Coexistence of coinvading species with mutualism and competition

Abstract

All interactions between multiple species invading together (coinvasion) must be accounted for to predict species coexistence patterns across space. Mutualisms, particularly, are known to influence species' population dynamics and their invasive ability (e.g., mycorrhizal fungi with partner plants). Yet, while modeling coinvasion, their role in mediating coexistence is overlooked. Here, we build a spatially explicit model of coinvasion of two competing plant species with a shared fungal mutualist to study how mutualism and competition interact to shape the local and regional coexistence of competitors. We observe four main results. First, mutualist presence generates regional coexistence between competitors even when local coexistence between them is impossible. Second, increasing partner mutualist dispersal leads to abrupt changes in competitor coexistence outcomes. Third, differences in mutualist partner dependence and competitive ability interact to produce a variety of local and regional coexistence outcomes. Fourth, asymmetry in the dispersal ability arising from dependence-dispersal trade-offs leads to greater exclusion of species less dependent on mutualist partners for growth. In toto, incorporating mutualism-specific trait trade-offs and dispersal asymmetries into coinvasion models offers new insights into regional coexistence and invasive species distributions.

Keywords: coexistence; coinvasion; competition; dispersal; integro‐difference equations; mutualism; mutualism dependence; range expansion.

FIGURE 1

Schematic representation of interactions in the model. Species $F_1$ and $F_2$ are the focal competitor species (congeneric plant species) with shared mutualist P (fungal partner) where all species disperse and coinvade new territory. $F_1$ has greater dependence on mutualist partner P (in blue) but also lower intrinsic growth rate (in green) than $F_2$. Interspecific competition is denoted by dotted red arrows. Silhouette images contributed by T. Michael Keesey at phylopic.org and reused under Creative Commons license. The figure was made by author Naven Narayanan.

FIGURE 2

Set of qualitative outcomes observed. All figures are density versus space plots with species P in blue, species $F_1$ in orange and $F_2$ in green. (a) Local coexistence of competitors; (b) local coexistence with exclusion of $F_2$ by $F_1$ at their range edges; (c) competitive exclusion of $F_2$ across space; (d) regional coexistence of both species (but not local coexistence); (e) local coexistence with $F_2$ excluding $F_1$ at the edges; and (f) $F_2$ competitively excluding $F_1$ across all space. The horizontal lines above the graph indicate the ranges of each of the individual species (population at non‐zero densities). Parameter values used for these simulations are: $r_i=0.3\left(i=P,F_1,F_2\right)$, ${\mathrm{\delta }}_{F_1}=0.9,{\mathrm{\delta }}_{F_2}=0.1$, ${\mathrm{\sigma }}_{F_1}^2={\mathrm{\sigma }}_{F_2}^2={\mathrm{\sigma }}_P^2=0.05$ (${\mathrm{\sigma }}_P^2=0.02$ for subpanel f), $\left({\mathrm{\tau }}_{12},{\mathrm{\tau }}_{21}\right)=\left(\mathrm{0.05,0.02}\right),\left(\mathrm{0.05,0.05}\right),\left(\mathrm{0.05,0.15}\right),\left(\mathrm{0.15,0.05}\right),\left(\mathrm{0.3,0.2}\right),\left(\mathrm{0.02,0.02}\right)$.

FIGURE 3

Coexistence of competitors of differing dependence arises in the presence of a coinvading mutualist. (a) Competitive exclusion of the more dependent $F_1$ without a mutualist; (b) different possible coexistence outcomes between the competitors in the presence of P for differing relative competitive abilities. Parameters: $r_i=0.3\left(i=P,F_1,F_2\right)$, ${\mathrm{\delta }}_{F_1}=0.9,{\mathrm{\delta }}_{F_2}=0.1$, ${\mathrm{\sigma }}_{F_1}^2={\mathrm{\sigma }}_{F_2}^2={\mathrm{\sigma }}_P^2=0.05$ (only for b).

FIGURE 4

Increasing mutualist dispersal ability alters coexistence type in qualitatively different manners based on competition coefficients. When competition coefficients are low (yellow circles), regional coexistence outcome (denoted by $\mathrm{\rho }$) shifts from $F_1$ exclusion to local coexistence with $F_1$ dominance. When the competition coefficients are intermediate (red squares) or strong (open green triangles), abrupt shifts arise from $F_1$ exclusion to $F_2$ exclusion with regions of regional coexistence for small regions of ${\mathrm{\sigma }}_P^2$. Parameters chosen: $r_i=0.3\left(i=P,F_1,F_2\right)$, ${\mathrm{\delta }}_{F_1}=0.9,{\mathrm{\delta }}_{F_2}=0.1$, ${\mathrm{\sigma }}_{F_1}^2={\mathrm{\sigma }}_{F_2}^2=0.05$ (${\mathrm{\tau }}_{12},{\mathrm{\tau }}_{21}=\left(\mathrm{0.02,0.02}\right),\left(\mathrm{0.2,0.15}\right),\left(\mathrm{0.37,0.29}\right)$) for low, intermediate, and high competition respectively.

FIGURE 5

Coexistence outcomes are shaped by mutualist's dispersal ability and asymmetry in competitors' dispersal kernels arising from dependence‐dispersal trade‐offs. In (a–c), we assume $F_1$ and $F_2$ have symmetric dispersal kernels (${\mathrm{\sigma }}_{F_1}^2={\mathrm{\sigma }}_{F_2}^2$) and in (d–f), we assume $F_1$ and $F_2$ have asymmetric dispersal kernels (${\mathrm{\sigma }}_{F_1}^2\ne {\mathrm{\sigma }}_{F_2}^2$). We consider P to have lower (${\mathrm{\sigma }}_P^2<{\mathrm{\sigma }}_{F_1}^2,{\mathrm{\sigma }}_{F_2}^2$), similar (${\mathrm{\sigma }}_P^2\approx {\mathrm{\sigma }}_{F_1}^2,{\mathrm{\sigma }}_{F_2}^2$), and greater (${\mathrm{\sigma }}_P^2>{\mathrm{\sigma }}_{F_1}^2,{\mathrm{\sigma }}_{F_2}^2$) dispersal ability than the competitors. When competitors are asymmetric dispersers, only two outcomes are observed. Parameters: $r_i=0.3\left(i=P,F_1,F_2\right)$, ${\mathrm{\delta }}_{F_1}=0.9,{\mathrm{\delta }}_{F_2}=0.1$. ${\mathrm{\sigma }}_P^2=0.01\left(a\right)0.05\left(b\right)0.075\left(c\right)$; (d–f)${\mathrm{\sigma }}_{F_1}^2=0.03,{\mathrm{\sigma }}_{F_2}^2=0.02;{\mathrm{\sigma }}_P^2=0.01\left(d\right),0.025\left(e\right),0.075\left(f\right)$.