The distribution of positive and negative species interactions across environmental gradients on a dual-lattice model

There has been considerable recent interest in understanding the role of positive inter-specific interactions within ecology, and significant progress has been made both empirically and theoretically. Similarly, considerable progress has been made in improving our understanding of the mechanisms that limit species' ranges. In this contribution, we seek to understand the setting of species' borders when some species within the assemblage exhibit positive inter-specific interactions. We use a spatially explicit dual-lattice simulation model to explore the distribution of different interactions across environmental gradients. We first simulate community dynamics when there is either a gradient in reproductive rate or in mortality. We then consider what happens when gradients in reproduction and mortality run in parallel or perpendicular to one another. If the stress gradient impacts on reproductive potential, positive interactions are found where there is high abiotic stress. In this instance, the mutualists are able to tolerate an environment that the cheaters cannot. However, when the stress gradient influences mortality, we find that the mutualists occur as a stripe surrounded by cheaters both towards the better and the harsher ends of the gradient. Previous theory and most empirical evidence tend to indicate that net positive interactions are likely to occur in environments characterized by high abiotic stress. However, evidence from some stress gradients suggests that the distribution of positive and negative interactions can be more complex, with the most stressful environments being occupied by individuals engaging in negative rather than positive interactions. Our results provide a potential theoretical explanation for these recent field observation, and highlight the need for further theoretical and empirical work to better our understanding of how positive and negative interactions act to determine the limits to species' ranges.