Predicting the influence of river network configuration, biological traits and habitat quality interactions on riverine fish invasions

The relationships between species and their landscape are important for understanding migration patterns. In fluvial systems, the complexity of the river network can strongly influence the dispersal and colonization rates of invading alien fishes, but habitat quality, species’ biological traits and their location of introduction are also potentially important. However, understandings of how these factors interact in the wild to influence the spatial distribution of invasive species over time are limited from empirical studies.


| INTRODUC TI ON
The relationships between animal movements and the structure of their environment are important to understand, with the variability in these movements driven both by species' ecology and the spatiotemporal scale being considered (Roberts & Angermeier, 2007).
Relationships between animal movements and their environment are especially important in the context of newly introduced alien species, as they will determine the species' rate of spread, and hence potential negative ecological impacts (Davis & Darling, 2017;Fraser et al., 2015;Ross et al., 2001). In alien plants, simulated invasion dynamics have revealed the importance of both the connectivity of the entire landscape and the structure of the local landscape (e.g. the presence of corridors), as well as the species' dispersal ability (Andrew & Ustin, 2010). Assessments of how newly introduced alien species invade novel landscapes thus requires understanding of how the landscape structure impacts upon the main processes that contribute to their spread (Grant et al., 2007;Lurgi et al., 2016), especially dispersal (important for successful colonization) and demography (important for successful population establishment) (With, 2004).
The range expansion/spread of alien species requires their ability to move from colonized into novel areas (Havel et al., 2015). For some freshwater alien taxa, adaptations for persisting in temporary environments can assist their overland dispersal by passive or active means (Havel et al., 2015), such as the cryptobiosis of rotifers (Wallace & Snell, 2001). For alien fishes, however, their natural dispersal from invaded to uninvaded areas requires some level of fluvial connectivity (Gozlan et al., 2010), and while canals can provide movement corridors between river catchments (Hickley, 1986), movements and dispersal rates within catchments are dependent upon the structure and connectivity of the river network (Goldberg et al., 2010). This structure and connectivity will also affect the potential movements and distributional shifts in native species as they respond to the invasion (Crowl et al., 2008).
River networks are branched, corridor-like structures that have a number of sources (headwaters) and a mouth (where it joins either the sea or a lake); the distribution of branches (tributaries) and confluences determines the shape of the network, which can be classified using stream order methods (Shreve, 1966;Strahler, 1957).
They can be considered as landscapes in which a set of patches form a dendritic structure that is arranged in a non-linear, spatially explicit manner (Goldberg et al., 2010). The directional flow of water within the network means that for two adjacent patches, one will be downstream from the other, and this will influence the movement of fish between them, such as whether the movement is more likely to be active (upstream direction) or passive (downstream direction) (Goldberg et al., 2010). These fish movements continue until a confluence is encountered, when a decision is required as to which branch the fish enters. Branching is often asymmetric, as one channel is often larger than the other and has a different flow regime, and this can strongly influence the decision over which branch is taken (Byers & Pringle, 2006). These inter-patch movements are likely to be influenced by factors including the fish life-stage and their dispersal abilities (Goldberg et al., 2010;Phang et al., 2016). They will also depend on habitat quality of the patches, where there can be a higher energetic cost for a fish for settling into a lower versus higher habitat quality patch due to, for example reduced prey availability, that increases their searching time (Phang et al., 2016).
Understanding the colonization rates of alien fish in river networks is crucial for conservation management, including protecting native communities from the adverse impacts of alien invasions, especially as the ability to manage invasive fishes in the environment is inversely proportional to the extent of their spatial spread Rytwinski et al., 2019). For an invasive freshwater fish whose distribution is still spatially limited within rivers, eradication can be a feasible option for eliminating their impacts on native species, whereas for those invaders that are spreading rapidly, control and/or containment methods are usually the only feasible options . The traits of invasive fish also often differ between the "invasion front" and the areas where the population has already colonized ("invasive core"): individuals at the front are more likely to express "dispersal-enhancing traits" that provide them with the highest probability of dispersal success (Masson et al., 2018). There are, however, considerable knowledge gaps on how the interactions of the spatial variability in river network complexity and habitat quality with the location of the release site influence the invasion success of alien fishes, especially across species of differing dispersal abilities and life-history traits.
While this is likely to relate to the complexity of these interactions and a lack of empirical data (Dominguez Almela et al., 2020), recent increases in computing power and the development of individualbased models (IBM) enable the use of predictive approaches to help overcome these knowledge gaps (Day et al., 2018;Rodríguez-Rey et al., 2019).
The aim of this study was thus to determine how the invasion of alien river fishes is likely to be influenced by river network complexity and habitat quality, the location of their introduction into the network and how this varies across a range of species' dispersal abilities and life-history traits. An IBM was developed and parameterized to predict how these factors interacted to influence the rates of population increase and range occupancy of nine example alien fishes over time scales of 10 and 30 years in a range of virtual and realworld river networks. We posit that (a) river network complexity and spatial differences in habitat quality are a major determinant of the colonization rate of alien fishes, such that more branched networks K E Y W O R D S biological invasion, dispersal, individual-based model, RangeShifter, river catchment, simulation model are colonized faster than less branched networks through the formation of multiple invasion fronts; (b) the introduction location in the network influences the colonization rate, such that introductions in upstream locations result in more rapid colonization and population growth due to fish movements in a downstream direction into areas of higher stream order (and habitat quality); and (c) alien fishes with higher dispersal abilities and life-history traits that facilitate fast establishment (i.e. r-selected traits; Dominguez Almela et al., 2020) will colonize river networks more rapidly than fishes with the opposite suite of traits.

| River networks
Two sets of river networks were used: (a) randomly generated, virtual river networks that enabled predictions to be made on channel configurations whose physical differences were constrained with a set of rules: total size of catchment, number of cells and number of confluences (maximum stream order of 4); and (b) actual river networks that enabled testing of the predictions from (a) using "realworld" configurations with natural network variability between them.

| Randomly generated virtual river networks
Virtual river channel networks were built using the "OCNet" package in "R version 4.0.1" (Carraro et al., 2020;R Core Team, 2020). The configuration of the initial state of the network had four possible values (Factor Shape, "S"): "I" (representing a valley); "T" (T-shaped drainage pattern); "V" (V-shaped drainage pattern); and "H" (hip roof drainage pattern). Three catchments per configuration type were created (Factor Catchment, ID; Figure 1), and all 12 rivers had a similar number of confluences in their network (mean = 48.6 ± 0.76 (SD)). The network distance from the outflow point was used to develop raster maps of habitat quality (as described below) of cell size 50 m using "ArcGIS Pro," where catchments were divided into sections limited by the river nodes. The network distance from the mid-point of each section to the outflow point was converted to a quality score by: Using this formula, habitat quality for the alien fish increased with distance downstream, and so habitat quality increased as stream order increased (Matthews, 1986;Smith & Kraft, 2005). The rationale behind this assumption was that as river width increased with distance downstream, this would increase the heterogeneity of the habitat (e.g. increased size and complexity of littoral areas) that, overall, would enhance habitat quality for fish. While this can be considered a simplification of habitat quality, it meant that a single variable that relates to stream order and is relevant to alien fishes could be used (Smith & Kraft, 2005).

| Real-world river networks
Seven river catchments in England and Wales, chosen in relation to their geographic spread and differences in their network configurations, were extracted from Ordnance Survey data: Frome, Stour, Rother, Great Ouse, Esk, Weaver and Conwy ( Figure 2). Tiles of geometric mark-up language from OS MasterMap Water Network data (Ordnance Survey, 2021) were converted into shapefiles using "QGIS 3.16.3," and the individual rivers were cleaned, removing minor drainage branches (width ≤1 m), using "ArcGIS Pro." The mean width of the channels was used to develop raster maps of habitat quality of cell size 50 m using "ArcGIS Pro" by As with the virtual river networks, as the river width increased, so did the habitat quality for the alien fish. However, unlike the virtual river networks, mean channel widths of real rivers are inherently variable, and so although there were general patterns of wider sections increasingly occurring with distance downstream, areas of wider widths could also be found in more upstream areas.

| Modelling the invasion of alien fish species
The platform "RangeShifter 2.0" (Bocedi et al., 2014(Bocedi et al., , 2020 was used to build a spatially explicit individual-based model for a virtual invasive fish species with a stage-structured life-cycle, juveniles (<1 year old), sub-adults (1-2 years) and adults (over 2 years) as per Dominguez Almela et al. (2021). The model was implemented using a cell-based approach (see Table 1 for full list of parameters).
Reproduction was set to occur annually, after which all individuals could migrate up to once during their lifetime. The transfer phase of dispersal was modelled using the stochastic movement simulator (SMS; Palmer et al., 2011), for which the relative cost of movement was set inversely to a cell's habitat quality (i.e. it is more costly for an individual to move upstream and into areas of poorer habitat quality). In many fish species, there is a tendency for mature males to arrive on spawning grounds before females and leave last in order to maximize their reproductive fitness, so males could settle in any non-natal cell. Mature females could only settle in cells where males were already present.
For the virtual river networks, nine models were then constructed using a set of invasive-like species (Factor "SpID"), ex- F I G U R E 1 Randomly generated virtual river networks. a1-3 "H" shape; b1-3 "I" shape; c1-3 "T" shape; and d1-3 "V" shape. The outflow point is shown by a black circle For model initialization, three rules were set that marked the release point for the virtual alien fish (Factor Release point, "R"): upstream (stream order ≤2), mid-catchment (stream order: 2 to 3) and downstream (stream order: 4) ( Figure 1). The initial population sizes used for each initialization rule were similar (random generated river networks: mean 3857 ± 61 (SD); real-world rivers: mean = 5575 individuals ± 80 (SD)). The initial population sizes between the simulated and real-world river systems differed due to the real-world rivers being larger and having higher quality habitats compared to the virtual rivers. Raster cost maps were developed using "ArcGIS Pro" that followed the assumptions from the habitat quality maps that habitat quality decreased, with an increased cost of dispersal, in cells that were closer to the headwater and/ or where the channel was narrower. The mean cell quality scores from the release points (R) were used to build the factor variable "Mean habitat quality" (H). The number of confluences over specific distances (Factor "Dn"), described for a given release cell (which was located in the centre-most cell of the patch of initial distribution), was the sum of the number of confluence cells within a certain distance, for four distances: 500 m (D5), 1000 m (D10), 2500 m (D25) and 5000 m (D50). An additional three distances were added to analyse the real-world rivers due to their larger size: 10000 m (D100), 25000 m (D250) and 50,000 (D500) (

| Model predictions and statistics
For the virtual catchments for each virtual species, 36 models were run (12 landscapes ID × 3 release points R), resulting in 324 models overall with five replicates each. For the real-world rivers, 21 models   were run for each virtual species (7 ID × 3 R) with five replicates each. Subsequent testing focused on high-level summary statistics for each replicate that compared values between the catchments and according to their major differences. Four population-level variables were extracted from the model outputs: (a) rate of population increase across 10 years (P 10 ) and ( were added into the models. For the real-world rivers, a similar model selection process involved assessment of the following factors: release point (R), habitat quality (H) and number of confluences over a distance (D5-D500). The factor catchment ID was included as a random effect, and log transformation was applied as above.
As the release points (R) and mean habitat quality (H) were always highly correlated (i.e. R for upstream reaches always had low H scores and vice versa; Table 3c), all final models were manually modified to examine the variance attributable to explanatory variables present by changing their order. The number of confluences over a distance (D5-D500) were also correlated, and only one of them was retained in the final LMMs based on the lowest AIC. The estimates of the best-fitting models were used to make predictions of P 10 , P 30 , Q 10 and Q 30 as functions of H and R (Table 3c).

| Virtual river networks
In the virtual rivers, increased values of P 10 and P 30 were mainly driven by both the release point of the species (R) and mean habitat quality (H), which were highly correlated (i.e. depending which term is included first, this term explains most of the variance). In the best fitting models, R and H together accounted for 96% of the model variance in 10 years and 91% in 30 years (Table 4). Shape (S) always accounted for low variance in these models and the number of confluences (Dn) was not included in the best-fitting models for P 10 or P 30 (Table 4). For Q 10, R and H were also the most important variables (90% of variation; Table 4), but for Q 30 , the number of confluences within 5000 m (D50) explained 91% of the variance (Table 4), the rate of range expansion increasing as the number of confluences encountered by the invader increased. P 10 and Q 10 were predicted to vary with H and R (Figure 3), where population growth rates would increase as the mean quality of the invaded area increased; in contrast, range expansion rates decreased as quality decreased. P 10 and Q 10 were predicted to be higher when the species had faster dispersal ability (Figure 3).
When considering the virtual fish species separately, the variance in P 10 and Q 10 was, for most species, mainly explained by R and H (P 10 : 85-99% variance explained; Q 10 : 85-99%; Table S1). For P 10 , the only exceptions were the intermediate and r-selected individuals with fast dispersal, for which R and H accounted for only 5-10% of the variance (Table S1). For Q 10 , the exceptions were fast dispersers of all three demographic types, where R and H only explained 2-4% of variance (Table S2). The influence of R and H on P 10 and Q 10 was lowest for fast dispersers and highest for slow dispersers; the rate of colonization and population growth for species with faster dispersal was affected more by the number of confluences (Dn), whereas species with slower dispersal rates were affected more by habitat quality (Tables S1 and S2).
For P 30 and Q 30 , the number of confluences (Dn) explained most of the variance in the best-fitting models across most species (P 30 :

| Real-world river catchments
Model predictions of the rate of population growth (P 10 and P 30 ) of the nine virtual alien species revealed that the best-fitted models included H and R, which together explained 97% of the variance in 10 years and 93% in 30 years, leaving only a small percentage explained by Dn (P 10 : 2%; P 30 : 5%; Table 5). As H increased, the TA B L E 4 Principal sources of variance explained (%) in the best-fitting models for rate of population increase (P 10 and P 30 ) and rate of change of cell occupancy (Q 10 and Q 30 ) in randomly generated catchments  For predictions of Q 10 and Q 30 , most model variance was again explained by H and R (Q 10 : 96% and Q 30 : 78%; Table 5). Approximately 10% of the variance in Q 30 was explained by Dn within 1000 m distance and 9% was explained by the dispersal behaviour of the invader (Table 5). For upstream releases, higher rates of colonization were predicted when the initial invaded area was of higher habitat quality (Figure 4). Initial invaded areas in mid-catchment or downstream areas had an inverse relationship with H. For species of higher dispersal ability, higher rates of colonization were predicted compared to intermediate or slow dispersers (Figure 4).
At the species level, the number of confluences (Dn) was always included in the best-fitting models predicting P 10 and P 30 , but with the effective distance (D5 to D500) varying between species, although R and/or H were the most important explanatory variables (P 10 : 92-99% variance explained; P 30 : 81-99%; Table S3). For Q 10 and Q 30 , R and H were the most important variables in models (Q 10 : 62-99% variance explained; Q 30 : 51-94%; Table S4), although Dn was also highlighted in 5 out of the 9 models for Q 30 (13-25%; Table   S4).

| DISCUSS ION
The management of alien species in the environment generally aims to minimize their impacts on the native communities and requires assessment of the current spatial distribution of the invader and predictions of how this will change over time (Britton, Gozlan, TA B L E 5 Principal sources of variance explained (%) in the best-fitting models for rate of population increase (P 10 and P 30 ) and rate of change of cell occupancy (Q 10 and Q 30 ) in real-world rivers  , 2011). For alien riverine fishes, these assessments require information on how their dispersal rates and population demographics influence their colonization rates following their introduction (Dominguez Almela et al., 2020). Here, we applied an IBM to predict how different river network configurations and habitat quality influenced the invasion of nine virtual alien fish that varied in their dispersal abilities and life-history traits, and by the location of their introduction into the network. In both the virtual and real-world river networks, the general prediction was that both population growth and cell occupancy rates were mainly driven by the location of the introduction of the species and its mean habitat quality, as predicted, but with the configuration of the network often having a relatively minor influence, contrary to prediction. The influence of the location of introduction into the network was important as it determined the overall direction of spread, that is whether the wider range expansion of the species required upstream or downstream movements, where downstream movements had a higher benefit as they involved movements into cells of higher habitat quality. In addition, downstream movements in fish can be passive as well as active, whereas upstream movements can only be active (Benjamin et al., 2007). It was only over the longer 30-year time period that the rate of catchment colonization increased as the spreading population encountered more confluences (i.e. tributaries). This aspect was consistent with our prediction and conforms with empirical studies that suggest that invasion dynamics can be strongly dependent on changes in stream order, with larger, mainstem rivers having faster colonization rates than headwaters (Radinger & Wolter, 2014).
Network complexity was predicted to be important in the invasion success of virtual species with high dispersal ability, as increased numbers of river confluences elevated their colonization rates. The movements of the fish into numerous branches opens up a larger number of range fronts, and so the expression of high dispersal ability at numerous range fronts increases their colonization rate (Masson et al., 2018). In contrast, slow dispersers were more affected by the habitat quality of the cells into which they were introduced, as this affected their population growth during the early years of colonization. This habitat selection and conditiondependent movement can be seen in many fish species, for which the relationship between individual decisions of movement and largerscale population dynamics over time and space are generally important for understanding the importance of movement for species' persistence (McMahon & Matter, 2006). The relationship between individual decisions and population dynamics is arguably even more important for alien species during their colonization period, given the relationship between their establishment within cells (metric Q) and the species' rate of population growth (metric P). For example, while dispersal enables movement into new cells, it has energetic, mortality risk and time costs that can decrease the probability of establishment in those new cells (Bonte et al., 2012). Longer distance dispersers also often arrive in poorer condition than those moving shorter distances (Lange & Marshall, 2016), to invade these actual catchments, where the Great Ouse appears more vulnerable to the invasion by alien fishes with a wider range of traits than the Conwy. Only after these species-specific traits are considered would the location of their release be important, but with this also likely to be influenced by the actual species concerned and their ability to adapt to the new conditions. For example, rainbow trout Oncorhynchus mykiss is regularly released for angling into many head-waters in Britain, albeit with low invasion success (Fausch, 2007), but their ability to survive in reaches downstream is likely to be much reduced due to their requirements for relatively cool, highly oxygenated waters.
Invasive freshwater fishes can present a variety of dispersal traits, with the interaction of these traits with the river network important in determining invasion outcomes (e.g. Almeida et al., 2014;Fukuda et al., 2013). The characteristics of the area of first introduction can be an important predictor of the success of colonization as, while rivers vary considerably in their network configurations, their upper reaches tend to be relatively narrow and less suitable for fish (Kim et al., 2021). If the invader was introduced into these areas then it is likely it would need to expend considerable amounts of energy to disperse into more suitable habitats. Our simulations predicted that upstream releases resulted in higher rates of spread, mainly due to the fish being able to quickly reach the maximum carrying capacity of the low-quality cells, so they keep moving into new cells of similar or lower costs (i.e. downstream direction). Fast dispersers were predicted to colonize the real-world rivers more rapidly than the intermediate and slow invaders. Areas that were highly branched and of good habitat quality especially positively affected fast dispersers, as these enabled the fish to invest their energy on establishing abundant populations while occupying new cells in the river.
The IBM applied here provided a predictive approach for investigating the relationship between newly introduced alien species and their novel riverine environment. While investigating these relationships empirically is difficult, predictive models can also have limitations due to their simplification of real-world situations (With, 2002). We made several model assumptions for reasons of parsimony. For example, the habitat quality of the randomly generated rivers was created with the assumption of upstream areas being of lower habitat quality according to their narrower width (i.e. through littoral areas potentially having less vegetation for refugia, and with the main channel having a higher flow regime and lower water level capacity). Indeed, many British rivers conform to this pattern, especially for alien cyprinid fishes where areas further downstream of higher stream order are more likely to provide more suitable habitats (Kim et al., 2021). While this simplified the modelling process, we acknowledge that some alien species introduced in downstream areas would be capable of moving upstream and could even pass structures that fragment the river (Starrs et al., 2017). Our model did not consider anthropogenic barriers, so the dispersal of the species was only limited by the costs of their dispersal. Given the extensive fragmentation of rivers in Britain (Jones et al., 2019), and indeed in Europe (Belletti et al., 2020) and the world more generally (Grill et al., 2019), future work should consider incorporating barriers into network configurations, especially as these barriers can affect the behaviour of freshwater organisms (Rodeles et al., 2021;Starrs et al., 2017). However, this would require an additional algorithm relating to barrier permeability, such as the ability of fish to move upstream according to river level (Davies et al., 2021), and whether the barrier incorporated a fish by-pass structure (Pereira et al., 2017). Interactions of the invading fish with the native community were also not considered within the model, and it is acknowledged that these interactions can be an important factor in the outcome of biological invasions where, for example, the extent of native biotic resistance and resilience to the invader can determine the extent of its establishment and spread (Alofs & Jackson, 2014;Svenning et al., 2014;Thompson & Fronhofer, 2019). Nevertheless, we argue that despite not being able to include the impacts of barriers on fish movements and the extent of resistance and resilience by native communities, the simulations provided a series of novel insights on the abiotic factors that influence the invasiveness of alien riverine fish and can be used within invasion risk assessment processes to help identify the most appropriate interventions (Bampfylde et al., 2010;Dominguez Almela et al., 2020).
In summary, our application of this IBM has filled a considerable knowledge gap in understanding how river network complexity, habitat quality and location of introduction influence the invasion success of alien fishes of differing life-history traits and dispersal abilities. The predictions indicated that, in general, the location of the release is fundamentally important through its influence on the direction of dispersal required for the species to locate favourable habitat conditions. River network configuration was important in the longer term, such that more complex networks enabled the opening of more invasion fronts that drove an elevated colonization rate.
Species with higher dispersal abilities were able to colonize networks faster, especially when they had r-selected traits that facilitated establishment within cells. Correspondingly, these predictions reveal that the combination of biotic and abiotic variables can affect both dispersal and establishment processes, but that can be better understood when these processes are decoupled within predictive models.

ACK N OWLED G EM ENTS
The RangeShifter software and manual can be downloaded from https://range shift er.github.io. VDA was supported by an iCASE studentship from the Natural Environment Research Council (NE/ R008817/1) and the Environment Agency.

CO N FLI C T O F I NTE R E S T
None of the authors have any conflicts of interest.

PEER R E V I E W
The peer review history for this article is available at https://publo ns.com/publo n/10.1111/ddi.13459.

DATA AVA I L A B I L I T Y S TAT E M E N T
All data used are available in the main text and supporting information. Author contributions: All authors contributed to the study design. VDA led analyses and writing, assisted by SCFP, PKG, DA, JMJT and JRB. All authors contributed to revising the manuscript and approved its submission.

S U PP O RTI N G I N FO R M ATI O N
Additional supporting information may be found in the online version of the article at the publisher's website.