% and 10-20%, the PE was increasing, suggesting a stabilizing effect of low dispersal rates followed by a gradual decline in the PE with dispersal rates above 20%. This declining trend of network stability with high dispersal rates can be explained by the synchronizing effect of dispersal, which counter-balances its initial positive effect. Indeed, we found that the synchrony of population dynamics was increasing linearly with dispersal (+70% from 0 to 50% of dispersal, Fig. 4 B).

At the local population level, dispersal tended to decrease the coefficient of variation of the abundance of adult returns, suggesting a stabilizing effect of dispersal on population dynamics (Fig. 4 C). Dispersal rates also reduced the extinction risk of small and sink populations, whereas the extinction risk of other populations appeared insensitive to dispersal (Fig. 4 D).

Altogether, these results suggest a demographic rescue of populations by dispersal, especially for those behaving as sink populations.

Intra-and interpopulation phenotypic and genotypic diversity

Our results showed that dispersal per se can induce phenotypic diversity between populations.

Indeed, we observed a slight decrease of median juvenile and adult size with dispersal for sink populations and an increase in source populations, which might have consequences on lifehistory tactics illustrated by shifts in the age at sea maturation (Fig. 5,A,B,D). Note that we assessed phenotypic changes on philopatric individuals only, to test the consequences of dispersal on each population's trait distribution without the direct influence of immigrants. As immigrants do not differ from philopatric adults in terms of size and growth potential at initialization, this unexpected result could be explained by density-dependent effects on river growth. Indeed, dispersal increased juveniles density in sink populations (due to higher immigration than emigration) and decreased it in source ones (Supporting information 4), affecting juvenile growth and adult life history traits as a consequence. This effect was less visible when considering phenotypic traits of all individuals (philopatric adults and immigrants) of populations (Supporting information 5).

As expected due to similar genetic distribution parameters at initialization between populations, no interpopulation genotypic diversity emerged with dispersal (Fig. 5 C).

However, dispersal rates rapidly increased intrapopulation genetic variance in sink populations (Fig. 6).

DISCUSSION

We aimed to draw attention to the consequences of dispersal on the portfolio effect and ecoevolutionary dynamics of Atlantic salmon. To do so, we extended a demo-genetic agent-based model (IBASAM, Piou and Prévost 2012) into a metapopulation framework by integrating a dispersal process to simulate a set of fifteen interconnected populations of Atlantic salmon (MetaIBASAM). MetaIBASAM is freely available and can be modified to mimic various networks of Atlantic salmon populations and their demo-genetic characteristics. Although similar models exist (see Table 1), whether generic or applied to salmonid species, our model was designed to reproduce the life cycle of Atlantic salmon by integrating the knowledge available on this species. Moreover, it has been calibrated on one of the populations constituting the network of populations in Brittany. In particular, we used a simple but realistic spatial network to explore the influence of dispersal on stability and rescue effects. Our model induced a source-sink dynamic, though all populations showed stable dynamics. Despite this parsimonious design (populations only differ in their size and distance between each pair), we showed that dispersal rates from 10% to 50% can have significant consequences on persistence (at both local and metapopulation levels), stability, phenotypic and genetic features. Below we expand on these results and also highlight the potential of demo-genetic ABMs (such as MetaIBASAM focused on Atlantic salmon) to identify knowledge gaps and investigate dispersal, adaptive capacity, and responses of metapopulations to environmental change and management practices.

Evidence of a non-linear relationship between dispersal and portfolio effect: stabilizing vs synchronizing effects of dispersal

Our study emphasizes a non-linear relationship between dispersal rates and the stability of the metapopulation, resulting in an optimal portfolio effect for dispersal rates around 20% with the particular parameterization of our model. Using a network of two populations, Yeakel et al.

(2018) also found non-linear effects of dispersal on metapopulation robustness (PE) and identified two optimums (strongest PE, called alternative stable state regimes in their paper) at levels of dispersal below 10% and 30% of the population respectively. Interestingly, the optimal dispersal rate that we report is consistent with the few empirical studies reporting dispersal rates in Atlantic salmon [START_REF] Jonsson | Atlantic salmon straying from the River Imsa[END_REF][START_REF] Jonsson | Differences in life history and migratory behaviour between wild and hatchery-reared Atlantic salmon in nature[END_REF], 2017[START_REF] Keefer | Homing and straying by anadromous salmonids: a review of mechanisms and rates[END_REF]. However, it is important to note that it might depend on the adjustment of the dispersal kernel parameter and reported rates in the literature are highly variable and likely biased (e.g., site/year dependence, low sample size, hatchery influence; [START_REF] Jonsson | Atlantic salmon straying from the River Imsa[END_REF][START_REF] Consuegra | Asymmetric gene flow and the evolutionary maintenance of genetic diversity in small, peripheral Atlantic salmon populations[END_REF][START_REF] Jonsson | Maternal inheritance influences homing and growth of hybrid offspring between wild and farmed Atlantic salmon[END_REF][START_REF] Keefer | Homing and straying by anadromous salmonids: a review of mechanisms and rates[END_REF]. When the dispersal rate was below 20% in our model, dispersal had a stabilizing effect on population dynamics and fostered the demographic rescue of small, sink populations by increasing population size and/or limiting demographic stochasticity. Using a theoretical two-patch metapopulation model, [START_REF] Hill | The Effects of Small Dispersal Rates on Extinction Times in Structured Metapopulation Models[END_REF] also demonstrated that dispersal rates between 0% and 20% increased the time before extinction two-to four-fold, and a recent Population Viability Analysis revealed the benefit of population connectivity for persistence of diadromous fishes more generally under high productivity scenarios [START_REF] Bowlby | Evaluating whether metapopulation structure benefits endangered diadromous fishes[END_REF]. However, we found that the positive effects of dispersal on metapopulation stability are overcome by increased synchronization of population dynamics with higher dispersal rates (>20%), which could increase the metapopulation risk of collapse [START_REF] Carlson | Weakened portfolio effect in a collapsed salmon population complex[END_REF]. The "antirescue" effects [START_REF] Harding | A unifying framework for metapopulation dynamics[END_REF] associated with higher dispersal rates have been demonstrated both theoretically and empirically on patterns of synchrony [START_REF] Paradis | Dispersal and spatial scale affect synchrony in spatial population dynamics[END_REF][START_REF] Yeakel | Eco-evolutionary dynamics, density-dependent dispersal and collective behaviour: implications for salmon metapopulation robustness[END_REF]), but also on genetic homogenization [START_REF] Tinnert | The role of dispersal for genetic and phenotypic variation: insights from comparisons of sympatric pygmy grasshoppers[END_REF], and reduced local adaptation [START_REF] Schiffers | Limited evolutionary rescue of locally adapted populations facing climate change[END_REF].

The parsimonious configuration we simulated, using phenotypically and genetically homogeneous populations, did not allow us to fully consider the homogenizing effect of dispersal. But introducing more variability between populations in their demographic dynamics (e.g., unstable trends) or in their phenotypic and genotypic composition would open up new perspectives to better address the portfolio effect. However, we found that intrapopulation genetic variance was enhanced in sink populations receiving immigrants from nearby populations, potentially increasing adaptive capacity [START_REF] Jump | Environmental change and the option value of genetic diversity[END_REF][START_REF] Seaborn | Building a bridge between adaptive capacity and adaptive potential to understand responses to environmental change[END_REF]).

In our study, populations did not show inbreeding depression, but one can assume that dispersal might reduce it through genetic rescue. More surprisingly, interpopulation phenotypic diversity also emerged from the dispersal process. Indeed, the asymmetric flows between source and sink populations within the network induced phenotypic changes via density-dependent effects on the growth of individuals rearing in the river, ultimately influencing their life-history strategies (e.g., age at maturation) through phenotypic plasticity. Altogether, we show that there may be a dispersal optimum at the metapopulation level that favors its stability (i.e., portfolio effect), and selection should favor local dispersal rates (within populations) that tend towards this metapopulation optimum. Thus, metapopulation optimum value would depend on species characteristics (e.g., propensity to disperse), spatial configuration (e.g., distance between populations), but also local population features (e.g., population size, density, environmental conditions, attractiveness, local adaptation, costs of migration, etc.).

Model significance, limits, and perspectives

Like any modeling study, our results are influenced by the model structure (functional relationships, parameterization, etc.) and hypotheses retained in MetaIBASAM. However, our study showcases the utility of agent-based models as virtual laboratories for exploring the possible consequences of poorly understood processes and mechanisms on eco-evolutionary dynamics, in particular dispersal which is difficult to study in the wild. Here, we used MetaIBASAM to demonstrate the implications of dispersal on the persistence and dynamics of a network of Atlantic salmon populations. Although it was not our intention to represent the dynamics of a particular Atlantic salmon metapopulation, the network modelled here was realistic both in its complex spatial scale and structure. This provided a unique source-sink metapopulation with a diversity of local dynamics, showing variable consequences of dispersal on local populations depending on their spatial distribution and demographic features.

Additionally, by its integrative nature, our modeling approach took into account all ecoevolutionary processes involved and allowed the emergence of non-trivial patterns because of complex interactions between these processes. Overall, our approach emphasizes the importance of assessing the demographic, phenotypic, and genetic consequences of dispersal in metapopulations in a single framework.

However, despite the model complexity, some processes are still represented in an overly simplified manner, especially the causes of dispersal. Like other models focused on salmonids (see Table 1), we simulated dispersal as a random individual process, with a probability of dispersing that was constant in space and time, and limited to a fixed expansion range. and theoretical models are starting to explicitly include phases of dispersal since it may strongly influence patterns of dispersal (e.g., [START_REF] Travis | Modelling dispersal: an ecoevolutionary framework incorporating emigration, movement, settlement behaviour and the multiple costs involved[END_REF][START_REF] Bocedi | RangeShifter: a platform for modelling spatial eco-evolutionary dynamics and species' responses to environmental changes[END_REF]). However, identification of these three phases and knowledge of the underlying mechanisms are still limited in salmonids. By integrating these mechanisms (e.g., condition and densitydependence, genetic basis) in our model, we could expect dispersal rates to vary in space (between populations) and time. This could sharpen our results on the relationship between dispersal and metapopulation stability.

2/ We need to evaluate how diversity between and within populations may shape an adaptation network fostering response to environmental changes.

Our study focused on the consequences of dispersal scenarios to shed light on the influence of connectivity alone on eco-evolutionary processes. However, adaptation network theory (Webster et al. 2017, Fig. 7) states that the resilience of ecological systems, such as metapopulation, relies on the connectivity as well as response diversity of its components [START_REF] Elmqvist | Response diversity, ecosystem change, and resilience[END_REF]. Recent theoretical studies of coral reefs have emphasized that population diversity is beneficial for metapopulation persistence and stability in the context of a changing and uncertain climate [START_REF] Walsworth | Management for network diversity speeds evolutionary adaptation to climate change[END_REF], McManus et al. 2021a). Moreover, among population variability in thermal tolerance (e.g., [START_REF] Eliason | Differences in Thermal Tolerance Among Sockeye Salmon Populations[END_REF][START_REF] Mckenzie | Intraspecific variation in tolerance of warming in fishes[END_REF] could increase species resistance to climate change especially if associated with dispersal (fostering evolutionary rescue). Evaluating the adaptation network theory in this context should Prior work has warned about the danger of ignoring spatial structure and connectivity of populations [START_REF] Cooper | The dangers of ignoring metapopulation structure for the conservation of salmonids[END_REF], but few studies have compared different management strategies while also considering the spatial structure of populations (but see [START_REF] Tufto | Effective size in management and conservation of subdivided populations[END_REF]Hindar 2003, Moore et al. 2021). While mixed-stock fisheries explicitly consider variation in productivity among harvested stocks, rarely is connectivity considered. Our preliminary results

suggest that any alteration in a source population could affect demography and phenotypic traits of surrounding populations. Moreover, selective exploitation within spatially structured populations could drive complex evolutionary trajectories in the whole network -whether local populations are exploited or not -because selective exploitation can induce evolution of life history traits [START_REF] Piou | Modelling the interactive effects of selective fishing and environmental change on Atlantic salmon demogenetics[END_REF][START_REF] Ayllón | Eco-evolutionary responses to recreational fishing under different harvest regulations[END_REF].

Conclusions

In summary, we have introduced a metapopulation version of IBASAM, MetaIBASAM, a demo-genetic agent based model of Atlantic salmon populations, which we believe provides a useful and flexible framework to fill knowledge gaps about the role of dispersal in Atlantic salmon metapopulation eco-evolutionary dynamics and portfolio strength. We highlight the importance of dispersal for metapopulation stability and evolutionary pathways. Additionally, we discuss ideas for future directions using the model to explore responses of interconnected Atlantic salmon populations to environmental change and spatially structured management.

Finally, we advocate for a management of populations within the adaptation network framework [START_REF] Webster | Who Should Pick the Winners of Climate Change?[END_REF], Fig. 7) because maintaining diversity and evolutionary options within a network of populations is a critical step for fostering species persistence and stability in the face of environmental change [START_REF] Walsworth | Management for network diversity speeds evolutionary adaptation to climate change[END_REF].

ACKNOWLEDGEMENTS

  2 A), ensuring stable size distributions in a neutral context (without selection, Supporting information 1). 2.3. Dispersal modeling: extending IBASAM into a metapopulation context MetaIBASAM considers the connectivity between populations by implementing a dispersal process, i.e., adults can disperse toward other rivers of the system during their breeding 12 migration. While there is growing interest in understanding factors influencing salmon dispersal (see Keefer and Caudill 2014 for review, and Westley et al. 2015 for a discussion of collective behavior), quantitative estimations of dispersal are rare and the underlying mechanisms remain poorly understood. In line with models proposed by Landguth et al. (2017)

  (e.g.,[START_REF] Consuegra | Asymmetric gene flow and the evolutionary maintenance of genetic diversity in small, peripheral Atlantic salmon populations[END_REF]; see Keefer and Caudill 2014 for review). The spatial structure of the network in the model is inspired by the salmon populations of Brittany (France;[START_REF] Bouchard | Synchrony in population dynamics of juvenile Atlantic salmon: analyzing spatiotemporal variation and the influence of river flow and demography[END_REF], see also Supporting information 2), for which one population (Scorff) was used to calibrate IBASAM, and gene flow among populations was demonstrated[START_REF] Perrier | Determinants of hierarchical genetic structure in Atlantic salmon populations: environmental factors vs. anthropogenic influences[END_REF]).

  Yet, it has been shown in several species and also suggested for salmonids that dispersal depends on individuals traits (e.g., sex-biased dispersal,[START_REF] Li | Sex-biased dispersal: a review of the theory[END_REF] Kokko 2019, genetic basis, Saastamoinen et al. 2018) or populations characteristics (e.g., density-dependent dispersal,[START_REF] Berdahl | A collective navigation hypothesis for homeward migration in anadromous salmonids[END_REF]). These features might modify the intensity and direction of flow of individuals and the consequences of our dispersal scenarios, because dispersal could evolve towards dispersal rates which optimize the portfolio effect. For example,[START_REF] Berdahl | On the evolutionary interplay between dispersal and local adaptation in heterogeneous environments[END_REF] tested a model including joint evolution of dispersal and local adaptation and showed that dispersal should evolve towards lower values in the context of heterogeneous populations environments. Additionally, we did not represent explicitly the consequences (e.g., costs) of dispersal, such as additional mortality or reduced reproductive success[START_REF] Mobley | Home ground advantage: Local Atlantic salmon have higher reproductive fitness than dispersers in the wild[END_REF]). However, this is limited by the lack of knowledge on processes and mechanisms of dispersal in salmonids (but see[START_REF] Jonsson | Atlantic salmon straying from the River Imsa[END_REF] for Atlantic salmon and[START_REF] Bett | Causes and Consequences of Straying into Small Populations of Pacific Salmon[END_REF] for Pacific salmon). Thus, there is considerable room for improvement in our model, and below we highlight some potential research avenues and ideas that could be addressed by MetaIBASAM and any other demo-genetic ABM of salmonid metapopulation, based on burgeoning theoretical and empirical research on causes and implications of dispersal. 1/ We need more studies to understand dispersal mechanisms and their consequences on ecoevolutionary dynamics of metapopulations.Along with additional work estimating dispersal rates between wild populations, empirical studies focusing on individual and population factors influencing dispersal are needed to better appreciate the causes and consequences of dispersal in salmonids. Increasing attention focuses on the three distinct phases of dispersal (emigration, transfer, and settlement,[START_REF] Bonte | Costs of dispersal[END_REF]

Fig. 1 :Fig. 2 :Fig. 3 :Fig. 4 :Fig. 5 :Fig. 6 :Fig. 7 :

 1234567 Fig. 1: Conceptual framework of the MetaIBASAM model, adapted from Piou and Prévost

  using values extracted from the literature and empirical studies (see Piou and Prévost 2012, and Supporting information 2), and adjusted using a long-term monitoring program of the salmon population in the Scorff River (Brittany, France). We adjusted the parameters of the growth-survival tradeoff (see Supporting information 1 and 2) to ensure that abundances and size at different life stages are within the range of observed values on the Scorff River. All other parameters of each population are kept identical to the IBASAM version (Piou and Prévost 2012), except for

Table 1 :

 1 Comparison between MetaIBASAM and existing modeling frameworks to explore metapopulation dynamics of salmonids (generic models also included). SS=spatial structure; Em=emigration; Im=immigration.

	References	Model type	Species	Dispersal/Connectivity	Eco-evolutionary dynamics	Key mechanistic processes
				-Explicit SS: multiple
	Bowlby and Gibson 2020, Fullerton et al. 2011	Population dynamics models, graph theory	Salmonids	populations, size and distance -Em: fixed emigration rate	No	No
				-Im: distance dispersal kernel
	Berdahl et al. 2015, Yeakel et al. 2018	Analytical model/adaptive dynamics, quantitative genetic model	Generic, Salmonids	-Not explicit SS/ two populations -Em: inherited -Im: random destination independent or dependent probability/density-	-Inherited ecological trait (fixed) trait-site optimum -Fitness: mismatch	No
	Guillaume and Rougemont 2006, Rebaudo et al. 2013, Bocedi et al. 2014, Schiffers and Travis 2014, Landguth et al. 2017	Demo-genetic agent-based model of metapopulation (Nemo, SimAdapt, RangeShifter, ALADYN, CDMetaPOP)	Generic	-SS: grid landscape dispersal kernel -Em: fixed emigration rate/density-dependent/individual trait among nearest/distance -Im: random destination	-Multi locus system genotype (fixed) -Spatially explicit fitness for each	Simple life cycle
	Landguth et al. 2017	Demo-genetic agent-based model of metapopulation (CDMetaPOP)	Brook trout	-SS: grid landscape -Em: fixed emigration rate -Im: distance dispersal kernel	-Multi locus system -Spatially explicit fitness for each genotype (fixed)	-Growth ~ temperature -Survival ~ patch fitness, density -Maturation ~ size -Sexual selection
	Lin et al. 2017	Demo-genetic agent-based model of two populations (extension from Bromaghin et al. 2011)	Sockeye salmon	-SS: two populations -Em: fixed emigration rate	-Multivariate quantitative genetic model -Fitness: mismatch trait-site optimum (fixed)	-No growth: inherited length, age at maturation -Survival ~ density, phenotype -Sexual selection
	MetaIBASAM	Demo-genetic agent-based model of metapopulation	Atlantic salmon	-SS: multiple populations, size and distance -Em: fixed emigration rate	-Bi-allelic multi locus system	-Growth ~ temperature, flow, density, growth potential

Canadian Journal of Fisheries and Aquatic Sciences (Author's Accepted Manuscript)

Canadian Journal of Fisheries and Aquatic Sciences (Author's Accepted Manuscript) © The Author(s) or their Institution(s) Can. J. Fish. Aquat. Sci. Downloaded from cdnsciencepub.com by INRAE on 07/29/22 For personal use only. This Just-IN manuscript is the accepted manuscript prior to copy editing and page composition. It may differ from the final official version of record.

We want to thank the Bretagne Grands Migrateurs association and angling clubs for allowing us to access to Atlantic salmon datasets from Brittany. We also wish to thank Guillaume Thirel for providing us with the air temperature and river flow data, as well as Marie Nevoux, Emanuel Fronhofer, Charlotte Récapet, and Philip Crowley for helpful discussions on this work. Finally, we thank Jacques Labonne for reviewing an earlier version of this manuscript and two anonymous reviewers for their thoughtful feedback and suggestions that greatly improved this manuscript.

obtained via the ORE-DiaPFC observatory and can be accessible on https://github.com/ORE-DiaPFC/Abondance/tree/master/Scorff, and on demand, respectively.

DATA AVAILABILITY STATEMENT

Modelling code and R scripts are freely available at https://github.com/Ibasam/Portfolio. Adult abundance and size data from the Scorff population used for model calibration have been

provide information on the ability of metapopulations with variable degrees of diversity to persist under various projected climate scenarios (Fig. 7).

3/ We need to assess the interplay between diversity and dispersal by considering spatial structure and local adaptation.

Dispersal and diversity are key processes influencing metapopulation functioning and persistence and previous studies have highlighted the importance of potential interactions between the two (Berdahl et al. 2015, Fig. 7). For example, considerable research has focused on gene flow impeding local adaptation [START_REF] Moore | The interplay between dispersal and gene flow in anadromous Arctic char ( Salvelinus alpinus ): implications for potential for local adaptation[END_REF]. The strength of gene flow may vary with the intensity of dispersal [START_REF] Garant | The multifarious effects of dispersal and gene flow on contemporary adaptation[END_REF]) and the reproductive success of immigrants [START_REF] Mobley | Home ground advantage: Local Atlantic salmon have higher reproductive fitness than dispersers in the wild[END_REF]. Interestingly, several recent theoretical studies focused on this interplay between diversity and dispersal (e.g., Tomasini 4/ We need to consider the implications of spatially structured populations for management.

Our results highlight the importance of interpreting the dynamics of local populations and defining management strategies by considering the potential connectivity between populations.

COMPETING INTERESTS STATEMENT

The authors declare there are no competing interests.

AUTHORS' CONTRIBUTIONS STATEMENT

AL: conceptualization, methodology, formal analysis, writing (original draft, review and editing), MB: conceptualization, methodology, writing (review and editing), SMC: conceptualization, writing (review and editing), FH: methodology, CP: methodology, JP: methodology, EP: methodology.

FUNDING STATEMENT

We gratefully acknowledge funding from the Region Nouvelle Aquitaine, E2S-UPPA, and OFB Pôle Migrateur. This work was conducted within the International Associated Laboratory MacLife.