Ideal free flows of optimal foragers: Vertical migrations in the ocean

We consider the collective motion of animals in time-varying environments, using as a case diel vertical migration in the ocean. The animals are distributed in space such that each animal moves optimally, seeking regions which offer high growth rates and low mortalities, subject to costs on excessive movements as well as being in regions with high densities of conspecifics. The model applies to repeated scenarios such as diel or seasonal patterns, where the animals are aware of both current and future environmental conditions. We show that this problem can be viewed as a differential game of mean field type, and that the evolutionary stable solution, i.e. the Nash equilibrium, is characterized by partial differential equations, which govern the distributions and migration velocities of animals. These equations have similarities to equations that appear in the fluid dynamics, specifically the Euler equations for compressible inviscid fluids. If the environment is constant, the ideal free distribution emerges as an equilibrium. We illustrate the theory with a numerical example of vertical animal movements in the ocean, where animals are attracted to nutrient-rich surface waters while repulsed from light during daytime due to the presence of visual predators, aiming to reduce both proximity to conspecifics and swimming efforts. For this case, we show that optimal movements are diel vertical migrations in qualitative agreement with observations.

Ideal free eagles: Bald Eagle distribution in relation to salmon availability on four salmon spawning rivers

The movement of individuals according to the availability of resources has a fundamental effect on animal distributions. In the Pacific Northwest, Bald Eagles (Haliaeetus leucocephalus (Linneaus, 1766)) rely heavily on scavenging opportunities during the non-breeding period, and their distribution and movements are thought to be strongly influenced by the availability of post-spawning Pacific salmon (genus Oncorhynchus Suckley, 1861) carcasses. We surveyed the abundance of eagles and salmon on four adjacent rivers on Vancouver Island, British Columbia, Canada, during the 2017 fall spawning season. Salmon began to arrive in late September, peaked in abundance in mid-November, and were absent after early December. The seasonal progression of Bald Eagle abundance matched that of salmon carcass availability. The slope of proportional eagle – salmon relationship was significantly positive, though lower than the 1:1 match predicted by Ideal Free Distribution theory. The numerical response of Bald Eagles to salmon abundance was elevated on one of the rivers, potentially due to physical features such as sandbars and mudflats that increased the availability of carcasses and provided access points for eagles.

No neighbour-induced increase in root growth of soybean and sunflower in mesh divider experiments after controlling for nutrient concentration and soil volume

Root competition is a key factor determining plant performance, community structure and ecosystem productivity. To adequately estimate the extent of root proliferation of plants in response to neighbours independently of nutrient availability, one should use a setup that can simultaneously control for both nutrient concentration and soil volume at plant individual level. With a mesh-divider design, which was suggested as a promising solution for this problem, we conducted two intraspecific root competition experiments one with soybean (Glycine max) and the other with sunflower (Helianthus annuus). We found no response of root growth or biomass allocation to intraspecific neighbours, i.e. an ‘ideal free distribution’ (IDF) norm, in soybean; and even a reduced growth as a negative response in sunflower. These responses are all inconsistent with the hypothesis that plants should produce more roots even at the expense of reduced fitness in response to neighbours, i.e. root over-proliferation. Our results suggest that neighbour-induced root over-proliferation is not a ubiquitous feature in plants. By integrating the findings with results from other soybean studies, we conclude that for some species this response could be a genotype-dependent response as a result of natural or artificial selection, or a context-dependent response so that plants can switch from root over-proliferation to IDF depending on the environment of competition. We also critically discuss whether the mesh-driver design is the ideal solution for root competition experiments.

Evolution of heterogeneous perceptual limits and indifference in competitive foraging

The collective behaviour of animal and human groups emerges from the individual decisions and actions of their constituent members. Recent research has revealed many ways in which the behaviour of groups can be influenced by differences amongst their constituent individuals. The existence of individual differences that have implications for collective behaviour raises important questions. How are these differences generated and maintained? Are individual differences driven by exogenous factors, or are they a response to the social dilemmas these groups face? Here I consider the classic case of patch selection by foraging agents under conditions of social competition. I introduce a multilevel model wherein the perceptual sensitivities of agents evolve in response to their foraging success or failure over repeated patch selections. This model reveals a bifurcation in the population, creating a class of agents with no perceptual sensitivity. These agents exploit the social environment to avoid the costs of accurate perception, relying on other agents to make fitness rewards insensitive to the choice of foraging patch. This provides a individual-based evolutionary basis for models incorporating perceptual limits that have been proposed to explain observed deviations from the Ideal Free Distribution (IFD) in empirical studies, while showing that the common assumption in such models that agents share identical sensory limits is likely false. Further analysis of the model shows how agents develop perceptual strategic niches in response to environmental variability. The emergence of agents insensitive to reward differences also has implications for societal resource allocation problems, including the use of financial and prediction markets as mechanisms for aggregating collective wisdom.

Machine Learning Data Imputation and Prediction of Foraging Group Size in a Kleptoparasitic Spider

Cost–benefit analysis is widely used to elucidate the association between foraging group size and resource size. Despite advances in the development of theoretical frameworks, however, the empirical systems used for testing are hindered by the vagaries of field surveys and incomplete data. This study developed the three approaches to data imputation based on machine learning (ML) algorithms with the aim of rescuing valuable field data. Using 163 host spider webs (132 complete data and 31 incomplete data), our results indicated that the data imputation based on random forest algorithm outperformed classification and regression trees, the k-nearest neighbor, and other conventional approaches (Wilcoxon signed-rank test and correlation difference have p-value from < 0.001–0.030). We then used rescued data based on a natural system involving kleptoparasitic spiders from Taiwan and Vietnam (Argyrodes miniaceus, Theridiidae) to test the occurrence and group size of kleptoparasites in natural populations. Our partial least-squares path modelling (PLS-PM) results demonstrated that the size of the host web (T = 6.890, p = 0.000) is a significant feature affecting group size. The resource size (T = 2.590, p = 0.010) and the microclimate (T = 3.230, p = 0.001) are significant features affecting the presence of kleptoparasites. The test of conformation of group size distribution to the ideal free distribution (IFD) model revealed that predictions pertaining to per-capita resource size were underestimated (bootstrap resampling mean slopes <IFD predicted slopes, p < 0.001). These findings highlight the importance of applying appropriate ML methods to the handling of missing field data.

Breakdown of the ideal free distribution under conditions of severe and low competition

Under the ideal free distribution (IFD), the number of organisms competing for a resource at different sites is proportional to the resource distribution among sites. The ideal free distribution of competitors in a heterogeneous environment often predicts habitat matching, where the relative number of individuals using any two patches matches the relative availability of resources in those same two patches. If a resource is scarce, access might be restricted to individuals with high resource holding potential, resulting in deviation from the IFD. The distribution of animals may also deviate from the IFD in the case of resource abundance, when social attraction or preference for specific locations rather than competition may determine distribution. While it was originally developed to explain habitat choice, we apply the habitat matching rule to microscale foraging decisions. We show that chickens feeding from two nondepleting feeders distribute proportionally to feeder space under intermediate levels of competition. However, chicken distribution between the feeders deviates from the IFD when feeder space is limited and competition high. Further, despite decreasing aggression with increasing feeder space, deviation from IFD is also observed under an excess supply of feeder space, indicating different mechanisms responsible for deviations from the IFD. Besides demonstrating IFD sensitivity to competition, these findings highlight IFD’s potential as a biological basis for determining minimal resource requirements in animal housing. Significance statement The ideal free distribution (IFD) predicts how animals ought to distribute themselves within a habitat in order to maximize their payoff. Recent studies, however, have questioned the validity of the IFD concept following anomalous results. We studied the IFD in chickens by systematically varying the amount and distribution of space at two feed troughs. We show that when tested over a sufficiently large range, the distribution of birds depends on the overall resource availability. Furthermore, behavioral data suggest that distinctly different mechanisms account for deviations from the IFD at shortage and excess supply of feeder space, respectively.

Specialist Birds Replace Generalists in Grassland Remnants as Land Use Change Intensifies

The ideal free distribution theory predicts that mobile species distribute themselves among habitat patches so as to optimize their fitness. Changes in land use alter the quality of habitat patches and thereby affect the distribution of species. Following the loss of native habitat, habitat specialists are expected to move to patches where native habitat still remains in order to survive. Competition for resources in habitat remnants should consequently increase. As generalists are able to use other habitats, generalists are expected to gradually disappear in remnants in order to avoid increasing competition with specialists. Here, we test these predictions by studying the response of habitat specialist and generalist birds to land-use change in Brazil's southern grasslands. Using a space-for-time substitution approach, we surveyed bird communities in native grassland sites (~4 ha) in 31 regions (10 × 10 km) with differing levels of conversion to agriculture (1–94%). We found a higher abundance of specialists in native grassland patches with increasing agricultural cover in the region, while the total number of individuals in remnants remained constant. At the same time, the share of generalists in total abundance and total species richness decreased. To gain insights into whether these patterns could be driven by shifts in competition, we tested whether generalists that continued to co-occur with specialists in remnants, had less dietary overlap with specialists. As a consequence of community composition in remnants, a higher proportion of generalists were omnivorous and the average generalist species fed less on seeds, whereas the average specialist species fed more on seeds when agricultural cover was high in the region. Our results, therefore, support predictions of the ideal free distribution theory. Specialists that are assumed to have a low survivorship outside of their specialized habitat, distribute to remnants of this habitat when it is converted elsewhere, while generalists, being able to survive in other habitats, disappear gradually in remnants. Such a process could partly explain the segregation of habitat specialist and generalist birds observed in many agricultural landscapes. Finally, our results suggest that native habitat remnants can be important temporary refugia for specialists.