Adaptive movement of both species
The models in Section 10.5 both assumed a MacArthur system within each patch; in this system, the per capita risk of consumption is not directly affected by resource abundance. This independence disappears when the consumers’ per capita capture rates change with resource abundance, a characteristic of every nonlinear functional response.
Most measurements of functional responses have found nonlinearity (Jeschke et al. 2004). (Note that Jeschke et al. overstate the number of linear responses, by including in the ‘linear’ category responses with approximate linearity up to a threshold prey/food abundance, beyond which the response is constant.) Nonlinearity raises two types of issues that are important for the dynamics of spatially structured systems. The first is that the expected fitness of a prey individual depends on the number of other individuals in its patch. Such frequency dependence significantly affects the dynamics of traits that affect the vulnerability to consumption (Abrams et al. 1993; Geritz et al. 1998). In most biological systems, either high local prey abundance or high vulnerability of local prey to the predator produce predator satiation (increased total ‘handling time’). This satiation, in turn, lowers the risk to prey individuals, and therefore makes it less likely that a prey individual will leave a patch. This can lead to unstable behavioural dynamics, as predators increase in the patch where prey have congregated, eventually producing a rapid exodus of prey individuals. The second issue raised by nonlinear consumer capture rates is their interaction with temporal variation. Saturating functional responses can cause temporal variation via predatorprey cycles in the absence of any adaptive movement by prey. In this case, or in the case of cycles driven by sustained temporal environmental variation, mean population abundances in systems with nonlinear per capita growth rate functions will not equal the equilibrium abundance. Such cycles can even reverse the sign of an interaction between two species (Abrams et al. 2003).In real communities, consumers have their own predators, which are also likely to have saturating functional responses. Such a functional response in a higher-level predator has the potential to lead to temporal cycles in the movement behaviour of the lower-level predator (consumer). A type II response by the higher-level predator can also generate cycles directly within each patch, even if the lower-level predator does not exhibit adaptive movement. This combination of different sources of instability (both movement and population dynamics) on two trophic levels leads to various potential outcomes, the full range of which has yet to be explored. The rest of this section of the chapter will look at the potential effects of adaptive movement in some of these more complicated scenarios. Unfortunately, relatively little is known about these scenarios in systems with more than one consumer species. Most of the work reviewed below has dealt with a single consumer. This work is directly relevant to intraspecific competition; however, its extension to competition between consumers is largely a task for the future.
Simple predator-prey models having two patches and either adaptive or random movement with nonlinear per capita growth rates were analysed in Jansen (2001), Koelle and Vandermeer (2005), Rowell (2010), Abrams and Ruokolainen (2011), Ruokolainen et al. (2011), Abrams et al. (2012), and Gramlich et al. (2016), among others. All these works have found a wide range of effects of dispersal on mean abundances and the pattern of population variation. Abrams (2007a) discussed the complex cycles in a 2-patch model involving a single species on each of three trophic levels. That model also assumed type II functional responses for both top and middle trophic levels. A wide range of complex cycles occurred in the full model. Even the (unlikely) assumption of fixed abundances of each species led to some unexpected outcomes.
In a simple case with fixed population sizes of all species, the type II responses favour prey aggregation in one of the patches, where their higher numbers reduce their per capita risk of being eaten. This results in predators moving to that patch, eventually favouring movement by the prey to the formerly less-occupied patch. This process of cyclic movement can persist over the long term, and cycles are more likely to occur when prey abundances are allowed to vary.Adaptive habitat choice by both of the top two trophic levels led to exceptionally complex dynamical outcomes. Adaptive movement can lead to asynchrony in many 2-patch systems where consumer-resource cycles would become synchronized in the presence of random movement (Abrams and Ruokolainen 2011; Ruokolainen et al. 2011). Asynchrony usually reduces system-wide variation in consumer abundance. Gramlich et al. (2016) present a more comprehensive analysis of 2-patch systems with a single consumer and resource; they found that antisynchronous oscillations were most common under adaptive dispersal. The variety of outcomes would seem likely to be greater in models that had two or more species per trophic level.
While adaptive movement models have still not been explored in the context of two or more competing consumers in a metacommunity, there have been some analyses of the two species LV competition model in 2-patch systems (Cressman and Krivan 2006; Abrams et al. 2007). The second of these showed that adaptive habitat selection can lead to large amplitude cycles in the locations and population sizes of competing species that would have a stable equilibrium in the absence of adaptive movement.
A variety of different adaptive movement models and food web configurations involving some competition have been investigated. One of the first studies to find that adaptive movement could cause cycles was that of Schwinning and Rosenzweig (1990), who studied a system with intraguild predation. Amarasekare (2010) investigated the role of several types of movement functions in allowing coexistence of two consumers that share a single resource type and a single predator species (a ‘diamond food web').
Gross et al. (2020) review several different functional forms of the movement for interacting species in metacommunities. However, it is still unclear to what extent different rules for movement affect the potential for movement-driven cycles.In spite of the many unknowns, it seems likely that many of the impacts of adaptive consumer movement on the nature of competition in a simple 2-patch-2-consumer system will not depend sensitively on the exact form of the movement function, provided that it results in significant shifts of the consumer population towards better quality patches. Qualitative patterns that do not depend on the exact functional form of movement are particularly likely when neither within-patch dynamics nor movement produce instability. One of the more common effects of adaptive consumer movement in a stable metacommunity is to reduce the extent of competition close to the equilibrium point, by decreasing the spatial overlap of competitors relative to a situation with random movement. However, as shown in the simple 2-patch systems in Section 10.5, large magnitude perturbations can lead to abrupt increase or decrease in population size in this scenario. This is particularly likely when resources are overexploited, and a consumer can achieve a higher density in the patch where it has a lower resource capture rate (Abrams 1998).
10.7