In our simulations, we use a simple movement model on the one hand and landscapes with more or less spatially concentrated resource distribution on the other to simulate a collective of foraging individuals; the simulated populations show attributes of a spatially structured population as emergent properties. As such, the emergence of spatial structure cannot be a very surprising outcome as already common sense would make us expect that animals tend to concentrate in areas where critical resources are concentrated (up to population densities approx. 65 times larger inside clusters than outside - Fig. 6B). Nonetheless, we see a value in our simulations in making clear that neither the perception of a patch-matrix dichotomy nor any particular (decisions) rules for emigration are needed to generate spatial heterogeneity in the distribution of individuals. Further, the simulations implemented here also generate more specific patterns that are expected to emerge in spatially structured population systems, i.e., that individuals are more likely to emigrate from small vs. large resource clusters (viz. patches) and with greater probability from poor quality (low resource density) than from high quality clusters (but see below).
Foraging behavior and foraging success
As expected, a reduction of the number of clusters (larger cluster at the same time) and/or an increase resource density leads to more foraging success of each individual and also affects movement pattern of individuals. In the scenarios with high resource density or larger cluster, individuals tend to stay long within a patch and perform more area-concentrated search than straight line movement. Such effects of resource density and resource spatial arrangement on movement strategies and foraging success were also observed in previous studies [18, 39, 44]. Note that in our scenarios the tendency to remain in a resource aggregation is only driven by the attributes of the ACS but does not require that individuals respond to or even recognize (suitable) habitat per se. It also does not require that individuals apply different rules of movement to habitat and matrix or that individuals ever take a decision to emigrate from a habitat patch. Saying so, we do not want to exclude and even suggest that animals typically forage with more sophistication than we assume in our model, e.g., that they recognize environmental cues indicating that finding resources would be more likely in a certain region or base movement decisions on experience and memory [as examples in 34,45].
Interestingly, the greatest foraging success occurred in scenarios with a single resource cluster and highest resource density, but individuals did not stay longest within patches in this scenario: contrary to expectation, the longest residence times were observed in scenarios with moderate resource density, in particular in the scenarios with few, larger clusters. An underlying reason is that individuals tended to stay nearer to patch edges if resource density was very high and did not move as far into a patch (approaching the patch center) compared to individuals in scenarios with moderate resource density. Therefore, they tended to leave patches more often than in the other scenarios. Particularly with high resource concentration, many emigrations resembled foray loops, however, where individuals return to the same patch [42, 43]. On the other hand, with very low resource density individuals often moved through resource clusters without encountering resources at all and consequently maintaining a very directed walk and leaving the patch quickly again. Emigration events as well as foray loops might become rarer if individuals were to apply more sophisticated movement rules than implemented here, e.g., when using memorized knowledge about patch location [28, 31, 34, 35], knowledge about patch quality [32], improved perception range [34, 46] or applying smarter Bayesian movement decision rules [45]. Indeed, in some preliminary simulations we found that even a simple ACS with a delayed change in movement randomness after encountering a resource item resulted in deeper penetration into resource clusters and longer patch residence times. Adding any of such behavioral components might lead to edge 'avoidance' and a more 'organized' and efficient resource utilization from clusters and should lead to a decrease in emigrations and foray loops in scenarios with high resource density.
We show that our system with a simple area-concentrated search develops properties of a spatially structured population over a wide parameter range but never matches the stricter attributes of a metapopulation [sensu 14]. A patch occupancy below 85% emerged in simulations with multiple patches (8 and 16 patches) and low resource density (Fig. 6A). However, in these scenarios individuals were hardly aggregating into resource clusters (Fig. 6B) -- that is, the distribution of individuals across the landscape was more or less random and not showing signs of spatial structure at all. We did not calculate turnover rates in this study as we were simulating in (approximately) continuous time so that calculation of turn-over would depend on an arbitrary decision on the time-window over which to make such calculation; the turn-over concept applies better in long-term studies and in populations with a distinct dispersal phase. Instead, a more meaningful criterion is the frequency of successful patch changes as a measure of gene flow and possible patch recolonization or rescue. The number of successful patch changes (emigration from one and immigration into another resource patch) was indeed quite low (Fig. 6C), but these values can only be interpreted in relation to the total period covered by our scenarios. For example, if we assume that a single time step (the time an individual needs to pass through its perceptional radius) is five minutes, the 2000 time steps analyzed cover a period of approximately 7 days. Further assuming that animals are active only 12h a day (e.g., because they are nocturnal) and do not move during more than 1/2 of their active time, the period covered would correspond to c. 3-4 weeks, a value is not unreasonable for the expected lifespan of many adult insects. Based on these assumptions we thus find that in many of our simulations only a small fraction of individuals (mostly <20%) successfully 'dispersed' from one habitat cluster to another during their lifetime. This infrequent dispersal events emerged despite the fact that we did not assume a mortality risk for individuals moving outside habitat, e.g., due to exhaustion or predation. In this regard our simulations indeed meet the metapopulation criterion defined by Fronhofer et al. (2012) [14] but as explained above, the patch occupancy criterion is only satisfied in those scenarios that showed at best weak symptoms of spatial structure. Our results thus support the idea that spatial population structure covers a continuum in terms of patch occupancy and migration rate [47, 48] but that true metapopulation attributes rarely emerge as long as external factors do not lead to the sudden extinction of local populations [14, 49, 50]. Unfortunately, only few empirical studies focused on resource density per se on emigration and immigration rate. For several insect species, the density of nectar sources or host plants has a negative effect on emigration and possibly a positive effect on immigration [51–53] and possibly increases patch occupancy [54–56].
In this study, we varied patch structure (many small patches to single large patch and low to high resource density) but within a scenario all patches were identical. Creating landscapes with resource clusters of variable attributes might enable us to investigate the emergence of spatially structure in populations in other landscape settings, e.g., settings that show attributes of a mainland-island system [13] or a system with varying patch quality (resource density) like in source–sink systems [57]. It must also be mentioned that we did not investigate the effect of the two parameters
, but previous studies showed that our choice of parameter values is adequate to result in good foraging success in a broad spectrum of parameters for the spatial distribution of resources (cf. Bartoń and Hovestadt (2013) [18] for more details). Generally, a decrease of the half-saturation constant h should lead to an increase in emigration rates and a reduction of patch residence times.
In this model, we assumed no birth and death events in the population. By excluding natality and mortality, we also did not include factors that might affect the emergent spatial structure such as dispersal mortality, starvation, or environmental stochasticity which were reported to influence dispersal probability and spatial population structure [14, 58, 59]. A full model should in fact also account for a proper resource dynamic, e.g., by either simulating abiotic resources with a constant supply rate (patch specific) or by implementing it as a prey population with its own population dynamics.