colonization tradeoffs between short and long distance movement strategies affect species ranges

Ecological Modelling 297 (2015) 80–85

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A spatially explicit model to investigate how dispersal/colonization tradeoffs between short and long distance movement strategies affect species ranges Giovanni Strona * European Commission, Joint Research Centre, Institute for Environment and Sustainability, Via E. Fermi 2749, I-21027 Ispra, Italy

A R T I C L E I N F O

A B S T R A C T

Article history: Received 19 September 2014 Received in revised form 7 November 2014 Accepted 10 November 2014 Available online xxx

Many organisms can alternatively expand their range through long- and short-distance movements. Understanding the relative importance of these two strategies in determining species range size is of great interest in ecology and conservation biology. The more distant species move, the lower their probability of finding suitable conditions for survival. Thus, a species has a lower probability to succeed in colonization through long-distance dispersal than through short-distance dispersal, i.e., a tradeoff exists between the two strategies. Here, I investigate this issue by using a spatially explicit model where species move from patch to patch across a fragmented landscape. By analyzing the outcomes of 10,000 simulations run on the model under a wide range of tradeoff scenarios, I identified colonization ability as the strongest predictor of species range, followed by short distance dispersal ability, short distance colonization ability and long distance dispersal ability. Thus, range size of species having two different movement strategies is mainly determined by how far the species can move in the short distance strategy, and by its likelihood to succeed in colonization of distant localities, even if the dispersal/colonization tradeoffs between the two strategies are very small. ã 2014 Elsevier B.V. All rights reserved.

Keywords: Colonization Dispersal Area of occupancy Extent of occurrences Model simulations

1. Introduction There exists a natural relationship between how far a species can disperse, and its odds to succeed in colonization (i.e., in establishing a stable population). In particular, the likelihood of colonization tends to decrease at increasing dispersal distances, as the more distant a species moves from its native range, the lower its probability of finding environmental and climatic conditions suitable for its survival (see, for example, Nathan, 2006; Buston et al., 2012). Although this pattern can be ideally modeled as a long-tailed probability curve (Nathan and Muller-Landau, 2000), its experimental investigation poses several challenges, mostly related to difficulties in measuring dispersal, and in identifying the mechanisms regulating the process of establishment, which is needed to assess colonization likelihood (Nathan, 2001). This issue is also complicated by the fact that several organisms can have two distinct strategies to expand their range size, sometimes separated in time. Typical examples are found in

* Tel.: +39 332783047. E-mail address: [email protected] (G. Strona). http://dx.doi.org/10.1016/j.ecolmodel.2014.11.011 0304-3800/ ã 2014 Elsevier B.V. All rights reserved.

marine organisms, where several species can be transported by currents for hundreds of kilometers in their larval phase, but then, once settled, are only capable of small movements (James et al., 2002; Shanks et al., 2003; Torda et al., 2013). Most plant species can either colonize contiguous or far areas through different seed dispersal strategies (Nathan et al., 2002), and different range expansion mechanisms (sometimes more than two) can be found in many insects, often associated to wing polymorphism (see, for example, Harrison, 1980; Keller and Holderegger, 2013). For these species, the relationship between dispersal distance and colonization probability can be considered at two different levels, i.e., within and between range expansion mechanisms. In other words, two different dispersal and colonization kernels can be identified for, respectively, the short distance and the long distance movement strategies. Knowing the roles played by the different strategies in the determination of range size is much relevant in ecology (Caughlin et al., 2014), and conservation biology (Trakhtenbrot et al., 2005), since they clearly relate to the proportion of external vs. autochthonous recruitment which, in turn, is a key aspect in the design and management of networks of protected areas (see, for example, Sala et al., 2002; Planes et al., 2009). In most cases, however, the success in reaching a locality

G. Strona / Ecological Modelling 297 (2015) 80–85

and/or colonizing it is strongly affected by chance (especially as regarding for long distance strategies), so that a broad investigation of the ongoing processes is far from experimental reach (Nathan, 2001). It is commonly assumed that short distance dispersal events affect species geographical ranges more than long distance ones, due to the rarity of the latters (Bolker and Pacala, 1999; Harries and Clement, 2014). Yet long distance dispersal events may be more common than usually thought (Alsos et al., 2007; Anderson et al., 2011), and various authors claim that occasional long-distance jumps may be more effective in expanding species ranges and connecting isolated populations than numerous short distance dispersal events (Trakhtenbrot et al., 2005; Nathan, 2006; Pergl et al., 2011; Gillespie et al., 2012; Keller and Holderegger, 2013; Caughlin et al., 2014). This suggests that the frequency balance between short and long distance movement events is likely to have a stronger effect on species ranges than fine differences between the dispersal and colonization kernels within the two movement strategies. Tradeoffs exist in dispersal and colonization ability between the short and long distance movement strategies. For example, larvae of marine organisms have a good chance to reach distant areas, but are also subjected to very high mortality before settlement (Vaughn and Allen, 2010). This pattern is reversed for adult individuals, that have less chances to reach a far locality, but are more likely to succeed in colonization (Frisk et al., 2014). Here I use a spatially explicit model to show how investigating the effects of these tradeoffs on species ranges can improve our understanding of range expansion mechanisms. 2. Methods 2.1. Model overview Each model runs in a single fragmented landscape, which is generated by randomly positioning isolated patches in a Cartesian plane. A random value (Spmax) is associated to each patch, indicating the maximum number of species the patch can host. The dispersal kernel, i.e., the function describing the probability of a species to disperse from patch i to patch j is given by:  a 1  dij Dij ¼ ; dmax

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Fig. 2. Response of species colonization kernel, i.e., the function describing the probability of a species coming from patch i to succeed in colonizing patch j, given by Cij = [(1Spj/Spmax)  (1dij/dmax)]b, to variations in the colonization coefficient b (see Section 2). The color scale indicates the values of Cij. The parameter dij indicates the Euclidean distance between patch i and patch j, dmax is the distance between the two farthest points in the landscape, Spj is the number of species already present in the j-th patch, and Spmax is the maximum number of species the j-th patch can host.

The probability that a species, after having reached a patch, successfully colonizes it takes into account both the number of species already present in the patch, according to the classical MacArthur and Wilson (1967) model, and the distance between the arrival and the departure patches. The first aspect accounts for resource availability, while the second takes care of the fact that the farther a species moves, the lower are its chances to find favorable climatic/environmental conditions (i.e., conditions similar to those of the departure patch). Thus, the colonization kernel, i.e., the function describing the probability of a species coming from patch i to successfully colonize patch j is given by: C ij ¼

   b 1  Spj 1  dij ;  Spmax dmax

where Spj is the number of species already presented in the j-th patch, Spmax is the maximum number of species the j-th patch can host, and b is the colonization coefficient for the species under study. The response of Cij to variations in the ratios Spj/Spmax and dij/dmax for different values of b is illustrated in Fig. 2.

where dij is the Euclidean distance between patch i and patch j, dmax is the distance between the two farthest points in the landscape, and a is the dispersal coefficient for the species under study. The response of Dij to variations in the ratio dij/dmax for different values of a is shown in Fig. 1.

1) A landscape is generated by placing at random N patches (with

Fig. 1. Response of species dispersal kernel, i.e., the function describing the species’ probability to disperse from patch i to patch j, given by Dij = (1dij/dmax)a, to variations in the dispersal coefficient a. The parameter dij indicates the Euclidean distance between patch i and patch j, while dmax is the distance between the two farthest points in the landscape.

N being extracted with uniform probability from the interval [500,1500]) in a Cartesian plane. The boundaries of the Cartesian plane are set as N  X for the x-axis, and N  Y for the y-axis, with both X and Y extracted at random from the interval [50,100]. Each patch is populated with an initial set of species extracted at random from the species pool (see point 2), having size equal to 1% of Spmax of that patch. This value is rounded to the nearest integer, thus the initial set of species is empty for patches having Spmax smaller than 50. An example of random landscape is provided as Supplementary material (Fig. S1). 2) A set including a random number of species (SpN) varying between 500 and 1500 is generated. It should be highlighted that this set includes only the species of interest, i.e., a set of species having both a short and a long distance dispersal strategy. Nonetheless, the model considers the presence of other species, which contribute to turnover and compete for resources (see also points 4 and 5).

2.2. Model functioning The model runs as follows:

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3) A unique identifier and 4 values, indicating, respectively, the

4)

5)

6)

7)

8)

dispersal and colonization coefficient for the short distance strategy (a1  DT, b1), and the dispersion and colonization coefficient for the long distance strategy (a2, b2  CT) are associated to each species of interest. In order to explore uniformly a wide range of different shapes of dispersal and colonization kernels (Figs. 1 and 2), a1, b1, a2 and b2 are assigned individual values using the formula R1  R2, with R1 varying randomly in the interval (0,1), and R2 being a number extracted with uniform probability from the set {1,10}. DT and CTconstitute the tradeoffs in dispersal and colonization abilities between short and long distance movement strategies, and can vary in the interval (0,1). The smaller they are, the more pronounced are the differences in dispersal and colonization ability between the short and the long distance movement strategies. A value indicating the maximum number of species (Spmax) a patch can host is associated to each patch in the landscape. This value is extracted, for each patch, from a normal distribution with mean m and standard deviation s . For each model, m is extracted at random from the interval [0, SpN  0.25], and s is equal to 0.1  m. The minimum value of Spmax is constrained to 1. Two patches i and j are extracted at random. A species is extracted from patch i. The species moves with equal probability by short or long distance strategy, and reaches patch j with probability Dij. If the species reaches patch j, it colonizes it with probability Cij. Dij and Cij are computed using the dispersal and colonization coefficients of the selected movement strategy. To account for the possible beneficial effect of enemy release (Torchin et al., 2003; Strona and Fattorini, 2014), in a relatively small percentage of cases (5%), if the number of species already present in the patch is smaller than Spmax, the species successfully colonizes the patch independently from Cij. A patch is extracted at random, and a new species (not belonging to the set of species of interest and new to that patch) colonizes it with probability 1/Spmax. A patch is extracted at random, and a species from that patch (either of interest or not) goes extinct with probability Sp/Spmax, where Sp is the total number of species (either of interest or not) already present in the patch. The steps 5–8 are reiterated until the system reaches equilibrium, i.e., after 10,000 consecutive iterations having a balance between the number of colonization and extinction events equal to 0.

of average normalized r values in response to dispersal and colonization tradeoffs using a bi-linear spline interpolation algorithm (with the R package ‘akima’, Akima et al., 2013). I replicated the analyses using the extent of occurrences (EOO) as a measure of species range size, which I computed, for each species, as the product of its x and y ranges in the Cartesian plane. In addition, to evaluate how the relative effects of the dispersal and colonization coefficients varied throughout model evolution, in a random set of 100 models I replicated the same procedure as above by evaluating the relationships between the short and long distance dispersal and colonization coefficients, and species range every 1000 model iterations. I used Canonical Correlation Analyses (CANCOR) to examine the overall relationships between area of occupancy and extent of occurrences (dependent variables), and the corresponding short and long distance dispersal and colonization coefficients (i.e., a1  DT, b1, a2 and b2  CT, independent variables) in a sample of 1 million species extracted at random from all model simulations. I evaluated the strength of canonical relationships using canonical roots, and I used Rao’s F test to assess significance of the relationships (Mardia et al., 1979). I evaluated the effects of dependent and independent variables on the respective canonical variates by examining cross canonical loadings, and I used redundancy analysis to evaluate the amount of variance in the set of dependent variables explained by that of independent variables (Hair et al., 2006). I conducted all CANCORs using the R package ‘yacca’ (Butts, 2012). 3. Results and discussion Long distance colonization coefficient was the strongest predictor of species area of occupancy in most tradeoff scenarios (Fig. 3D), being not relevant only for dispersal tradeoff values close to 1 and colonization tradeoff values close to 0, i.e., in a situation where long and short distance dispersal coefficients were very similar, and short distance colonization coefficients were, on average, much higher than long distance ones. Conversely, long distance dispersal coefficients had little effect on species ranges under any combination of dispersal and colonization tradeoffs (Fig. 3C). Short distance colonization coefficients were important when dispersal tradeoff was moderate, i.e., when dispersal ability was similar for the short distance

2.3. Simulations and analysis I run 10,000 model simulations (i.e., I replicated 10,000 times the steps 1–8 described in Section 2.2) varying at random dispersal and colonization tradeoffs (i.e., DT and CT). At the end of each model run, I computed, for each species, its area of occupancy (AOO), as the total number of patches where it occurred. I used Spearman’s rank correlation coefficients (r) to evaluate the pairwise relationships between area of occupancy of each species, and its short and long dispersal and colonization coefficients (i.e., a1  DT, b1, and a2, b2  CT). I normalized each r value between [0,1] as:

rnorm ¼

½maxðrs Þ ; ½maxðrs Þ  minðrs Þ

where max(rs) and min(rs) are, respectively, the maximum and minimum r observed in the model. Then, to show the variation in the individual effect of short and long distance dispersal and colonization coefficients under different tradeoff scenarios, I performed a bivariate interpolation

Fig. 3. Heatmaps showing the relationships between dispersal and colonization tradeoffs (DT and CT), and the normalized correlation coefficients (rnorm) expressing the relationship between species range (measured as area of occupancy, AOO) and, respectively, the short distance dispersal coefficient (a1  DT, panel A), the short distance colonization coefficient (b1, panel B), the long distance dispersal coefficient (a2, panel C), and the long distance colonization coefficient (b2  CT, panel D). Correlations were computed on the entire set of model run outcomes (n = 10000), and the bivariate interpolation was performed using a bilinear spline interpolation algorithm.

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Table 1 Results of canonical correlation analysis conducted to investigate the overall relationships between range size (measured both as AOO and EOO), and the corresponding short and long distance dispersal and colonization coefficients (a1  DT, b1, a2 and b2  CT) in a sample of 1 million species extracted at random from all model runs. Canonical dimension

1

2 0.569 0.324 0.210

0.015 0.000 0.000

54043.718 8 0.000

73.418 3 0.000

0.319 0.262 0.207 0.331 0.563 0.321

0.007 0.013 0.002 0.001 0.002 0.012

Coefficient Root Redundancy Rao’s F test F Num df Pr(>F)

Fig. 4. Pairwise comparisons of Spearman’s rank correlation coefficients expressing the relationships between short and long distance dispersal and colonization coefficients vs. species range computed on all model run outcomes (n = 10000) using, alternatively, area of occupancy (AOO) and extent of occurrences (EOO) to measure range size.

and the long distance movement strategies (Fig. 3B). Short distance dispersal coefficients were much relevant in all situations where colonization tradeoff was moderately high (CT < 0.2), i.e., when the probability of colonization success for the short distance strategy was much higher than that of the long distance strategy (Fig. 3A). The same patterns were observed in the comparisons between dispersal and colonization coefficients, and the corresponding species ranges measured as extent of occurrences (see Fig. 4, which shows the very high correlations between the results obtained using the two different measures of species range size). Moreover, the relative importance of the four coefficients in the determination of species range became stable after relatively few model iterations (Fig. 5). Results of CANCOR analysis performed on a large sample of species (1 million) representative of all possible model settings (both in respect to dispersal and colonization tradeoffs, and to general model parameters, such as number of patches, average patch distance, total number of species and local species diversity) supported this picture (Table 1). The observation/variable ratio was more than 4 orders of magnitude larger than that recommended to ensure robustness in CANCOR results (1:10, Barcikowski and Stevens, 1975). Although the analysis identified significant canonical relationships for both canonical dimensions (with p < 0.000), canonical roots indicated the first one as much more relevant than the second in all cases, thus I will focus on the cross loadings of the first dimension. Differences in long and short distance dispersal and colonization coefficients had more effect on area of occupancy than on extent of occurrences. Long distance colonization coefficient (b2  CT) had the greatest overall effect on species range size. A similar effect was observed for short distance

Cross loadings

a1  DT b1 a2 b2  CT AOO EOO

dispersal coefficient (a1  DT), while short distance colonization coefficient (a2) and long distance dispersal coefficient (b1) were less relevant. Fig. 6 shows how much short and long distance dispersal and colonization coefficients affect species range sizes in case of violation of the tradeoff between long and short distance dispersal and colonization ability. The first plots (Fig. 6A and B) report the average trend of standardized r values computed between the short and long distance dispersal and colonization coefficients, and species range sizes in response to the ratio between the dispersal and the colonization tradeoffs. High values of the DT/CT ratio indicate a situation where there is little difference between how far a species can move by short and long distance strategies, but there is great difference in its odds to succeed in colonization. The short distance dispersal coefficient becomes already much relevant for moderately low DT/CT ratios, while the relative importance of the other coefficients decreases quite rapidly. In the other plots (Fig. 6C and D), the standardized r values are plotted against CT/DT. High values of this ratio indicate the opposite situation, i.e., a scenario where there is much difference in the distances that a species can cover through short and long distance strategies, but there is little difference in its chances to succeed in colonization. High CT/DT ratios increase the importance of long distance colonization ability, while limiting the contribution of long distance dispersal ability. Conversely, the

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Fig. 5. Trends of the normalized correlations (rnorm) between the long and short distance dispersal and colonization coefficients, and species range size (expressed both as area of occupancy, panel A, and extent of occurrences, panel B) throughout model evolution, quantified as the percentage of performed iterations from model start to model completion. The lines represent the interpolated means of 100 correlations recorded in 100 different model runs.

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Fig. 6. Response of normalized correlation coefficients (rnorm) assessing the relationships between species range (expressed both as area of occupancy, panels A and C, and extent of occurrences, panels B and D) and the corresponding short and long distance dispersal and colonization coefficients (a1  DT, b1,a2 and b2  CT) to increasing violations of the tradeoff between dispersal and colonization ability in favor, respectively, of the short distance movement strategy (A and B), and of the long distance movement strategy (C and D). The lines represent the interpolated means of the normalized correlation coefficients computed on all model run outcomes (n = 10000).

relevance of short distance dispersal and colonization abilities settles quite rapidly on stable, intermediate values. The simulations took into account a wide spectrum of settings with very different geographical and ecological features (in terms of landscape size, patch density, overall species richness, local biodiversity, and resource availability). In addition, the analysis of model evolution revealed that the effects of short and long distance dispersal and colonization ability became relevant since the early stage of the model, and persisted steadily thereafter, regardless of species turnover. Thus, the results presented here apply to a wide variety of different systems at various degrees of maturity. In designing the model, I have focused on species having two distinct mechanisms of range expansion. Yet by focusing on the dispersal/colonization tradeoffs, I have, in practice, investigated also the effect of dispersal and colonization ability for species having a single movement strategy by permitting scenarios were the tradeoff was very low, or even absent (DT, CT  1). This, however, goes beyond the purposes of this work, and requires some caveats. Most notably, to investigate the effect of dispersal/colonization tradeoffs, I have not allowed DT and CT to vary within a single scenario, which could be an interesting option for future studies focusing on other aspects not considered here. The model assumes that all species consume the same amount of resources and does not consider the potential effects of positive and negative species interactions on colonization success. These differences between the simulations presented here and real world scenarios are partly accounted for by the inclusion in the model of other species different from the target ones. This introduces a random effect possibly reducing the chances of a target species to succeed in colonization, and thus representing a proxy for negative interactions and for the progressive temporal reduction of resource availability due to the growth of populations. Yet future integration

of the model with local population dynamics and species interaction networks (including both positive and negative interactions) could extend its use to explore other issues than those investigated here. 4. Conclusions The obvious difficulties in investigating the processes generating species range through experimental studies often make the use of mathematical modelling an obligate choice, especially when focusing on community/meta community patterns (Nathan, 2001; Lowe and McPeek, 2014). Here I introduce a spatially explicit model based only on a few simple, well-founded assumptions, to investigate some specific mechanisms of dispersal and colonization in species having two distinct movement strategies. Many species have been observed to be capable of long distance movements during a single lifetime (see, for example, Nathan, 2006; Alsos et al., 2007; Anderson et al., 2011; Pergl et al., 2011; Torda et al., 2013; Caughlin et al., 2014; Harries and Clement, 2014). In general, however, there are difficulties in finding strong relationships between species dispersal ability and range size (Alsos et al., 2007; Mora et al., 2012; Strona et al., 2012), which suggests that range size is more affected by the chance of a species to succeed in colonization, than by how far it can travel (Nathan, 2006; Caughlin et al., 2014). Analysis of model outcomes strongly supports this view: on the one hand, it identifies long distance colonization ability as the strongest predictor of species ranges; on the other hand, it highlights how, in most simulated scenarios, long distance dispersal ability had little effect on species range sizes. Under most possible scenarios, the model identified as much important also species short distance dispersal ability. This is consistent with the commonness of nestedness in insular/ fragmented systems, as nested patterns are expected to emerge

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when species move from a center of diversity, and progressively colonize contiguous areas (Strona et al., 2011). Thus, if a species can expand its range using two different movement strategies, its range size will be determined by how far it can travel using the short distance movement strategy, and by its likelihood to succeed in colonization of distant localities, even in cases where the dispersal/colonization tradeoff between the two strategies is very small. For example, the range of a marine species moving both as a larva and as an adult will be mostly affected by the likelihood of species colonization success in the larval stage, and by the extent of short distance movements carried out by the species during its adult phase. Conversely, the species range will be little affected by the adult colonization ability, and even less by the distance potentially covered by larvae. This last aspect sounds like a good news, considering the general lack of empirical data on how far larvae can travel (Planes et al., 2009). These findings offer a perspective on the investigation of the determinants of species range substantially different from the established view, which does not pay much attention to how species move outside their long distance dispersal phase. Actually, the relationship between short distance dispersal ability and species range may have wide-ranging implications in several applicative fields, such as conservation biology. For example, establishing networks of protected areas has been suggested as an optimal procedure to promote biodiversity (Gaston et al., 2008). To be included in a network, an area must be both self-sustaining, and host populations well connected to other areas in the network, in order to reduce the risk of biodiversity loss due to local extinctions (Planes et al., 2009). However, evaluating the connectivity between different areas in a network is a complex task. Some studies have addressed this issue by evaluating connectivity both indirectly, focusing on the degree of self-recruitment (see, for example, Jones et al., 2005), and directly, using DNA parentage analysis (Planes et al., 2009; Christie et al., 2010). However, most of these studies have focused exclusively on long distance dispersal, by comparing areas out of the reach of short distance dispersal movements. The model presented here suggests that this may constitute an unbalanced approach, and that short distance movements may be indeed important in determining species ranges. I believe that investigating potential short distance dispersal paths could shed more light on this fundamental issue, and I hope that my findings could promote further experimental studies focusing on population connectivity between contiguous areas. Acknowledgments I would like to thank Jesus San Miguel-Ayanz, Simone Fattorini, Pieter S.A. Beck and four anonymous reviewers for their useful suggestions on a previous version of the manuscript. The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ecolmodel.2014.11.011. References Akima, H., Gebhardt, A., Petzoldt, T., Maechler, M., 2013. Akima: interpolation of irregularly spaced data. R package version 0. 5–11, http://CRAN.R-project.org/ package=akima. Alsos, I.G., Eidesen, P.B., Ehrich, D., Skrede, I., Westergaard, K., Jacobsen, G.H., Landvik, J.Y., Taberlet, P., Brochmann, C., 2007. Frequent long-distance plant colonization in the changing arctic. Science 316, 1606–1609.

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