Simulating the effects of long‐distance dispersal and landscape heterogeneity on the eco‐evolutionary outcomes of range expansion in an invasive riverine fish, Tench (Tinca tinca)

Predicting how quickly populations expand their range and whether they will retain genetic diversity when they are introduced to new regions or track environmental conditions suited to their survival is an important applied and theoretical challenge. The literature suggests that long‐distance dispersal, landscape heterogeneity and the evolution of dispersal influence populations' expansion rates and genetic diversity. We used individual‐based spatially explicit simulations to examine these relationships for Tench (Tinca tinca), an invasive fish expanding its geographical range in eastern North America since the 1990s. Simulated populations varied greatly in expansion rates (1.1–28.6 patches year−1) and genetic diversity metrics, including changes in observed heterozygosity (−19 to +0.8%) and effective number of alleles (−0.32 to −0.01). Populations with greater dispersal distances expanded faster than those with smaller dispersal distances but exhibited considerable variation in expansion rate among local populations, implying less predictable expansions. However, they tended to retain genetic diversity as they expanded, suggesting more predictable evolutionary trajectories. In contrast, populations with smaller dispersal distances spread predictably more slowly but exhibited more variability among local populations in genetic diversity losses. Consistent with empirical data, populations spreading in a longer, narrower dispersal corridor lost more neutral genetic variation to the stochastic fixation of alleles. Given the unprecedented pace of anthropogenic environmental change and the increasing need to manage range‐expanding populations, our results have conservation ramifications as they imply that the evolutionary trajectories of populations characterised by shorter dispersal distances spreading in narrower landscapes are more variable and, therefore, less predictable.


| INTRODUC TI ON
Understanding range-expansion dynamics, a long-standing topic of interest in ecology and evolution (Shigesada, 1986;Skellam, 1951), is essential to predict the rate at which introduced species invade new habitats and native species shift in response to changing environments (Hastings et al., 2005;Parmesan & Yohe, 2003). When populations expand geographically, individuals disperse through heterogenous landscapes and settle in new habitats to reproduce.
Variation in range-expansion dynamics shape species' distribution, population density and their genetic composition (Excoffier et al., 2009;Miller et al., 2020). Theoretical studies have highlighted the influence of long-distance dispersal, landscape heterogeneity, biotic interactions and evolution, on shaping populations' rate of spread and genetic diversity (Birzu et al., 2019;Burton et al., 2010;Ibrahim et al., 1996;Phillips, 2015;Phillips & Perkins, 2019;Shigesada et al., 1995;Travis & Dytham, 2002;Williams, Snyder, & Levine, 2016). However, understanding and predicting the outcomes of range expansions remains challenging as empirical investigations are not always consistent with theoretical predictions (Bronnenhuber et al., 2011;Swaegers et al., 2013). Given the increasing incidence of range shifts in response to the unprecedented pace of anthropogenic environmental changes, it is important to improve our understanding -and ability to predict -the eco-evolutionary outcomes of range expansions.
Much of our current understanding of range expansions relies on theoretical models which assume that individuals disperse over short distances in their lifetime (Edmonds et al., 2004;Hallatschek et al., 2007;Klopfstein et al., 2006;Skellam, 1951). These models have shown that neutral genetic diversity generally decreases from the core to the front of range expansions owing to sequential bottlenecks and mating between a limited number of genetic lineages (typically good dispersers) on expanding fronts (De Austerlitz et al., 1997;Excoffier et al., 2009;Hallatschek & Nelson, 2008;Klopfstein et al., 2006;Phillips et al., 2010). This well-accepted theory is often used to detect the occurrence and the origin of range expansion from neutral genetic data, such as the expansion of humans from East Africa (Peter & Slatkin, 2013;Prugnolle et al., 2007). Yet, occasional movements over large spatial scales (long-distance dispersal, LDD), relative to small-scale dispersal, are widespread in the animal kingdom (Jordano, 2017;Kot et al., 1996).
Numerous studies have reported that LDD increases expansion rates and results in a lack of agreement between theoretically predicted expansion rates and empirical data (Hastings, 1996;Ibrahim et al., 1996). In contrast, the effects of LDD on neutral genetic diversity are not well understood. Specifically, while some studies argue that LDD consistently mitigates genetic diversity losses in expanding populations, others suggest that losses may still occur under certain circumstances, including narrow colonised regions and intermediate levels of LDD (Bialozyt et al., 2006;Fayard et al., 2009;Paulose & Hallatschek, 2020). Furthermore, how LDD interacts with genetic drift to influence variability in genetic diversity among replicates of a single range expansion has not been previously investigated.
As LDD tends to homogenise the gene pool by facilitating gene flow throughout the species' range (Bohrer et al., 2005;Garant et al., 2007), it might limit neutral dynamics (i.e. allele surfing and genetic drift) of allele frequencies (Paulose & Hallatschek, 2020), thereby reducing variability among local gene pools throughout expanding populations. As neutral dynamics can affect the spatial frequency distribution of neutral, beneficial and deleterious alleles (Hallatschek & Nelson, 2009), understanding this variability might be key to forecasting the evolutionary trajectories of range-shifting populations, something increasingly asked of conservation and invasive species researchers (Lässig et al., 2017;Williams et al., 2019).
Empirical investigations of the genetic consequences of range expansion suggest substantial variability in range-expansion dynamics among species, with some species showing decays in genetic diversity along expansions (Demastes et al., 2019;Garroway et al., 2011) while others maintain high levels of genetic diversity (Robalo et al., 2020;Swaegers et al., 2013;Wang et al., 2016). Theoretical predictions related to the eco-evolutionary outcomes of contemporary range expansions have rarely been tested in riverine fishes and received mixed empirical support thus far. For example, Sea Lamprey (Petromyzon marinus) populations exhibited a loss of genetic diversity when they expanded into the Laurentian Great Lakes (Bryan et al., 2005); conversely, Round Goby (Neogobius melanostomus) maintained high levels of genetic diversity as they spread throughout the same region (Bronnenhuber et al., 2011). Another species, Tench (Tinca tinca) exhibited contrasted changes in genetic diversity in different directions from a single point of introduction (Bernos et al., 2023). Variability in the magnitude and significance of genetic diversity losses associated with range expansion may be partially explained by differences in the number of genetic markers used in empirical studies and their statistical power (e.g. Swaegers et al., 2013Swaegers et al., , 2015. Alternatively, speciesspecific characteristics might interact with landscape heterogeneity to shape the outcomes of range expansions. Individual-based simulations are powerful tools to understand variability in range expansion dynamics because they can account for demographic stochasticity (Melbourne & Hastings, 2009). Variation among individuals in their realisation of demographic processes (e.g. birth and dispersal) is known to result in variability among rangeexpansion outcomes, even in constant environments (Melbourne & Hastings, 2009). Individual-based models aiming to test and contribute to the formulation of range-expansion theories tend to be abstract, with individuals represented as particles spreading in homogeneous landscapes (Bialozyt et al., 2006;Hallatschek et al., 2007;Paulose & Hallatschek, 2020;Phillips, 2015). Comparatively, those aiming to inform pragmatic management focus on detailed representations of individuals, often based on extensive empirical data and expert knowledge in complex landscapes (Dominguez et al., 2020;Fraser et al., 2015). This is important because landscape heterogeneity is pervasive in nature and interacts with other sources of stochasticity to influence range-expansion dynamics (Fraser et al., 2015;Williams, Snyder, & Levine, 2016). Another benefit of individual-based simulation is that, by focusing on lower levels (e.g. individual loci and organisms) to model the emergence of population-level processes, results developed in a specific study system can potentially transfer well to different contexts (Radchuk et al., 2019). Recently developed modelling frameworks, such as Range Shifter (Bocedi, Palmer, et al., 2014) and Cost-Distance Meta-POPulation (CDMetaPOP: Landguth et al., 2017), provide opportunities to understand and improve predictions related to the consequences of range expansions for wild populations' geographical range and genetic diversity.
Much of the literature examining the eco-evolutionary outcomes of range expansions using simulations has focused on highly abstract systems or specific case studies. Here, we extend these previous research efforts by using an individual-based, spatially explicit demogenetic model to broadly simulate the movement of Tench introduced to a river. Tench provides a good model system because individual attributes influencing population dynamics (e.g. growth and fecundity), within-population structure, recent demographic history and the genetic consequences of range expansion, are well characterised (Avlijas et al., 2018;Bernos et al., 2023 ;Dumont et al., 2002). As in other riverine fishes, Tench exhibit both short-and longrange dispersal, with the latter hypothesised as being largely responsible for driving range expansions (Morissette et al., 2021;Radinger & Wolter, 2014). We developed 300 model scenarios anchored with empirical data spanning a wide range of dispersal scales in spatially heterogeneous landscapes, leading to a deep understanding of the systems dynamics and testable predictions related to the effects of LDD, landscape heterogeneity, and evolution, on populations' expansion rate and genetic diversity (Grimm, 1999).
Specifically, we used simulations to address the following questions: (1) how are expansion rate and genetic diversity impacted by the shape of the dispersal kernel, landscape heterogeneity and the degree to which dispersal propensity differs among individuals? and (2) how do expansion rate and genetic diversity changes vary across replicates for an introduced riverine fish exhibiting both short-and long-distance movements? Overall, we seek to advance existing theory on how demographic stochasticity and landscape heterogeneity influence range-expansion dynamics by focusing on predicting variability in their eco-evolutionary outcomes.
2 | MATERIAL S AND ME THODS 2.1 | Simulated range expansion for riverine fishes

| Study design
Our models were based on the documented introduction of Tench in eastern North America, which involved the escape of farmed individuals into the Upper Richelieu River (Avlijas et al., 2018;Bernos et al., 2023;Dumont et al., 2002). Specifically, simulations were eco-evolutionary consequences of recent and ongoing range expansions, presumably not at equilibrium, we simulated each scenario over 50 years.

| Model overview
We simulated 300 scenarios of range expansion for an introduced riverine fish using the individual-based spatially explicit model CDMetaPOP (for full model description see Landguth et al., 2017).
In the CDMetaPOP framework, a landscape is represented by discrete habitat patches, themselves populated by individuals. Within each habitat patch, length-and age-based class structures are used to simulate stochastic processes, and individuals are assumed to share common environmental conditions (e.g. carrying capacity). At each annual cycle of the simulation and within all patches (including the one where range expansion was initiated), individuals grow, mature, reproduce, disperse and die based on probabilistic distributions. Between patches, individual dispersal is a function of spatially explicit cost-distance matrices. As genes are inherited from parents to offspring in a Mendelian fashion, CDMetaPOP can be used to simulate the genetic processes (e.g. gene drift and gene flow) resulting from inter-individual variability in demographic processes such as dispersal and death.

| Patches
To investigate the effect of habitat availability, we conducted the simulations in three landscapes. The first landscape contained 229 habitat patches (Figure 1), which were defined as the centroid of grid cells (4 × 4 km = 16 km 2 ) overlapping with water throughout the invaded region ( Figure 1). We then produced two additional landscapes with 170 and 115 habitat patches by randomly subsetting 75% and 50% of the patches respectively. Within each landscape, expansion occurred southward, northeastward and northwestward.
Patch quality did not vary throughout the landscape: based on available estimates of catch-per-unit-effort in areas of high Tench density (J. Hill, unpubl. data), we assumed that all patches had a carrying capacity of 600 fish.

| Individual growth, maturity, fecundity and mortality
We initialised the simulation with a random distribution of seven age classes, a number derived from empirical age distributions based on otolith chemistry data (Morissette et al., 2021). At each annual cycle, growth followed the trajectory of the Von Bertalanffy equation (Von Bertalanffy, 1957). Specifically, we used the following equation with parameters derived from length survey data from the eastern North American Tench population (O. Morissette, unpubl. data) (see Figure S1 for Von Bertalanffy growth curve for Tench and Table 1 for parameters): With L∞ the asymptotic size, R 0 the growth coefficient, i the age class, t0 a modelling artefact said to represent the age when the average length is zero (−0.2 in our model), and L the new size. This equation is particularly well-suited to model fish growth as growth rate is fastest during the early stages of life and declines with age and body length.
The probability of maturation was modelled as a function of size based on a logistic probability curve derived from unpublished maturity data provided by J. Hill ( Figure S2, Table 1). Based on these data, individuals had a 50% probability of reaching maturity at ~30 cm in length (~3 years). Although fecundity data were not available for this Tench population, Tench can produce hundreds of thousands of eggs (Ablak Gürbüz, 2011). Due to computational limitations, it was not possible to simulate such high fecundity. We explored a range of values, and modelled fecundity (the number of eggs produced per

Parameter Value Notes
Landscape

Number of loci 100
Number of allele/loci 2 female) as a power function of size (Ablak Gürbüz, 2011), with a mean of 822 eggs at first reproduction ( Figure S3, Table 1). Reproduction was strictly sexual, polygamous, and occurred via random mating between individuals occupying the same habitat patch. Mature individuals were capable of reproducing every year.
Finally, mortality occurred as a function of density-dependent processes to simulate length-based competition and partition of resources within each habitat patch (e.g. Ray et al., 1996). Briefly, size-structured density-dependent mortality was based on the Ricker equation operating within each size class (Ricker, 1954

| Dispersal phenotypes and behaviours
In our simulations, dispersal was regulated by two overlapping processes ( Figure 2). First, individuals were assigned one of two genetically determined (see 'genetics of dispersal') dispersal phenotypes at birth, with good dispersers being more likely to depart from their habitat patch relative to the poor dispersers. The extent of the difference (Δ dispersal) was determined by reducing departure probability for the poor dispersers relative to the good dispersers by a factor between 0 and 1 (see Table 1 for range of values). Second, each year, the probability for a departing individual -including all good dispersers and the departing proportion of poor dispersers -to move to any given patch relative to and including its current patch followed a leptokurtic dispersal kernel. Specifically, the movement of individuals was governed by resistance surfaces implemented with a costdistance matrix where each entry represented the shortest in-water distance (in km) between two patches and rescaled to a probability between 0 and 1. A transformation of the resulting probability vector using the leptokurtic movement function (Fidimo) was then used to determine the probability for a fish to disperse to any patch relative to their current one. The Fidimo function, which includes two superimposed normal distributions ( In other words, the probability for good dispersers to move to any given patch (including the one they are in) always followed the Fidimo dispersal kernel, meaning that dispersal distances were heterogeneous as good dispersers included both sedentary and mobile fish. In simulations where the extent of the difference between good and poor dispersers was 1, all individuals with a poor-disperser genotype stayed in their initial habitat patch throughout their lifetime.
When it was 0.5, each year, the poor dispersers had a 0.5 probability of staying in their habitat patch, and a 0.5 probability of dispersing to any position relative to their current patch based on the fidimo dispersal kernel. Then, the probability that good dispersers moved to any given patch always followed the fidimo dispersal kernel, with poor dispersers exhibiting sedentary or mobile dispersal distances F I G U R E 2 Flowchart representing the process for assigning dispersal phenotypes and probability to move to any given patch relative to and including its current patch a function of the hybrid index (H), the difference between good and poor dispersers (Δ dispersal), the proportion of stationary fish (p sedentary) and mean dispersal distances (α sedentary and α mobile); n, the average of the parental H indexes, is a number between 0 and 1. The arrow indicate processes occurring through each annual time loop of the model. based on p sedentary. From (and including) their current patch, individuals could disperse to existing patches in any direction with probability of movement to a given patch varying based exclusively on transformed patch-to-patch riverine distances.
To describe the movement of Tench, we first defined leptokurtic dispersal kernels using the R package fishmove (Radinger and Wolter, 2014). In this package, mean dispersal distance is computed as a function of fish length, aspect ratio of the caudal fin, and stream size, as shown in a recent meta-analysis of dispersal distances for riverine fishes (Radinger & Wolter, 2014). To predict a range of dispersal distances for Tench, we used an average fish size of 36 cm, aspect ratio of 1.82 (as measured from Figure 5 of Avlijas et al., 2018 using imageJ), and a stream order (a proxy for channel size, watershed area, and stream discharge with a positive relationship on mean dispersal distances) of 9 (Strahler, 1957). This predicted a mean dispersal distance of 1 km (0.5-2 km) for the sedentary fish (α sedentary) and 19 km (95% CI = 10-35 km) for the mobile fish (α mobile). We then widened this range to include scenarios that were less likely to occur in natural fish  2.1.7 | Neutral genetic diversity Individuals' neutral genotypes were initialised based on an allele frequency file for diploid individuals assuming maximum genetic diversity (i.e. allelic frequencies were all equal to 0.5), comprised of 100 loci with two alleles per locus. Our models assumed that all genetic diversity was present at the initialisation of the range expansion and that mutation and intrachromosomal recombination did not occur.
Offspring received genotypes based on Mendelian inheritance, meaning that they inherited one allele from each one of their diploid parents.

| Metrics of range expansion and genetic diversity
At simulation in observed heterozygosity (Ho) and in the effective number of alleles (Ae) respectively. We computed Ae as defined by Weir (1990), with gene diversity defined as the average probability that two randomly selected alleles are different in a population (Nei, 1973): To gain further insights into within-population variability, we also computed two metrics of variation among expansion fronts: mean annual variability in expansion rate was computed as the standard deviation in expansion rate (expansion rate was calculated within each of the expanding fronts, effectively accounting for local differences in the number of patches); and, spatial variability in genetic diversity losses as the standard deviation of Ho and Ae losses between the three expansion fronts. Thus, whereas the populationlevel genetic diversity loss metrics described temporal changes, the variability loss metrics described spatial variation. In this study, we considered the invaded landscape as a closed system (i.e. fish could only disperse to existing patches). To evaluate the effect this might have had on population dynamics, all metrics were computed after completion of 30-year cycles (the average number of years it took for the landscape to be fully invaded; see results) and 50-year cycles.
As the results were qualitatively similar, we only report results on 50-year cycles.

| Baseline scenario
We first ran a scenario to create a baseline against which we replicates, ensuring that our conclusions were robust to the number of replicates.

| Alternative scenarios and global sensitivity analysis
Simulation studies examining the eco-evolutionary outcomes of range expansions typically rely on local sensitivity analyses to quantify the effects of input parameters on model outputs and infer their relative influence on range expansions. Compared to local sensitivity analyses, where researchers vary input parameters one at a time in a factorial design, global sensitivity analyses can be used to vary several parameters simultaneously (Wagner, 1995). This offers two key advantages over local sensitivity analyses. First, global analyses examine sensitivity related to the entire parameter space, while local sensitivity analyses have a limited scope (i.e. researchers typically focus on extreme parameter values or ignore uncertainties around parameters estimated from empirical data) (Wagner, 1995). Second, varying multiple parameters simultaneously enables the detection of nonlinear relationships as well as complex interactions among input variables (Prowse et al., 2016). Recent advances in statistics and computing can be leveraged to analyse and summarise the results of global sensitivity analyses (Elith et al., 2008).
We used global sensitivity analyses to investigate how parameter values related to the dispersal kernel (p, α mobile, α sedentary), the differences in dispersal traits between genetically determined dispersal phenotypes, and landscape patchiness, influenced four metrics of range expansion outcomes in 300 scenarios. The first step of the global sensitivity analysis was to adequately sample the parameter space representing the range of possible parameter values (Table 1) (Friedman & Meulman, 2003), and we generated 1000 bootstrap replicates to produce 95% confidence intervals. Finally, we visualised the most important interactions between predictors using partial interaction plots.

| Differences and similarities between baseline and alternative scenarios
In the baseline scenario, at the population level, Ho and Ae declined the most rapidly during the period associated with rapid population growth ( Figure S5) and concomitant range expansion ( Figure 4, Table 2), which occurred for 29.6 years on average (28-32 years) after the introduction. Results from alternative scenarios indicated some variability in mean expansion rate and genetic diversity losses.

| Predicting expansion rate and genetic diversity losses
Overall, the BRT made accurate predictions regarding mean and year, after which the magnitude of the loss was below average for that metric.
In addition to mean dispersal distance of the mobile fish, landscape patchiness and mean dispersal distance of the sedentary fish were uniquely ranked as more influential than expected by chance in, respectively, the mean and variability in expansion-rate models ( Figures 5 and 6). Specifically, the BRT predicted faster mean expansion rates (28.7%) in landscapes with more habitat patches (less patchiness) than in those with fewer habitat patches. In the other models, the relative influence of landscape patchiness was ranked last and second to last. In the variability among expansion fronts model (22.9%), the relationship between variability and mean dispersal distance of the sedentary fish was generally positive, with variability in expansion rate increasing most steeply as mean dispersal distances increased from 0 to 1 km/year. In the other models, the relative influence of mean dispersal distance of the sedentary fish was ranked second and third.
The proportion of sedentary fish and extent of the difference in dispersal ability between good and poor dispersers were not more influential than expected by chance in any of the models (Figures 5   and 6). The only significant interaction across all four models ( Figure 7) was between mean dispersal capacity of the mobile fish and landscape patchiness in the mean expansion-rate model. This interaction involved a two-to three-fold weakening of the positive effect of high dispersal capacity on expansion rates in patchier landscapes.

| DISCUSS ION
Understanding how range expansions determine species' geographical ranges and the distributions of their genetic diversity TA B L E 2 Range expansion rate and changes in genetic diversity (observed heterozygosity and effective number of alleles) across 10 replicated runs for the baseline scenario. The table shows the mean and the standard deviation for each metric at the population level and within three expansion fronts (Southern, Northwestern and Northeastern).

F I G U R E 5
Relative influence of predictors on expansion rate, loss of observed heterozygosity (Ho) and loss in allelic richness (Ae) derived from boosted regression trees. Predictors included difference in dispersal probability between mobile and less-mobile fish (Δ dispersal), landscape patchiness (Landscape), mean dispersal distance for sedentary (α sedentary) and mobile fish (α mobile), and proportion of sedentary fish in the population (p sedentary). Metrics of range expansion outcomes include mean at the population level and variability among expansion fronts. Dotted line indicates threshold above which predictors' influence is greater than expected by chance.
can provide important insights into the ecological success of spreading populations. This study demonstrates that LDD had two main effects on range expansions. First, increasing LDD distance dramatically accelerated the rate of range expansion and favoured the retention of neutral genetic diversity in the entire population during range expansion. Second, there was a trade-off between dispersal and genetic diversity lowering the predictability of range expansions when LDD distance was relatively small (< three-fold larger than short-range dispersal distances). Furthermore, the shape of the dispersal corridor was also important in differentially shaping expansion rate and genetic diversity losses among local populations. These findings suggest that some of the variability in the eco-evolutionary outcomes of range expansion, which affects how precisely we can predict the trajectories of range expansions, might be predictable based on species and landscape attributes.

| Predicting range expansion dynamics
Large dispersal distance exerted a powerful influence on expansion rate and neutral genetic diversity. As in several other studies, greater LDD distance boosted expansion rate for the entire population (Kot et al., 1996;Paulose & Hallatschek, 2020;Ray & Excoffier, 2010). In contrast, the effects of LDD on genetic diversity were less linear.
Specifically, increasing mean LDD distance was most effective at facilitating the retention of genetic diversity when distances were relatively small (<< 20 km/year). Beyond this distance threshold, most of the genetic variation (i.e. > 97% of the Ho and Ae of the originating population) was preserved during range expansion, and a small number of populations even experienced small gains in Ho (<0.001%). This result suggests that LDD can maintain genetic diversity throughout expanding populations, but only when it is above a critical distance threshold, below which the effects of sequential founder effects on neutral genetic diversity are not eliminated (Hallatschek & Fisher, 2014;Paulose & Hallatschek, 2020). In practice, this critical distance threshold may depend on (1) the deviation in dispersal distances around mean LDD distance and (2) the geographical scale of the range expansion.

F I G U R E 6
Partial dependence plots showing the effect of influential predictors derived from boosted regression trees on expansion rate, loss of observed heterozygosity (Ho) and loss in allelic richness (Ae), while holding other predictors constant. Influential predictors included landscape patchiness (Landscape) and mean dispersal distance for mobile (α mobile) and sedentary (α sedentary) fish. Metrics of range expansion outcomes include mean and variability among expansion fronts in expansion rate and genetic diversity loss (Ho and Ae). Since landscape patchiness is categorical, its partial dependence is displayed as a barplot. Effects are centred around a mean of zero (grey dotted line).

F I G U R E 7
Partial dependence plot showing the interaction between the effects of mean dispersal distance for mobile fishes (α mobile) and landscape patchiness on mean expansion rate while holding other predictors constant. Range expansion simulations were conducted in three landscapes: the initial landscape contained 229 habitat patches, and two additional landscapes with 170 and 115 habitat patches were produced by randomly sub-setting 25% and 50% of the patches respectively.
Although populations with low LDD distances expanded more slowly, they exhibited greater losses in genetic diversity and greater among-replicate variability (i.e. variation among newly established local populations) in neutral genetic diversity losses. This is consistent with the theoretical expectation that LDD mitigates the effects of genetic drift and gene surfing as the flux of individuals dispersing from the core to the expanding front precludes the fixation of other alleles and the erosion of genetic diversity on the expanding front (Klopfstein et al., 2006;Paulose & Hallatschek, 2020). The corollary is that changes in the gene pool due to neutral processes might in- selection to operate on expansion fronts (Peischl et al., 2013;Peischl & Excoffier, 2015).
The effects of increasing LDD distance on expansion rate were stronger in continuous landscapes, where populations tended to spread faster than in patchier landscapes (Barros et al., 2016;Cumming, 2002;Shigesada, 1986;Travis & Dytham, 1999; but see Bocedi et al., 2014). For a given mean LDD distance, individuals had more patches to which to disperse in continuous landscapes.
However, while patchiness did not influence among-replicate variability in expansion rate (e.g.  nor genetic diversity, the shape of the habitat influenced both population-level and among-replicates variability in expansion rate and genetic diversity. In wider environments, the number of patches within shorter distances increased, thus resulting in higher expansion rates. However, local populations spreading in long, narrow dispersal corridors not only expanded more slowly and lost more genetic variation, on average, than those expanding in wider dispersal corridors (Cumming, 2002;Fayard et al., 2009). They also tended to exhibit more among-replicate variability in expansion rate and genetic diversity losses. This result implies that the degree of divergence between local populations might increase due to reduced connectivity when dispersal corridors are long and narrow, potentially creating opportunities for different alleles to rise in frequency (Crow & Aoki, 1984;Wright, 1951).
Although we expected populations with greater genetically based trait differences between good and poor dispersers to spread faster due to the spatial sorting of good dispersers on newly colonised habitat patches, the parameter did not significantly affect range-expansion dynamics in our study. In contrast, the evolution of dispersal led to faster and more variable range expansion rates in several empirical (Brown et al., 2014;Lombaert et al., 2014) and  (Brown et al., 2014;Rollins et al., 2015). One possible mechanism driving our result is that the probability to depart from the native habitat patch, rather than the probability to disperse farther, was genetically determined.
However, the lack of influence of the proportion of sedentary fish on range expansion outcomes implies that, in our study, the beneficial effects of large LDD distances were realised independently of their frequency of occurrence. This result implies that, at least for populations able to grow quickly at low abundance, the evolution of traits facilitating dispersal over longer distances (e.g. path straightness and daily dispersal rates) might have a greater effect on range expansion outcomes than that of departure-enhancing traits (e.g. bold and exploratory behaviours).

| Empirical relevance
Extrapolating our results to natural populations requires care because our simulations assumed that mutation and recombination did not occur, such that all genetic diversity was present when range expansion began. While the trends documented in our study should hold, we anticipate that the magnitude of the genetic diversity losses documented here would be diminished in scenarios where range expansion is accompanied by rapid population growth (Wright, 1931), as is typically the case (Excoffier et al., 2009). Mutations might occur especially frequently in highly fecund species (Williams, 1975) Our models also demonstrated that the observed variability in range expansion outcomes -faster expansion and slightly greater retention of genetic diversity on the Southern expansion front (Avlijas et al., 2018;Bernos et al., 2023) -can be explained by variability in the spatial arrangement of habitat patches, and was therefore relatively predictable. For invasive species with adverse consequences for native biodiversity, like Tench (Avlijas et al., 2018), timely knowledge of expansion variability could provide an opportunity to identify areas at imminent risk of invasion, initiate mitigation strategies, and encourage policies to stop the spreading population. From an evolutionary standpoint, we can expect losses in genetic diversity due to neutral dynamics in allelic frequency (i.e. genetic drift and gene surfing) to be limited. However, the impacts on Tench adaptive potential remain difficult to predict as the shuffling of alleles throughout the invaded range might enhance evolutionary potential by maintaining genetic variation, but could also prevent local adaptation and impair local fitness (Garant et al., 2007).

| Limitations of the modelling results
An important limitation of our study is that we do not include the role of density-dependent mechanisms on population persistence and dispersal rates. When populations experience reduced growth rate at low density (i.e. Allee effects), expansion is pushed from high-density populations behind the expansion front rather than pulled by long-range dispersers establishing new populations ahead of the expansion front (Miller et al., 2020), which may result in greater retention of genetic diversity and variability in expansion rates (Roques et al., 2012;Sullivan et al., 2017). Additionally, in the presence of positive density-dependent dispersal, the magnitude of genetic diversity losses might be reduced, even in populations where LDD distances are small, by the flux of individuals dispersing from the core (Birzu et al., 2019). Given the paucity of empirical data on the strength of density dependence and the processes it operates on (e.g. mortality, growth, dispersal and settlement) for Tench, and more broadly riverine fishes, it was not possible to incorporate density dependence into our model. Nonetheless, the influence of density dependence on range expansion outcomes in riverine fishes warrants further investigation.
Finally, while our models focused on neural dynamics and patterns of genetic diversity derived from unlinked neutral loci, adaptive processes are known to influence neutral genetic diversity during range expansions. For example, neutral alleles located close to beneficially adaptive mutations can increase in frequency as adaptive alleles become fixed in the population (hitchhiking) (Gillespie, 2000;Min et al., 2022;Smith & Haigh, 1974). Alternatively, neutral variants

| Conclusions
As environmental conditions change due to the global intensification of human activities, so do many species' ranges. In this context, understanding how expansion rate, genetic diversity and their variability, are jointly shaped by species' dispersal attributes and landscape heterogeneity could improve our ability to accurately predict the ecological success of spreading populations (Williams et al., 2019).
We showed that varying LDD distances shifted the extent of neutral genetic diversity losses, as well as expansion rate, in a consistent direction. Specifically, populations characterised by mean LDD distances larger than a critical threshold expanded faster and lost minimal amounts of genetic diversity. Importantly, LDD also affected the variability in expansion rate and neutral genetic diversity losses among local populations: expanding populations with LDD distances smaller than the critical threshold exhibited lower variability in expansion rate among local populations, but a wider range of genetic diversity losses. Developing criteria for predicting this critical distance threshold, which likely depends on species-specific dispersal characteristics, landscape attributes, and the scale of the range expansion, is critical. Finally, the possibility that populations characterised by small LDD distances might exhibit more variable, and thus less predictable, genetic diversity losses due to the stochastic forces affecting allelic frequencies (e.g. gene drift and gene surfing) implies that local populations might follow divergent evolutionary trajectories, with different sets of alleles -beneficial, neutral or deleterious -fixed at the leading edges. Possibly mirrored by variation in traits related to dispersal or fitness, this variability in the evolutionary consequences of range expansions could affect our ability to predict range expansion dynamics.

B EN EFIT-S H A R I N G S TATEM ENT
A research collaboration was developed between all collaborators, including scientists in academic and government agencies. Results of the research were shared with the broader scientific community.
The research addresses an important topic for conservation, namely the eco-evolutionary consequences of range expansions, using Tench, an invasive species with adverse consequences for native biodiversity and ecosystems, as a model.

ACK N O WLE D G E M ENTS
The idea for this paper came while working on another project with CDMetaPOP; therefore, we thank S. Chang, K. Davenport, M-J.