When an environmental gradient is imposed on the landscape it frequently results in the coexistence of mutualists and non-mutualists. There is a striking pattern of spatial segregation, with the mutualists occurring in the harshest conditions and the non-mutualists in the more favourable environment (see ). This result supports that of Wilson & Nisbet (1997)
who found strong spatial patterns of strategy segregation in similar model systems. They also tie in closely with data from numerous field experiments showing a shift from the general dominance of competition in benign conditions to facilitation in severe conditions (e.g. Choler et al. 2001
; Callaway et al. 2002
). Intriguingly, we often find a zone between the mutualists and non-mutualists that has a low rate of occupancy (see and ). This no-man's land represents an area where mutualists would be able to persist in the absence of cheaters, but where cheaters are unable to persist in the absence of mutualists. Mutualists periodically colonize this area, but they are vulnerable to invasion by cheaters from the other side of the zone. After the cheaters invade, both mutualists and non-mutualists are doomed to become locally extinct until the next wave of mutualists moves in. This results in a dynamic boundary that separates the mutualists from the non-mutualists. This is an interesting result. In natural communities we do not observe zones with reduced vegetation cover at such a species interface because additional species may fill the empty space, but we might observe an area of increased turnover of both the cheater and the mutualist. However, this is an output from the model that lends itself to further investigation and which necessitates the collection of suitable field data for validation or refutation. From this simulation we predict that regions with an average net interaction of zero, which result from the balance of positive and negative effects, might be associated with greater rates of community turnover.
Figure 1 Positive interactions dominate the harsher environmental conditions, but are absent where conditions are more favourable. The spatial patterns shown in these four plates are typical of those observed for a wide range of parameter space. Dark red and dark (more ...)
Figure 2 Mean rates of patch occupancy along the gradient. (a) and (c) show the results when cheaters and mutualists are both present. (b) and (d) illustrate the effect that one species has on the other. In (a) and (c), red shading shows the abundance of cheaters (more ...)
In this model, mutualistic interactions permit species to exist in harsher environments than would otherwise be possible. enables a comparison of the environmental conditions that are occupied by mutualists in the absence of cheaters, cheaters in the absence of mutualists, and cheaters and mutualists co-occurring. Unsurprisingly, a positive interaction enables both mutualistic partners to persist in harsher conditions than their cheating counter-parts. It is worth noting that the cheaters can sometimes extend their range into harsher conditions when mutualists are present (b
). Our model thus supports the prediction that facilitation might extend the realized niche of species (Bruno et al. 2003
). Also, for some parameterizations, the mutualists do not occupy as many patches in harsh conditions when cheaters are present (d
). This is because the cheaters reduce the abundance of mutualists in better-quality habitats, and this reduces the strength of a mutualist source that supports a mutualist sink in the harsher conditions (d
). However, this effect is dependent upon the dispersal capabilities of the mutualists.
We have assumed that being in the presence of a mutualist confers a benefit in terms of an increased probability of reproduction, and that being a mutualist incurs a cost paid through reduced reproduction. However, for some associations it may be that these benefits and costs change the probability of mortality rather than reproduction. Results from a modified model show that all of the results and patterns are qualitatively very similar regardless of whether costs and benefits act on reproduction or mortality.
Models such as the one described in this paper provide considerable scope for future work on positive interactions. We identify a few areas where we feel future work might be valuable. Stanton (2003)
emphasized the need for theoretical work that moves beyond the traditional view of a single pair of interacting partner species, and instead considers guilds of mutualistic species on one or both sides of the interaction. Extending the model presented in this paper to incorporate a greater number of species should be relatively straightforward and would enable us to model the impact of changes in interactions on biodiversity. We have not considered any evolution in the strength of the positive interactions. Doebeli & Knowlton (1998)
recognized that evolution along a continuum of interaction strengths (with a corresponding trade-off) is likely, and constructed a model that allowed this evolution to occur. It would be interesting to explore the evolutionary impact of interaction strength on an environmental gradient. Predictions for the selective impact of positive interactions in plants from arctic and alpine systems were made by Brooker & Callaghan (1998)
. They pointed out that such adaptations might already exist in arctic and alpine species. However, in field studies it is not possible to examine whether facilitation alone is capable of producing such adaptations. With such a model system this would be possible.
Here, we have incorporated spatial environmental variability in the form of a simple environmental gradient. In reality, the pattern of spatial variability is likely to be far more complex. Travis & Dytham (2004)
presented a method for simulating patterns of habitat availability at species range margins, and these methods offer promise for future work investigating how patterns of habitat availability determine the ability of species and communities (including those with positive interactions) to shift their range in response to climate change (Travis 2003
We believe that combining modelling and field studies offers considerable promise for improving our understanding of the role of positive interactions in structuring communities. We have demonstrated that models can be used to generate testable predictions. Some empirical studies (Callaway et al. 2002
; Maestre & Cortina 2004
) have already generated the type of data that will allow these models to be validated and refined, but further field-based studies are needed.