MacArthur's Consumer-Resource Model: A Rosetta Stone for Competitive Interactions

AbstractRecent developments in competition theory-namely, modern coexistence theory (MCT)-have aided empiricists in formulating tests of species persistence, coexistence, and evolution from simple to complex community settings. However, the parameters used to predict competitive outcomes, such as interaction coefficients, invasion growth rates, and stabilizing differences, remain biologically opaque, making findings difficult to generalize across ecological settings. This article is structured around five goals toward clarifying MCT by first making a case for the modern-day utility of MacArthur's consumer-resource model, a model with surprising complexity and depth: (i) to describe the model in uniquely accessible language, deciphering the mathematics toward cultivating deeper biological intuition about competition's inner workings regardless of what empirical toolkit one uses; (ii) to provide translation between biological mechanisms from MacArthur's model and parameters used to predict coexistence in MCT; (iii) to make explicit important but understated assumptions of MacArthur's model in plain terms; (iv) to provide empirical recommendations; and (v) to examine how key ecological concepts (e.g., r/K-selection) can be understood with renewed clarity through MacArthur's lens. We end by highlighting opportunities to explore mechanisms in tandem with MCT and to compare and translate results across ecological currencies toward a more unified ecological science.

Niche Theory as an Underutilized Resource for the Study of Adaptive Radiations

Biologists are often stuck between two opposing questions: Why are there so many species and why are there not more? Although these questions apply to the maintenance of existing species, they equally apply to the formation of new ones. The more species specialize in terms of their niches, the more opportunities arise for new species to form and coexist in communities. What sets an upper limit to specialization, thus setting an upper limit to speciation? We propose that MacArthur's theories of species packing and resource minimization may hold answers. Specifically, resources and individuals are finite-as species become increasingly specialized, each individual has fewer resources it can access. Species can only be as specialized as is possible in a given resource environment while still meeting basic resource requirements. We propose that the upper limit to specialization lies below the threshold that causes populations to be so small that stochastic extinctions take over, and that this limit is likely rarely approached due to the sequential timing by which new lineages arrive.

Predator home range size mediates indirect interactions between prey species in an arctic vertebrate community

Indirect interactions are widespread among prey species that share a common predator, but the underlying mechanisms driving these interactions are often unclear, and our ability to predict their outcome is limited. Changes in behavioural traits that impact predator space use could be a key proximal mechanism mediating indirect interactions, but there is little empirical evidence of the causes and consequences of such behavioural-numerical response in multispecies systems. Here, we investigate the complex ecological relationships between seven prey species sharing a common predator. We used a path analysis approach on a comprehensive 9-year data set simultaneously tracking predator space use, prey densities and prey mortality rate on key species of a simplified Arctic food web. We show that high availability of a clumped and spatially predictable prey (goose eggs) leads to a twofold reduction in predator (arctic fox) home range size, which increases local predator density and strongly decreases nest survival of an incidental prey (American golden plover). On the contrary, a scattered cyclic prey with potentially lower spatial predictability (lemming) had a weaker effect on fox space use and an overall positive impact on the survival of incidental prey. These contrasting effects underline the importance of studying behavioural responses of predators in multiprey systems and to explicitly integrate behavioural-numerical responses in multispecies predator-prey models.

The relative importance of social information use for population abundance in group-living and non-grouping prey

Predator-prey relationships are fundamental components of ecosystem functioning, within which the spatial consequences of prey social organization can alter predation rates. Group-living (GL) species are known to exploit inadvertent social information (ISI) that facilitates population persistence under predation risk. Still, the extent to which non-grouping (NG) prey can benefit from similar processes is unknown. Here we built an individual-based model to explore and compare the population-level consequences of ISI use in GL and NG prey. We differentiated between GL and NG prey only by the presence or absence of social attraction toward conspecifics that drives individual movement patterns. We found that the extent of the benefits of socially acquired predator information in NG highly depends on the prey's ability to detect nearby predators, prey density and the occurrence of false alarms. Conversely, even moderate probabilities of ISI use and predator detection can lead to maximal population-level benefits in GL prey. This theoretical work provides additional insights into the conditions under which ISI use can facilitate population persistence irrespective of prey social organisation.

Density-dependent predatory impacts of an invasive beetle across a subantarctic archipelago

Biological invasions represent a major threat to biodiversity, especially in cold insular environments characterized by high levels of endemism and low species diversity which are heavily impacted by global warming. Terrestrial invertebrates are very responsive to environmental changes, and native terrestrial invertebrates from cold islands tend to be naive to novel predators. Therefore, understanding the relationships between predators and prey in the context of global changes is essential for the management of these areas, particularly in the case of non-native predators. Merizodus soledadinus (Guérin-Méneville, 1830) is an invasive non-native insect species present on two subantarctic archipelagos, where it has extensive distribution and increasing impacts. While the biology of M. soledadinus has recently received attention, its trophic interactions have been less examined. We investigated how characteristics of M. soledadinus, its density, as well as prey density influence its predation rate on the Kerguelen Islands where the temporal evolution of its geographic distribution is precisely known. Our results show that M. soledadinus can have high ecological impacts on insect communities when present in high densities regardless of its residence time, consistent with the observed decline of the native fauna of the Kerguelen Islands in other studies. Special attention should be paid to limiting factors enhancing its dispersal and improving biosecurity for invasive insect species.

Predator-mediated interactions through changes in predator home range size can lead to local prey exclusion

The strength of indirect biotic interactions is difficult to quantify in the wild and can alter community composition. To investigate whether the presence of a prey species affects the population growth rate of another prey species, we quantified predator-mediated interaction strength using a multi-prey mechanistic model of predation and a population matrix model. Models were parametrized using behavioural, demographic and experimental data from a vertebrate community that includes the arctic fox (Vulpes lagopus), a predator feeding on lemmings and eggs of various species such as sandpipers and geese. We show that the positive effects of the goose colony on sandpiper nesting success (due to reduction of search time for sandpiper nests) were outweighed by the negative effect of an increase in fox density. The fox numerical response was driven by changes in home range size. As a result, the net interaction from the presence of geese was negative and could lead to local exclusion of sandpipers. Our study provides a rare empirically based model that integrates mechanistic multi-species functional responses and behavioural processes underlying the predator numerical response. This is an important step forward in our ability to quantify the consequences of predation for community structure and dynamics.

From the distributions of times of interactions to preys and predators dynamical systems

We consider a stochastic individual based model where each predator searches and then manipulates its prey or rests during random times. The time distributions may be non-exponential and density dependent. An age structure allows to describe these interactions and get a Markovian setting. The process is characterized by a measure-valued stochastic differential equation. We prove averaging results in this infinite dimensional setting and get the convergence of the slow-fast macroscopic prey predator process to a two dimensional dynamical system. We recover classical functional responses. We also get new forms arising in particular when births and deaths of predators are affected by the lack of food.

Predator feeding rates may often be unsaturated under typical prey densities

Predator feeding rates (described by their functional response) must saturate at high prey densities. Although thousands of manipulative functional response experiments show feeding rate saturation at high densities under controlled conditions, it remains unclear how saturated feeding rates are at natural prey densities. The general degree of feeding rate saturation has important implications for the processes determining feeding rates and how they respond to changes in prey density. To address this, we linked two databases-one of functional response parameters and one on mass-abundance scaling-through prey mass to calculate a feeding rate saturation index. We find that: (1) feeding rates may commonly be unsaturated and (2) the degree of saturation varies with predator and prey taxonomic identities and body sizes, habitat, interaction dimension and temperature. These results reshape our conceptualisation of predator-prey interactions in nature and suggest new research on the ecological and evolutionary implications of unsaturated feeding rates.

Metabolic responses of predators to prey density

The metabolic cost of foraging is the dark energy of ecological systems. It is much harder to observe and to measure than its beneficial counterpart, prey consumption, yet it is not inconsequential for the dynamics of prey and predator populations. Here I define the metabolic response as the change in energy expenditure of predators in response to changes in prey density. It is analogous and intrinsically linked to the functional response, which is the change in consumption rate with prey density, as they are both shaped by adjustments in foraging activity. These adjustments are adaptive, ubiquitous in nature, and are implicitly assumed by models of predator–prey dynamics that impose consumption saturation in functional responses. By ignoring the associated metabolic responses, these models violate the principle of energy conservation and likely underestimate the strength of predator–prey interactions. Using analytical and numerical approaches, I show that missing this component of interaction has broad consequences for dynamical stability and for the robustness of ecosystems to persistent environmental or anthropogenic stressors. Negative metabolic responses – those resulting from decreases in foraging activity when more prey is available, and arguably the most common – lead to lower local stability of food webs and a faster pace of change in population sizes, including higher excitability, higher frequency of oscillations, and quicker return times to equilibrium when stable. They can also buffer the effects of press perturbations, such as harvesting, on target populations and on their prey through top-down trophic cascades, but are expected to magnify bottom-up cascades, including the effects of nutrient enrichment or the effects of altering lower trophic levels that can be caused by environmental forcing and climate change. These results have implications for any resource management approach that relies on models of food web dynamics, which is the case of many applications of ecosystem-based fisheries management. Finally, besides having their own individual effects, metabolic responses have the potential to greatly alter, or even invert, functional response-stability relationships, and therefore can be critical to an integral understanding of predation and its influence on population dynamics and persistence.

Stabilizing effects of group formation by Serengeti herbivores on predator-prey dynamics

Predator-prey theory often assumes that potential prey individuals are solitary and evenly distributed in space. This assumption is violated in social, mobile prey, such as many ungulates. Here we use data from 80 monthly field censuses to estimate the parameters for a power relationship between herd density and population density for eight species of large herbivores commonly found in the diet of Serengeti lions, confirming a power relationship proposed from a preliminary Serengeti dataset. Here we extend our analysis of that model to demonstrate how parameters of the power function relate to average herd size and density-dependent changes in herd size and evaluate how interspecific variation in these parameters shapes the group-dependent functional response by Serengeti lions for eight prey species. We apply the different prey-specific functional response models in a Rosenzweig-MacArthur framework to compare their impact on the stability of predator–prey dynamics. Model outcomes suggest that group formation plays a strong role in stabilizing lion–herbivore interactions in Serengeti by forcing lions to search over a larger area before each prey encounter. As a consequence of grouping by their prey, our model also suggests that Serengeti lions are forced to broaden their diets to include multiple species of prey in order to persist, potentially explaining the generalist foraging by lions routinely recorded across multiple ecosystems.

Functional Responses Shape Node and Network Level Properties of a Simplified Boreal Food Web

Ecological communities are fundamentally connected through a network of trophic interactions that are often complex and difficult to model. Substantial variation exists in the nature and magnitude of these interactions across various predators and prey and through time. However, the empirical data needed to characterize these relationships are difficult to obtain in natural systems, even for relatively simple food webs. Consequently, prey-dependent relationships and specifically the hyperbolic form (Holling’s Type II), in which prey consumption increases with prey density but ultimately becomes saturated or limited by the time spent handling prey, are most widely used albeit often without knowledge of their appropriateness. Here, we investigate the sensitivity of a simplified food web model for a natural, boreal system in the Kluane region of the Yukon, Canada to the type of functional response used. Intensive study of this community has permitted best-fit functional response relationships to be determined, which comprise linear (type I), hyperbolic (type II), sigmoidal (type III), prey- and ratio-dependent relationships, and inverse relationships where kill rates of alternate prey are driven by densities of the focal prey. We compare node- and network-level properties for a food web where interaction strengths are estimated using best-fit functional responses to one where interaction strengths are estimated exclusively using prey-dependent hyperbolic functional responses. We show that hyperbolic functional responses alone fail to capture important ecological interactions such as prey switching, surplus killing and caching, and predator interference, that in turn affect estimates of cumulative kill rates, vulnerability of prey, generality of predators, and connectance. Exclusive use of hyperbolic functional responses also affected trends observed in these metrics over time and underestimated annual variation in several metrics, which is important given that interaction strengths are typically estimated over relatively short time periods. Our findings highlight the need for more comprehensive research aimed at characterizing functional response relationships when modeling predator-prey interactions and food web structure and function, as we work toward a mechanistic understanding linking food web structure and community dynamics in natural systems.

Quantifying predator functional responses under field conditions reveals interactive effects of temperature and interference with sex and stage

Predator functional responses describe predator feeding rates and are central to predator–prey theory. Originally defined as the relationship between predator feeding rates and prey densities, it is now well known that functional responses are shaped by a multitude of factors. However, much of our knowledge about how these factors influence functional responses is based on laboratory studies that are generally logistically constrained to examining only a few factors simultaneously and that have unclear links to the conditions organisms experience in the field.

We apply an observational approach for measuring functional responses to understand how sex/stage differences, temperature and predator densities interact to influence the functional response of zebra jumping spiders on midges under natural conditions.

We used field surveys of jumping spiders to infer their feeding rates and examine the relationships between feeding rates, sex/stage, midge density, predator density and temperature using generalized additive models. We then used the relationships supported by the models to fit parametric functional responses to the data.

We find that feeding rates of zebra jumping spiders follow some expectations from previous laboratory studies such as increasing feeding rates with body size and decreasing feeding rates with predator densities. However, in contrast to previous results, our results also show a lack of temperature response in spider feeding rates and differential decreases in the feeding rates of females and juveniles with densities of different spider sexes/stages.

Our results illustrate the multidimensional nature of functional responses in natural settings and reveal how factors influencing functional responses can interact with one another through behaviour and morphology. Further studies investigating the influence of multiple mechanisms on predator functional responses under field conditions will increase our understanding of the drivers of predator–prey interaction strengths and their consequences for communities and ecosystems.

Digging into the behaviour of an active hunting predator: arctic fox prey caching events revealed by accelerometry

BACKGROUND

Biologging now allows detailed recording of animal movement, thus informing behavioural ecology in ways unthinkable just a few years ago. In particular, combining GPS and accelerometry allows spatially explicit tracking of various behaviours, including predation events in large terrestrial mammalian predators. Specifically, identification of location clusters resulting from prey handling allows efficient location of killing events. For small predators with short prey handling times, however, identifying predation events through technology remains unresolved. We propose that a promising avenue emerges when specific foraging behaviours generate diagnostic acceleration patterns. One such example is the caching behaviour of the arctic fox (Vulpes lagopus), an active hunting predator strongly relying on food storage when living in proximity to bird colonies.

METHODS

We equipped 16 Arctic foxes from Bylot Island (Nunavut, Canada) with GPS and accelerometers, yielding 23 fox-summers of movement data. Accelerometers recorded tri-axial acceleration at 50 Hz while we obtained a sample of simultaneous video recordings of fox behaviour. Multiple supervised machine learning algorithms were tested to classify accelerometry data into 4 behaviours: motionless, running, walking and digging, the latter being associated with food caching. Finally, we assessed the spatio-temporal concordance of fox digging and greater snow goose (Anser caerulescens antlanticus) nesting, to test the ecological relevance of our behavioural classification in a well-known study system dominated by top-down trophic interactions.

RESULTS

The random forest model yielded the best behavioural classification, with accuracies for each behaviour over 96%. Overall, arctic foxes spent 49% of the time motionless, 34% running, 9% walking, and 8% digging. The probability of digging increased with goose nest density and this result held during both goose egg incubation and brooding periods.

CONCLUSIONS

Accelerometry combined with GPS allowed us to track across space and time a critical foraging behaviour from a small active hunting predator, informing on spatio-temporal distribution of predation risk in an Arctic vertebrate community. Our study opens new possibilities for assessing the foraging behaviour of terrestrial predators, a key step to disentangle the subtle mechanisms structuring many predator-prey interactions and trophic networks.

Considerations When Applying the Consumer Functional Response Measured Under Artificial Conditions

Since its creation, considerable effort has been given to improving the utility of the consumer functional response. To date, the majority of efforts have focused on improving mathematical formulation in order to include additional ecological processes and constraints, or have focused on improving the statistical analysis of the functional response to enhance rigor and to more accurately match experimental designs used to measure the functional response. In contrast, relatively little attention has been given to improving the interpretation of functional response empirical results, or to clarifying the implementation and extrapolation of empirical measurements to more realistic field conditions. In this paper I explore three concepts related to the interpretation and extrapolation of empirically measured functional responses. First, I highlight the need for a mechanistic understanding when interpreting foraging patterns and highlight pitfalls that can occur when we lack understanding between the shape of the functional response curve and the mechanisms that give rise to that shape. Second, I discuss differences between experimental and real-world field conditions that must be considered when trying to extrapolate measured functional responses to more natural conditions. Third, I examine the importance of the time scale of empirical measurements, and the need to consider tradeoffs that alter or limit foraging decisions under natural conditions. Clearly accounting for these three conceptual areas when measuring functional responses and when interpreting and attempting to extrapolate empirically measured functional responses will lead to more accurate estimates of consumer impacts under natural field conditions, and will improve the utility of the functional response as a heuristic tool in ecology.