INTRODUCTION
Understanding the mechanisms governing the distribution of species in space and time is essential to ecology and has never been more important than during periods of large-scale change, characteristic of the Anthropocene (Zalasiewicz et al., 2010). Notably, the introductions and subsequent invasions of non-native species are becoming increasingly frequent due to human activities (Kueffer, 2017), and though widely studied, our understanding of their dynamics is rudimentary (Kumschick et al., 2015). Successful biological invasions all share three main components (each can be modified by humans): introduction of the non-native species to a new ecosystem, the establishment of breeding populations, and their geographic spread to new areas beyond the introduction point (Jeschke & Strayer, 2005). Though a biological invasion can be broken into these three components, it is often difficult to disentangle them (Catford et al., 2009). What is more, the success of these components is not only a function of the invasiveness of the species but also of the receiving ecosystem's ability to exclude it, called the “invasibility” (Hui et al., 2016). Understanding the relationship between invader and ecosystem characteristics is essential to the mitigation of current biological invasions and the prevention of future introduction events (Lenzner et al., 2020).
We follow Johnson et al. (2006) by defining spread as an increase in geographic extent according to a species-specific dispersal mechanism, dependent on the characteristics of the environment that make it suitable. Spread, in this context, does not include human transport. Common approaches to modeling the rate of spread of an invasion include the use of partial differential equations (Fisher, 1937; Kolmogorov et al., 1937) or integrodifference equations (Kot et al., 1996; Neubert & Caswell, 2000), and may incorporate dispersal kernels (Hudgins et al., 2017), metapopulation models (Hanski et al., 1995), probabilistic models (Leung & Mandrak, 2007), or spatially explicit simulations (Mang et al., 2018). The reaction–diffusion model, a partial differential equation commonly used in invasion ecology, uses a few simple parameters to predict the rate of spread of an invasion, propagating as an invasion front, while assuming a homogenous environment in continuous time (Ōkubo & Levin, 2001; Shigesada & Kawasaki, 1997). The reaction–diffusion model is spatially explicit and is simple enough to be easily adaptable to many different systems, as it predicts spread using demographic and dispersal parameters specific to the non-native population (Andow et al., 1990; Kot et al., 1996; Ōkubo & Levin, 2001). This type of model is more commonly applied to terrestrial systems (such as Andow et al., 1990; White et al., 2012 but see Suksamran & Lenbury, 2019), as terrestrial species generally face fewer barriers (i.e., mountains and rivers) than do freshwater species (i.e., any nonaquatic habitat), but the framework is likely relevant to aquatic ecosystems.
Once spread occurs during a successful invasion, populations may become naturally established in new areas and the process of spread and establishment is repeated. Establishment (or naturalization) is thus the ability of the species to overcome environmental barriers to colonize, grow, and successfully reproduce in a new area (Richardson et al., 2000), making it, like spread, a function of both the intrinsic characteristics of the non-native species and those of the native ecosystem (Alpert et al., 2000; Hui et al., 2016). While we predict that spread can be modeled simply using the characteristics of the invading population (i.e., intrinsic growth and dispersal), establishment dynamics should be explained by the characteristics of the receiving ecosystem (Alpert et al., 2000) as the invader's realized niche reflects the suitability of local environmental conditions (Hui et al., 2016; Korsu et al., 2007). These are often scale-dependent. For example, variables such as temperature, precipitation, and soil or water chemistry vary along spatial gradients, and the abiotic tolerance of a species determines in which areas along this gradient it is able to persist (Havel et al., 2002). In addition, biotic factors such as the presence of native competitors dictates the availability of resources, the niche space, and the potential for interactions between native and non-native species (Korsu et al., 2007). Such abiotic and biotic variables at the local scale will likely determine a non-native species' ability to establish and persist in a particular vacant patch (Harig & Fausch, 2002). More broadly, landscape-scale variables such as ecosystem productivity, environmental heterogeneity, connectivity, and topography can influence the genetic structure of invasive populations (Launey et al., 2010) and their ability to disperse, contributing to broader scale patterns of establishment (Muthukrishnan et al., 2018). The distance to the nearest established patch, sometimes used as a proxy for the intensity of propagule pressure (Havel et al., 2002), may influence the probability of establishment (Rouget & Richardson, 2003). This array of local- and landscape-scale environmental variables that influence the establishment of aquatic invasive populations illustrates the need to not only ask where an invader is spreading but also how they are able to establish there.
While the study of the various dynamics of invasion (i.e., introduction, spread, and establishment) is not new or uncommon, most often they are studied independently from one another (Kueffer et al., 2013). However, several recent studies have attempted to integrate two or more components of invasion to better predict and manage invasions. Terrestrial examples of integrative approaches to studying invasion include work on dung beetles (Onthophagus gazella and Onitis alexis) in Australia (Duncan, 2016), common ragweed (Ambrosia artemisiifolia) in central Europe (Mang et al., 2018), and various forest pests (i.e., insects, mites, and tree pathogens) in the United States (Hudgins et al., 2017). Integrative approaches have also emerged to study the aquatic invasions of smallmouth bass (Micropterus dolomieu) in British Columbia (Sharma et al., 2009), and zebra mussels (Dreissena polymorpha) in North America (Leung & Mandrak, 2007). These integrative approaches, however, have not been developed for invasive species with life histories that cross ecosystem boundaries, which include highly invasive species such as anadromous brown trout (Salmo trutta) and rainbow trout (Oncorhynchus mykiss). For example, brown trout and rainbow trout can disperse through freshwater and marine environments, and this anadromy may be an important driver of invasion success for these species (Thibault et al., 2010; Westley & Fleming, 2011). Such complex life histories may increase the probability of dispersal during an invasion (Morissette et al., 2021), and thus one invasive species has the potential to impact multiple ecosystems within an individual's lifecycle. Integrative approaches may be necessary to predict the invasions of species with life histories that cross ecosystem boundaries as environmental conditions and invasion dynamics vary across ecosystems.
Here, we build on previous work to integrate modeling and empirical data to study the rate of spread and the mechanisms of establishment of a pervasive invader (see Figure 1 for overview of analysis). Specifically, we study brown trout invasion on the Island of Newfoundland. Brown trout are native to Eurasia but have been introduced globally, and their life history variability makes predicting invasion and the accompanying ecological impacts complex (see review in Buoro et al., 2016). Brown trout were introduced to 16 watersheds on the Island of Newfoundland, Canada from 1883 to 1906 (Hustins, 2007). Using the introduction of brown trout to the Island of Newfoundland as a case study, we integrate several datasets, mathematical modeling, and statistical analyses to (1) make predictions about the rate of spread of an aquatic invasion using a simple reaction–diffusion model parameterized by values from independent literature; (2) compare it to the actual rate of spread estimated using the introduction history and several measures of marine migration distance; (3) identify the environmental variables that best explain the patterns in establishment of populations within the invasion; and (4) determine whether the influence of these variables differs along two coastal pathways of invasion.
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We hypothesize that parameterizing a simple model with data for demographic and diffusion parameters from the literature can make accurate predictions of the rate of spread of brown trout in Newfoundland, while assuming a homogenous environment (Figure 2a). We predict then that (1) the predicted rate of spread obtained from the classic reaction–diffusion model will be comparable to the actual spread rate observed (Andow et al., 1990; Shigesada & Kawasaki, 1997) using coastal distance (Labonne et al., 2013). Next, by first considering the ecological requirements of brown trout, we hypothesize that where natural establishment is possible, patterns in establishment can be explained using local abiotic, biotic, and landscape-scale environmental variables (Figure 2b,c). We thus predict that (2) of the local abiotic environmental variables, water conductivity (Enge & Kroglund, 2011), turbidity (Birtwell et al., 2008), calcium (Hartman et al., 2016), and pH (Matena, 2017) will be positively correlated with the presence of brown trout; (3) a local biotic variable, the presence of native Atlantic salmon (Salmo salar), will negatively correlate with brown trout establishment (Bietz et al., 1981; Korsu et al., 2007); and (4) landscape-level variables such as elevation (Carosi et al., 2020), watershed size (Harig & Fausch, 2002), and estuary area (Warner et al., 2015) will positively correlate with brown trout presence, whereas distance to original introduction point and distance to nearest introduction point (Havel et al., 2002) will be negatively associated with trout presence. Finally, as the north and south coasts of Newfoundland have more dramatic marine environmental differences than implied by latitude, and different trout introduction histories and established populations that are genetically different (O'Toole et al., 2021), we hypothesize that the brown trout invasion has split into two pathways, with differential establishment dynamics. We then predict that (5) different environmental variables will be responsible for explaining establishment patterns between the north and south coasts.
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METHODS
Study system
As a case study, brown trout in Newfoundland present the opportunity to predict salmonid invasions that are relevant to invasive species research because the introduction history of non-native salmonids on the Island of Newfoundland is well-documented (Westley & Fleming, 2011). Glacial gouging led to the creation of thousands of lakes and streams on the island (Protected Areas Association of Newfoundland and Labrador, 2008), making it both an ideal landscape for freshwater studies, and a potentially hospitable place for an anadromous invader (one that uses both freshwater and marine environments over the course of its life cycle). Native to Eurasia, brown trout were introduced to the Island of Newfoundland from 1883 to 1906. A total of 16 watersheds on the Avalon Peninsula of eastern Newfoundland were stocked with trout from Scotland (of the Loch Leven strain), England, or Germany (Frost, 1940; Hustins, 2007). Since then, brown trout have spread westward via migration through the marine environment. By 2010, brown trout were located in at least 67 watersheds in eastern Newfoundland including those that drain into Trinity Bay and Placentia Bay (Westley & Fleming, 2011), with populations reaching the eastern side of the Burin and Bonavista Peninsulas. However, it is unclear exactly what facilitates their spread. There is significant potential for future spread on the island due to the availability of higher productivity watersheds and estuaries in central and western Newfoundland (Warner et al., 2015).
Predicting the rate of spread using a reaction–diffusion model
To test Prediction 1 that the model's predicted rate of spread will approximate the actual spread rate, we parameterized a reaction–diffusion model (see Appendix S1 for details on the reaction–diffusion model). From the reaction–diffusion model, we could estimate the velocity of spread V using only the population growth rate α and diffusion coefficient D, the latter being independent from the model (Ōkubo & Levin, 2001). To make the model prediction, we obtained independent data on growth rate and movement from the literature for brown trout (see Appendix S1 for methods).
Armed with literature-based estimates of r and D, we estimated spread rate from Appendix S1: Equation S2 (Table 1), and then to test Prediction 1, we compared this model-estimated spread rate with the observed spread rate (see below). We used a range of values of r and D to capture the natural range of variability observed in the literature. Specifically, we used three values of r in our model: (1) the mean and (2) median across studies, and (3) the mean of all the positive values. Also, we used four values for the diffusion parameter that reflect the large variation in dispersal distances of brown trout in the ocean, corresponding to the minimum, mean, median, and maximum calculated from the distribution of values from our literature search. As a type of sensitivity analysis, we then crossed them and used all the 12 possible combinations of these two parameters as inputs to the reaction–diffusion equation to obtain estimates of V, velocity of spread.
TABLE 1 Rate of spread,
| Parameters | Model output | |
| Intrinsic growth, r (year−1) | Diffusion, D (km2/year) | Predicted velocity, V (km/year) |
| 0.0183 | 27.12 | 1.41 |
| 0.16 | 27.12 | 4.17 |
| 0.4 | 27.12 | 6.59 |
| 0.0183 | 630.54 | 6.79 |
| 0.16 | 630.54 | 20.09 |
| 0.4 | 630.54 | 31.76 |
| 0.0183 | 1485.54 | 10.43 |
| 0.16 | 1485.54 | 30.83 |
| 0.4 | 1485.54 | 48.75 |
| 0.0183 | 5292.51 | 19.68 |
| 0.16 | 5292.51 | 58.20 |
| 0.4 | 5292.51 | 92.02 |
Measuring the actual rate of spread from the current distribution
To estimate the actual spread of brown trout in Newfoundland, we determined the historic (Hustins, 2007) and current distribution of brown trout from multiple sources, including data from a set of previous studies in Newfoundland (see Porter et al., 1974) and validated using more recent, but less comprehensive work (Westley & Fleming, 2011), Fisheries and Oceans Canada (DFO) angler's guide (DFO, 2020), and our own sampling. We calculated actual spread using distance between the introduction points and the current invasion front, using two methods to measure the distance with the measuring tool on Google Maps (2021). Radial distance was measured as the direct line between the mean of the midpoint of the introduction points on the Avalon to the two furthest points of confirmed brown trout presence on each coast, one each in Trinity (north coast) and Placentia (south coast) Bays. In addition, we calculated the distance following the coast between introduction and the same two furthest points. The coastal distance is likely the most ecologically relevant as brown trout generally follow the coast while migrating in the ocean (Kristensen et al., 2019; Labonne et al., 2013). Data are not available to track spread at multiple points in time; therefore, each empirical estimate of spread is based on two “points” (or midpoint of several points; see above): one historical introduction point and one invasion front point.
To analyze the environmental correlates of brown trout establishment and to verify whether brown trout have spread to new watersheds since Westley and Fleming's study in 2011, we first validated the brown trout, Atlantic salmon, and brook charr (Salvelinus fontinalis) occurrence data from Porter et al. (1974) and Westley and Fleming (2011). During the summer of 2020, we sampled 21 rivers along the current invasion front, mostly draining into Placentia Bay and Trinity Bay. The choice of sites was informed by previous sampling (including Westley & Fleming, 2011, and ongoing government projects), environmental data, and using stream length and width to identify rivers large enough to potentially support anadromous salmonids. Stations were within 5 km upstream of the ocean, which is the section brown trout are most likely to be found (Budy et al., 2008) and were within 1 km of a road for accessibility. At each of the 21 rivers, we delineated two to five stations using barriers nets, each of which included runs, riffles, and pools to control for the differences in trout, charr, and salmon habitat use. We used a Smith-Root LR-24 backpack electro-fisher to conduct two-pass depletion at each station. We used counts of salmonids caught by electrofishing to estimate occurrence and relative abundance.
Analyzing the environmental correlates of establishment by coast
To test Predictions 2–5, that abiotic, biotic, and landscape environmental variables correlate with the presence of brown trout, we focused on explaining patterns only in the natural establishment of invasive brown trout. We assume that the presence of brown trout juveniles of different sizes in a river is evidence of establishment in a watershed. Only rivers that are likely to be reached by straying trout (i.e., on the east side of the initial invasion front) were included in the analyses—a total of 165 rivers (Appendix S2). We extracted data on natural and human-made barriers occurring on rivers in eastern Newfoundland (Porter et al., 1974). An impassable barrier to brown trout dispersal was defined as more than 5 m in height, based on adult trout's ability to jump over 3 m high on average (Reiser & Peacock, 1985), further if there is high flow. Rivers were then defined as allowing natural establishment if they did not have an impassable barrier at or near the river mouth (Budy et al., 2008; Westley & Fleming, 2011). We removed 11 rivers where natural establishment was not possible due to such barriers. As well, any sites where brown trout were established through known human-mediated introductions (n = 15 rivers) were not included in the analyses. Finally, we removed any rivers from the analyses that had incomplete environmental data in the Porter et al. dataset (Porter et al., 1974; n = 86 rivers, see MacDonald, 2022 and Appendix S2). In the end, we were left with 53 rivers in the analysis (Appendix S2: Table S1).
Based on previous work on salmonids (i.e., Hesthagen & Jonsson, 1998; MacCrimmon & Marshall, 1968; Westley & Fleming, 2011), we considered a suite of abiotic, biotic, and landscape-level environmental predictors that would likely affect brown trout's ability to establish in a river. For Prediction 2, that abiotic environmental variables will influence trout establishment patterns, we used continuous data on water conductivity, pH, turbidity, and calcium for each river (Porter et al., 1974). Related to Prediction 3, the effects of local biotic environmental variables, we obtained salmon occurrence data from Porter et al. (1974) and updated it with recent information from local anglers through a survey. The occurrence of Atlantic salmon is a binary predictor variable coded as being present or absent from a river. Brook charr presence–absence was not included in the statistical models because they are ubiquitous in rivers on the Island of Newfoundland. Next, for Prediction 4 pertaining to the influence of landscape-level environmental variables on brown trout establishment patterns, we again used data from Porter et al. (1974) for watershed relief and area, supplemented by distance to original introduction from Westley and Fleming (2011). We then measured estuary size and distance to nearest introduction using the measurement tool on Google Maps. All five landscape-level environmental variables were continuous predictors. Finally, to test Prediction 5 that establishment patterns will be explained by different environmental variables depending on the coast, we split the rivers and their corresponding environmental datasets (27 rivers in the north, 26 in the south) and separately analyzed them for establishment patterns. We defined the geographic boundary between the north and south coasts as the divide between the Cape Race and Chance Cove watersheds on the Avalon Peninsula (Figure 2a). This boundary divides the coast based on oceanographic differences caused by currents (i.e., Labrador Current to the north, and North Atlantic Drift to the south—which is an offshoot of the Gulf Stream) and is also used to define local Atlantic salmon population units by Fisheries and Oceans Canada (DFO, 2005).
We fitted generalized linear models with a binomial error distribution using a logit link. The response variable was brown trout presence–absence (i.e., established, not established) at 53 rivers within the invasion range. The 10 predictor variables were divided into three environmental categories based on our predictions: abiotic (conductivity, pH, turbidity, and calcium), biotic (salmon presence–absence), and landscape-level variables (watershed relief, area, estuary area, distance to original introduction, and distance to nearest introduction point; Table 2). We used variance inflation factor analysis (car package; Fox et al., 2021) to test for multicollinearity among covariates. We ran models with all possible combinations of variables within the same environmental categories (abiotic, biotic, and landscape), which were each ranked using corrected Akaike information criterion (AICc) for small sample size, using the AICcmodavg package (Mazerolle, 2020). AICc ranks models according to their ability to explain the most variation while maintain the fewest number of parameters possible. For each explanatory variable within the model, we calculated the exponent of the model coefficient, called the odds ratio (OR). This is used to evaluate the odds that brown trout will be present (i.e., established) in a river given a certain explanatory variable.
TABLE 2 The values of actual spread we calculated using current and historic distribution data of brown trout.
| Region | River/location | Latitude | Longitude | Radial | Coastal | ||
| Distance (km) | Spread rate (km/year) | Distance (km) | Spread rate (km/year) | ||||
| Origin | Coastal midpoint | 47.522969 | −52.969084 | … | … | … | … |
| North | Princeton Brook | 48.659278 | −53.115750 | 121 | 1.03 | 394 | 3.37 |
| South | Little Salmonier | 47.071158 | −55.179675 | 174 | 1.49 | 628 | 5.37 |
Finally, based on our results from the above analyses, we estimated how long it will take brown trout to spread to key areas on the Island of Newfoundland (see Figure 1 for overview of analyses). All mathematical and statistical models were run in the statistical software R (R Development Core Team, 2021).
RESULTS
Predicting the rate of spread using a reaction–diffusion model
Our literature search for parameter values revealed 11 studies that fit the search criteria for intrinsic population growth and 15 studies for diffusion. We did not find any studies of local Newfoundland trout populations that fit the criteria, although this would result in the most population-specific parameterization (Purchase et al., 2005; see Appendices S3 and S4 for details on data). For intrinsic growth (Appendix S3), the mean across studies, mean of all the positive values, and maximum were r1 = 0.018, r2 = 0.160, and r3 = 0.400, respectively. The minimum, mean, median, and maximum of the distribution of diffusion values (Appendix S4) were Dmin = 27.1 km2/year, Dmean = 630.5 km2/year, Dmedian = 1485.5 km2/year, and Dmax = 5292.5 km2/year, respectively. These values represent the range of short-distance (Dmin) to long-distance dispersal (Dmax) that naturally occurs within brown trout populations.
Using three values of intrinsic population growth (i.e., r) and four values for the coefficient of diffusion (i.e., D) for brown trout, we obtained 12 possible combinations of parameter values to be input into the reaction–diffusion model equation and 12 estimates of the rate of spread of brown trout on the Island of Newfoundland (Table 2, Figure 3). Estimates of rate of spread obtained from the model ranged from 1.4 to 92.0 km/year, with a mean of 27.6 km/year (SD = 26.0) and median of 19.9 km/year.
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Measuring the actual rate of spread from the current distribution
The furthest point of the brown trout invasion on the north coast is Princeton Brook on the Bonavista Peninsula (48°39′33.4″ N, 53°06′56.7″ W), and in the south, Little Salmonier River on the Burin Peninsula (47°04′16.2″ N, 55°10′46.8″ W). The mean radial estimate of spread to these furthest points is 1.26 km/year (north = 1.03, south = 1.49), whereas the mean coastal estimate is 4.4 km/year (north = 3.4, south = 5.4; Table 2). Of the 14 rivers we sampled in 2020 that overlapped with Porter et al.'s (1974) dataset for presence–absence of brown trout, only one, Renews River (46°56′05.3″ N, 52°57′14.3″ W), revealed conflicting occurrence between the datasets. The other 13 rivers (92.9%) were validated by our sampling. Other recent studies (Warner et al., 2015; Westley & Fleming, 2011) confirmed the presence of brown trout in Renews River; therefore, we use this river as a presence point.
Analyzing the environmental correlates of establishment by coast
Brown trout have been observed in 81 of the 165 watersheds (49%) that are located within the brown trout's current invasion range. Of these, brown trout have naturally established populations in 56 watersheds on the island, which span each of the bays between the first introduction point in St. John's and the current invasion front. Along the north coast, brown trout are present in 63 and absent in 30 watersheds (north total = 93 watersheds), while on the south coast, they are present in 18 and absent in 54 watersheds (south total = 72 watersheds). Eleven rivers were excluded from the analysis because barriers to dispersal (dams, waterfalls, etc.) precluded natural establishment. Fifty-three rivers from different watersheds within this range had complete environmental data and were used in the establishment analyses.
There were a broad range of abiotic freshwater variables, although they did not vary greatly between the north and south coasts (Table 3). The mean water conductivity was 31.5 μmS/cm (north = 34.7, south = 28.3), mean pH was 6.3 (north = 6.4, south = 6.2), mean turbidity was 1.1 JTU (north = 0.8, south = 1.7), and mean calcium was 1.4 ppm (north = 1.4, south = 1.5). As the biotic environmental variable, Atlantic salmon were present in 42 (79.3%) of the rivers used in the analysis (north = 18, south = 24), 19 (45.2%) of which overlapped with the presence of brown trout (north = 13, south = 6). Only four (7.6%) rivers did not contain any brown trout or Atlantic salmon (north = 2, south = 2). In general, the landscape-level environmental variables varied more between coasts. Mean watershed relief was 261.6 m (north = 259, south = 168). Watershed area averaged 101.0 km2 (north = 63.5, south = 140). Twenty-nine rivers (54.7%) had significant estuaries measuring at least 2 ha (north = 13, south = 16), of which the mean size was 71.3 ha (north = 21.0, south = 123.6). The mean distance to the first introduction location in St. John's was 268 km (north = 132, south = 405), whereas the mean distance to the nearest introduction point was 189 km (north = 41.9, south = 341.7).
TABLE 3 Measurements of the environmental variables used as explanatory variables in the series of generalized linear models (mean with SD in parentheses, except for salmon river counts).
| Environmental variable | North | South | Combined | ||
| Absent | Present | Absent | Present | Overall mean | |
| Abiotic | |||||
| pH | 6.37 (0.5) | 6.42 (0.3) | 6.20 (0.3) | 6.32 (0.3) | 6.32 (0.4) |
| Conductivity (μmS/cm) | 31.14 (4.9) | 35.9 (27.5) | 28.05 (9.7) | 29.0 (9.5) | 31.53 (18.3) |
| Turbidity (JTU) | 0.73 (0.2) | 0.90 (0.8) | 1.30 (1.0) | 1.84 (1.8) | 1.25 (1.1) |
| Calcium (ppm) | 1.11 (0.4) | 1.48 (1.3) | 1.55 (1.9) | 1.23 (0.4) | 1.43 (1.4) |
| Biotic | |||||
| Salmon rivers (count) | 7 | 20 | 20 | 6 | 53 |
| Landscape | |||||
| Watershed area (km2) | 55.43 (24.1) | 66.35 (28.7) | 114.95 (96.8) | 223.33 (284.7) | 101.02 (118.9) |
| Watershed maximum relief (m) | 248.0 (79.3) | 254.95 (43.4) | 263.6 (59.7) | 292.67 (64.6) | 261.57 (57.2) |
| Distance to original introduction (km) | 161.57 (49.1) | 121.45 (55.3) | 414.2 (112.6) | 374.0 (112.8) | 310.44 (242.7) |
| Distance to nearest introduction point (km) | 36.57 (49.1) | 43.8 (45.1) | 386.35 (268.1) | 193.0 (121.8) | 189.0 (234.4) |
| Estuary size (ha) | 43.48 (107.8) | 13.15 (23.7) | 52.97 (149.7) | 359.01 (507.3) | 71.34 (213.5) |
Our results do not support our abiotic or biotic predictions (Prediction 2 and Prediction 3, respectively) (Table 4). Specifically, the abiotic and biotic models for both north and south datasets all ranked below the intercept according to the AICc. The single biotic model (salmon presence/absence) did not converge for the south dataset likely because salmon are only absent from 2 of the 26 rivers. While our power to detect effects is relatively low (i.e., n = 53 total rivers), it is important to note that even univariate models for abiotic and biotic features (i.e., models with one predictor) do not rank above the null models, indicating no relationship of these features with brown trout presence/absence. Thus, we found no evidence that conductivity, pH, turbidity, calcium, and salmon presence–absence explained the variation in brown trout establishment patterns along the north or south coasts. As well, all landscape variable models were uninformative (i.e., not related to the response) for the north dataset, as were watershed area, relief, and distance to the origin in the south. However, three landscape models ranked above the intercept for the south dataset and were ΔAICc < 4 of the top model. The top-ranking model included the predictors estuary size and distance to nearest introduction point, and explained 38% of the variation in establishment patterns. Estuary and distance to nearest introduction as separate models made up the second and third ranked models, and explained 24% and 18% of the variation, respectively. The odds of establishment in this top ranked model of south coast river establishment were positively associated with estuary size (coefficient = 0.004, OR = 1.004, OR 95% CI = [0.999, 1.010]) and negatively associated with distance to nearest introduction point (coefficient = −0.04; OR = 0.995, OR 95% CI = [0.989, 1.002]; Appendix S5: Table S1).
TABLE 4 Subset of AICC outputs for a series of generalized linear models obtained for north and south datasets.
| Model parameter | K | AICc | ΔAICc | AICc weight | LL | R2 |
| North | ||||||
| Abiotic | ||||||
| Intercept | 1 | 33.06 | 0 | 0.29 | −15.45 | 0 |
| Calcium | 2 | 34.6 | 1.54 | 0.14 | −15.05 | 0.04 |
| Turbidity | 2 | 35.07 | 2 | 0.11 | −15.28 | 0.02 |
| Conductivity | 2 | 35.13 | 2.07 | 0.1 | −15.31 | 0.01 |
| pH | 2 | 35.32 | 2.26 | 0.09 | −15.41 | 0 |
| Biotic | ||||||
| Intercept | 1 | 33.06 | 0 | 0.75 | −15.45 | 0 |
| Salmon presence–absence | 2 | 35.31 | 2.24 | 0.25 | −15.4 | 0.01 |
| Landscape | ||||||
| Intercept | 1 | 33.06 | 0 | 0.2 | −15.45 | 0 |
| Estuary area | 2 | 34.11 | 1.04 | 0.12 | −14.8 | 0.07 |
| Watershed area | 2 | 34.53 | 1.46 | 0.09 | −15.01 | 0.05 |
| Distance to nearest introduction point | 2 | 35.26 | 2.2 | 0.07 | −15.38 | 0.01 |
| Watershed relief | 2 | 35.31 | 2.25 | 0.06 | −15.41 | 0 |
| Distance to original introduction | 2 | 35.36 | 2.29 | 0.06 | −15.43 | 0 |
| South | ||||||
| Abiotic | ||||||
| Intercept | 1 | 30.26 | 0 | 0.31 | −14.05 | 0 |
| pH | 2 | 31.94 | 1.68 | 0.13 | −13.71 | 0.04 |
| Calcium | 2 | 32.41 | 2.15 | 0.11 | −13.94 | 0.01 |
| Turbidity | 2 | 32.47 | 2.21 | 0.1 | −13.97 | 0.01 |
| Conductivity | 2 | 32.56 | 2.31 | 0.1 | −14.02 | 0 |
| Biotic | ||||||
| Intercept | 1 | 30.26 | 0 | 0.65 | −14.05 | 0 |
| Salmon presence–absencea | 2 | … | … | … | … | |
| Landscape | ||||||
| Distance to nearest introduction point + estuary area | 3 | 27.77 | 0 | 0.39 | −10.34 | 0.38 |
| Estuary area | 2 | 28.12 | 0.35 | 0.32 | −11.8 | 0.24 |
| Distance to nearest introduction point | 2 | 29.33 | 1.56 | 0.18 | −12.4 | 0.18 |
| Intercept | 1 | 30.26 | 2.49 | 0.11 | −14.05 | 0 |
| Watershed area | 2 | 30.74 | 4.43 | 0.01 | −13.11 | 0.11 |
| Watershed relief | 2 | 31.5 | 5.19 | 0.01 | −13.49 | 0.06 |
| Distance to original introduction | 2 | 31.82 | 5.51 | 0.01 | −13.65 | 0.05 |
Based on the mean observed coastal spread from the 1880s to present, we calculated that it would take another 33 years (i.e., 2054) for brown trout to spread to Terra Nova National Park, west of the Bonavista Peninsula (48°23′27.1″ N, 54°11′29.7″ W). In ~23 years (i.e., 2045), brown trout could spread around the tip of the Burin Peninsula to Point May (46°53′55.6″ N, 55°56′13.2″ W) and may begin to spread into Fortune Bay. As well, it would take 103 years (i.e., 2124) of spread for brown trout to reach the Conne River (47°47′40.5″ N, 55°49′39.9″ W) and 206 years to reach Cape Ray (47°37′12.9″ N, 59°18′24.6″ W) on the southwestern coast of Newfoundland. These spread predictions from observed establishment data fall within the range of spread predictions for our reaction–diffusion model parameterized based on brown trout growth and movement rates. Specifically, the reaction–diffusion model predicts that it would take 2 (min)–104 (max) years and 1 (min)–72 (max) years for brown trout to spread to Terra Nova National Park and Point May, respectively.
DISCUSSION
Though biological invasions are ubiquitous with human activity, our understanding of invasion success and our ability to make predictions about future spread and establishment remains uncertain, particularly for species with life cycles that cross ecosystem boundaries (Ricciardi et al., 2017). We build on existing studies that use mathematical models to study several components of aquatic invasions (e.g., Leung & Mandrak, 2007; Sharma et al., 2009) by integrating a simple mathematical model of spread rate with an analysis of the correlates of establishment to test our ability to make predictions and explain invasion dynamics. We observed much slower rates of brown trout spread on the Island of Newfoundland than the majority of predictions made by our empirically parameterized reaction–diffusion model. Also, two of our landscape-level variables explained some of the variation in occurrence patterns of brown trout, although only along one of the coastal pathways of the invasion.
The rate of spread of brown trout on the Island of Newfoundland
Our data suggest that brown trout on the Island of Newfoundland are spreading at an average rate of 4.4 km/year. This is a slow estimate of observed spread, but it is comparable to the 4 km/year estimated in a previous study on the Island of Newfoundland (Westley & Fleming, 2011). In Newfoundland, brown trout naturally established at least 56 watersheds in 125 years (0.4 watersheds per year; Westley & Fleming, 2011), compared with a rate of 0.8 watersheds per year in the Kerguelen Islands in the Southern Indian Ocean (Lecomte et al., 2013). The observed spread rate of brown trout in Newfoundland is also relatively slow compared with empirical spread rates reported for other invasive species. For example, the spread rate of exotic marine species into the Mediterranean Sea from the Suez Canal ranged from 20.9 km/year (diamondback puffer, Lagocephalus guentheri) to 705.4 km/year (Smith's cardinal fish, Jaydia smithi; Azzuro et al., 2022). Invasive hemlock wooly adelgid (Adelges trugae), gypsy moth (Lymantria dispar dispar), cereal leaf beetle (Oulema melanopus), and cabbage white butterfly (Pieris rapae) mean spread rates in North America are reported as 12.5 km/year (Evans & Gregoire, 2007), 20.8 km/year (Leibhold et al., 1992), 62.4 km/year (Andow et al., 1990), and 86.7 km/year (Andow et al., 1990), respectively. In Europe, invasive muskrat (Ondatra zobethica) and leafminer (Cameraria ohridella), mean spread rates are reported as 11.4 km/year (Andow et al., 1990) and 27.5 km/year (Augustin et al., 2004), respectively.
There are likely many ecological and environmental factors that can limit the growth and dispersal of non-native individuals, resulting in slow spread rate (Goldstein et al., 2019; Johnson et al., 2006). Newfoundland rivers are generally less productive than other areas with brown trout (Randall et al., 2017), which can reduce the rate of natural increase of fish populations (Lyon et al., 2019). Moreover, angling pressure on returning adults, which in Newfoundland is significant in estuaries where brown trout are known to frequent (Warner et al., 2015), could also limit the number of adults returning to fresh water to spawn and maintain low densities (Hard et al., 2008). The presence of other salmonids in Newfoundland waters could also limit brown trout's spread. For example, in New Zealand and the Kerguelen Islands, non-native brown trout are extremely successful invaders, possibly due to the absence of native salmonids in the southern hemisphere and the corresponding presence of a “vacant” niche (Townsend, 1996). On the Island of Newfoundland, native Atlantic salmon and brook charr have natural histories that considerably overlap with those of brown trout and so may slow the latter's invasion according to the “biotic resistance hypothesis” (Olden et al., 2006), or through hybridization (Purchase et al., in press).
The simple reaction–diffusion model's lowest predictions of spread were comparable to those observed in our study system (Table 1, Figure 3). Thus, the model only predicted spread rates near our empirically observed spread when dispersal and population growth were at the low end of the gradients observed in the literature. While rare, long-distance dispersal events may be important for biological invasions (Lewis et al., 2016; Suarez et al., 2001), given the slow spread in our system, it seems that it is unlikely that long-distance dispersers are successful in spread and subsequent establishment. Consequently, brown trout spread on the Island of Newfoundland is likely driven by more common, shorter distance dispersal events. Slower rates of observed spread than are predicted by a reaction–diffusion model may indicate the influence of an Allee effect (Kot et al., 1996; Lewis & Kareiva, 1993), which is a negative relationship between the fitness and size or density of a population. One possible mechanism of the Allee effect is the decrease in available mates that can occur at lower population densities (Lewis & Kareiva, 1993). Such low densities are often found at the front of an invasion and may directly slow the rate of spread (Hurford et al., 2006) and facilitate hybridization with other species (Quilodrán et al., 2020). Hybridization between brown trout and Atlantic salmon, or brook charr, occurs naturally in Newfoundland and may result in lower fitness of all species involved (Purchase et al., in press; Verspoor, 1988). Future work may benefit from a number of methods to refine the predictions of spread obtained from a reaction–diffusion model, including the way parameter values are estimated. Specifically, parameterizing the model using a density-dependent method of calculating intrinsic rate of growth (e.g., see Brook & Bradshaw, 2006) can lead to lower and more accurate estimates of population growth. As such, future models should incorporate population-specific parameter estimates (Purchase et al., 2005) that take into account such density-dependent mechanisms to avoid making predictions that overestimate spread (Hastings et al., 2005).
Finally, the reaction–diffusion model assumes environmental homogeneity. The spread of brown trout in the Kerguelen Islands was initially fast, but slowed somewhat after 30 years according to an ecological gradient at the front of the invasion (Labonne et al., 2013). The more westward the invasion front moved, the more inhospitable the landscape became, and the fewer resources available to juvenile brown trout (Labonne et al., 2013). If spread in Newfoundland is largely due to shorter distance dispersal, then perhaps environmental conditions (e.g., fishing pressure, estuary size, biotic interactions) need to be considered to make more accurate predictions of slower spread. Recent work has integrated environmental heterogeneity into reaction–diffusion models to study dispersal in patchy landscapes (Maciel et al., 2020) and the effect of spatial variation, competition, and individual movement on spread (Lutscher et al., 2020; Maciel & Lutscher, 2018). Given multiple components of environmental heterogeneity in Newfoundland waters as discussed above, future models of spread should integrate the environmental characteristics of the receiving ecosystem that may facilitate or limit growth and dispersal in the landscape to test the importance of these phenomena in this system.
Analyzing the environmental correlates of establishment by coast
We found no evidence that any of the abiotic or biotic variables that we analyzed were correlated with establishment patterns of brown trout in Newfoundland (Table 4). Though there is evidence that some water chemistry variables influence salmonid behavior (Sweka & Hartman, 2001), physiology (Liebich et al., 2011), and density (Enge & Kroglund, 2011) in different ecological contexts, there exists no real consensus in the literature on the importance of abiotic variables in structuring trout establishment. The lack of evidence supporting our abiotic predictions may reflect the coarse resolution of our data (Fernandez et al., 2017), as our measurements, which are the best available data, are a snapshot of the environmental conditions at one time and spatial scale, or else averaged over the summer. However, measuring water chemistry values at specific times of year (i.e., at spawning; Beechie et al., 2008) and incorporating abiotic and biotic factors at multiple spatial scales (Rich et al., 2003) may be more relevant than an average seasonal value. Though Bietz et al. (1981) found that resource competition increases between salmonids within smaller river systems, counter to our prediction, we did not find evidence of an influence of Atlantic salmon occurrence on brown trout presence in the rivers we studied. Perhaps, habitat segregation between brown trout and Atlantic salmon according to their preferences for different depths and water velocities occurs in our study rivers as observed elsewhere (Gibson & Cunjak, 1986), therefore reducing competition between the species.
On the other hand, our analyses provided weak evidence that two landscape variables influence brown trout establishment. There is consensus in the literature that landscape variables structure establishment patterns of invaders, although the key variables differ somewhat from those in our study (Labonne et al., 2013; Suarez et al., 2001). Consistent with our predictions and other research on brown trout invasion in the Kerguelen Islands (Labonne et al., 2013), shorter distance to nearest introduction point and larger estuary areas are associated with brown trout presence. That estuaries are important for brown trout in Newfoundland is well understood (Veinott et al., 2012; Warner et al., 2015), likely because estuaries provide trout with feeding opportunities and a transition zone in which to undergo the physiological changes required when entering or leaving a saline marine environment (McDowall, 1976). Our analyses of establishment dynamics suggest that brown trout may be more likely to establish in rivers with significant estuarine areas that are close to a source population.
The ability of some landscape-scale variables (Table 4, Appendix S5: Table S1) to explain variation in southern establishment patterns but not in the north is likely due to the vastly different introduction histories and marine environments between the coasts. Launey et al. (2010) found that patterns of genetic diversity of brown trout were best explained by the introduction history, whereby each established population was directly able to act as a source of colonization for the nearby rivers in the Kerguelen Islands. This generally corroborates the stepping-stone pattern found in Newfoundland by O'Toole et al. (2021). Launey et al. (2010) further found that within each establishment foci (or source), landscape factors such as river mouth accessibility, coastal characteristics, river length, and distance between rivers influenced the direction and rate of migration. Thus, perhaps the importance of landscape-level variables is moderated by the introduction history of the coast, or else it is only discernible on the scale of each source population. Along the northern coast of Newfoundland, there were many introductions dispersed throughout the range (Hustins, 2007), and thus, potentially many established foci from which migration could occur, moderating the importance of the landscape. However, along the southern coast, there existed only two introduction points (Hustins, 2007). Successful establishment of new rivers in the south could be influenced by the landscape factors that shaped migration from these foci and explain the differential importance of the landscape between the coasts. As well, coastal marine differences have been shown to affect the distribution and richness of non-native species (Ruiz et al., 2013). Such marine differences between the north and south coastal environments of Newfoundland, and resulting climates, may influence the relationship between landscape variables and brown trout establishment between the two invasion pathways.
Based on the current observed coastal spread rate of 4.4 km/year, within the next 50 years brown trout will likely spread around the tip of the Burin Peninsula into Fortune Bay, and in the north, it will spread to Terra Nova National Park, west of the Bonavista Peninsula. Though brown trout spread on the Island of Newfoundland is indeed slower than elsewhere and establishment is likely limited, it is paramount that we continue to synthesize information and make predictions about their invasion to mitigate any future ecological consequences. Atlantic salmon and brook charr populations in Newfoundland have suffered declines in the last century (DFO, 2005), and as important economic and cultural resources, it is vital that future research integrates studies of brown trout invasion with an analysis of their impacts on local salmonids, such as ability to hybridize (Lantiegne & Purchase, 2023; Purchase et al., in press). This project contributes to the growing body of invasion science that is seeking to refine knowledge, improve predictions, and explain patterns in order to minimize the introduction, establishment, and spread of current and future non-native species.
AUTHOR CONTRIBUTIONS
Data collection was conducted under Fisheries and Oceans Canada Experimental License NL-5933-20 granted to Craig F. Purchase and was approved by Memorial University Animal Use Protocol 20210062. Kelly J. MacDonald developed the project methodologies, conducted the sampling, analyzed the data, parameterized the model, interpreted the results, and wrote the manuscript. Shawn J. Leroux and Craig F. Purchase were awarded the funding, developed the project idea, and provided guidance on research design, sampling methodologies, and assisted with analyses, results, interpretation, and revisions.
ACKNOWLEDGMENTS
We thank M. Philipp, T. Lantiegne, G. McKeown, J. Phelan, M. Swain, A. Meyer, and J. Bosch for help with data collection, and I. Gall and B. Williams for sharing their local angling knowledge. We thank A. Hurford, T. Van Leeuwen, two anonymous reviewers, and the subject-matter editor for their feedback on the manuscript, and S. Duffy for sampling input. Funding was provided by the Fisheries and Oceans Canada (18-006-NL), the Natural Sciences and Engineering Research Council of Canada, the Canada Foundation for Innovation, Innovate NL, and Memorial University of Newfoundland.
CONFLICT OF INTEREST STATEMENT
The authors declare no conflicts of interest.
DATA AVAILABILITY STATEMENT
Data and code (MacDonald, 2022) are available from Figshare: .
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Abstract
Human‐mediated species introductions are contributing to the biotic homogenization of global flora and fauna. Despite extensive research, we lack simple methods of predicting how and where an introduced species will spread and establish, particularly in species with complex life histories in aquatic ecosystems. We predict that spread can be modeled simply using the characteristics of the invading population, specifically species growth rate and dispersal capacity. In addition, we predict that the establishment of introduced species should be explained by the characteristics of the receiving ecosystem. Using the brown trout (
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Details
; Leroux, Shawn J. 1
; Purchase, Craig F. 1
1 Department of Biology, Memorial University of Newfoundland, St. John's, Newfoundland and Labrador, Canada