Imperfect optimal foraging and the paradox of enrichment

Testing foraging optimization models in brown bears: Time for a paradigm shift in nutritional ecology?

How organisms obtain energy to survive and reproduce is fundamental to ecology, yet researchers use theoretical concepts represented by simplified models to estimate diet and predict community interactions. Such simplistic models can sometimes limit our understanding of ecological principles. We used a polyphagous species with a wide distribution, the brown bear (Ursus arctos), to illustrate how disparate theoretical frameworks in ecology can affect conclusions regarding ecological communities. We used stable isotope measurements (δ13 C, δ15 N) from hairs of individually monitored bears in Sweden and Bayesian mixing models to estimate dietary proportions of ants, moose, and three berry species to compare with other brown bear populations. We also developed three hypotheses based on predominant foraging literature, and then compared predicted diets to field estimates. Our three models assumed (1) bears forage to optimize caloric efficiency (optimum foraging model), predicting bears predominately eat berries (~70% of diet) and opportunistically feed on moose (Alces alces) and ants (Formica spp. and Camponotus spp; ~15% each); (2) bears maximize meat intake (maximizing fitness model), predicting a diet of 35%-50% moose, followed by ants (~30%), and berries (~15%); (3) bears forage to optimize macronutrient balance (macronutrient model), predicting a diet of ~22% (dry weight) or 17% metabolizable energy from proteins, with the rest made up of carbohydrates and lipids (~49% and 29% dry matter or 53% and 30% metabolizable energy, respectively). Bears primarily consumed bilberries (Vaccinium myrtillus; 50%-55%), followed by lingonberries (V. vitis-idaea; 22%-30%), crowberries (Empetrum nigrum; 8%-15%), ants (5%-8%), and moose (3%-4%). Dry matter dietary protein was lower than predicted by the maximizing fitness model and the macronutrient balancing model, but protein made up a larger proportion of the metabolizable energy than predicted. While diets most closely resembled predictions from optimal foraging theory, none of the foraging hypotheses fully described the relationship between foraging and ecological niches in brown bears. Acknowledging and broadening models based on foraging theories is more likely to foster novel discoveries and insights into the role of polyphagous species in ecosystems and we encourage this approach.

Population cycles emerging through multiple interaction types

Cyclic dynamics of populations are outstanding and widespread phenomena across many taxa. Previous theoretical studies have mainly focused on the consumer-resource interaction as the driving force for such cycling. However, natural ecosystems comprise diverse types of species interactions, but their roles in population dynamics remains unclear. Here, using a four-species hybrid module with antagonistic, mutualistic and competitive interactions, we analytically showed that the system with major interaction types can drive population cycles. Stronger interactions easily cause cycling, and even when sub-modules with possible combinations of two interactions are stabilized by weak interactions, the system with all interaction types can cause unstable population oscillations. Diversity of interaction types allows to add mutualists to the list of drivers of oscillations in a focal species' population size, when they act in conjunction to other drivers.

Scrounging by foragers can resolve the paradox of enrichment

Theoretical models of predator-prey systems predict that sufficient enrichment of prey can generate large amplitude limit cycles, paradoxically causing a high risk of extinction (the paradox of enrichment). Although real ecological communities contain many gregarious species, whose foraging behaviour should be influenced by socially transmitted information, few theoretical studies have examined the possibility that social foraging might resolve this paradox. I considered a predator population in which individuals play the producer-scrounger foraging game in one-prey-one-predator and two-prey-one-predator systems. I analysed the stability of a coexisting equilibrium point in the one-prey system and that of non-equilibrium dynamics in the two-prey system. The results revealed that social foraging could stabilize both systems, and thereby resolve the paradox of enrichment when scrounging behaviour (i.e. kleptoparasitism) is prevalent in predators. This suggests a previously neglected mechanism underlying a powerful effect of group-living animals on the sustainability of ecological communities.

Paradox of enrichment: A fractional differential approach with memory

The paradox of enrichment (PoE) proposed by Rosenzweig [M. Rosenzweig, The paradox of enrichment, Science 171 (1971) 385-387] is still a fundamental problem in ecology. Most of the solutions have been proposed at an individual species level of organization and solutions at community level are lacking. Knowledge of how learning and memory modify behavioral responses to species is a key factor in making a crucial link between species and community levels. PoE resolution via these two organizational levels can be interpreted as a microscopic- and macroscopic-level solution. Fractional derivatives provide an excellent tool for describing this memory and the hereditary properties of various materials and processes. The derivatives can be physically interpreted via two time scales that are considered simultaneously: the ideal, equably flowing homogeneous local time, and the cosmic (inhomogeneous) non-local time. Several mechanisms and theories have been proposed to resolve the PoE problem, but a universally accepted theory is still lacking because most studies have focused on local effects and ignored non-local effects, which capture memory. Here we formulate the fractional counterpart of the Rosenzweig model and analyze the stability behavior of a system. We conclude that there is a threshold for the memory effect parameter beyond which the Rosenzweig model is stable and may be used as a potential agent to resolve PoE from a new perspective via fractional differential equations.

Adaptive and variable intraguild predators facilitate local coexistence in an intraguild predation module

Background

Intraguild predation (IGP) is common in nature, but its ecological role is still illusive. A number of studies have investigated a three species IGP module that consists of an intraguild predator, intraguild prey, and resource species in which the intraguild predator and the intraguild prey exploitatively compete for the resource while the intraguild predator also consumes the intraguild prey. A common prediction of models of the IGP module is that the coexistence of the species is difficult, which is considered inconsistent to the ubiquity of IGP in nature. This study revisits the IGP module and provides an alternative coexistence mechanism by focusing on a commonly used analysis method (i.e., invasion analysis) in light of individual variation in adaptive behavior.

Results

Invasion analysis underestimates the possibility of coexistence regardless of the presence or absence of adaptive behavior. Coexistence is possible even when invasion analysis predicts otherwise. The underestimation by invasion analysis is pronounced when the intraguild predator forages adaptively, which is even further pronounced when the expression of foraging behavior is variable among intraguild predators.

Conclusions

The possibility of coexistence in the IGP module is greater than previously thought, which may have been partly due to how models were analyzed. Inconsistent conclusions may result from the same model depending on how the model is analyzed. Individual variation in adaptive behavior can be an important factor promoting the coexistence of species in IGP modules.

Individual variation in prey choice in a predator-prey community

One predator-two prey community models are studied with an emphasis on individual variation in predator behavior. The predator behaves according to a well-known prey choice model. The behavioral model predicts that predators should always attack the primary prey (more profitable prey of the two), but only attack the alternative prey (less profitable prey of the two) when the density of the primary prey is below a threshold density. The predator that accepts the alternative prey does not discriminate between the primary and alternative prey (all-or-nothing preference for the alternative prey). However, empirical studies do not result in clear all-or-nothing responses. Previous models examined the relaxation of the all-or-nothing response by assuming partial preference (e.g., predators preferentially forage on the primary prey even when they also attack the alternative prey). In this study, I consider individual variation in two predator traits (prey density perception and handling time) as the sources of the variation in the threshold density, which can make empirical data appear deviated from the expectation. I examine how community models with partial preference and individual variation differ in their dynamics and show that the differences can be substantial. For example, the dynamics of a model based on individual variation can be more stable (e.g., stable in a wider parameter region) than that of a model based on partial preference. As the general statistical property (Jensen's inequality) is a main factor that causes the differences, the results of the study have general implications to the interpretation of models based on average per-capita rates.

Consumer-resource dynamics: quantity, quality, and allocation

BACKGROUND

The dominant paradigm for modeling the complexities of interacting populations and food webs is a system of coupled ordinary differential equations in which the state of each species, population, or functional trophic group is represented by an aggregated numbers-density or biomass-density variable. Here, using the metaphysiological approach to model consumer-resource interactions, we formulate a two-state paradigm that represents each population or group in a food web in terms of both its quantity and quality.

METHODOLOGY AND PRINCIPAL FINDINGS

The formulation includes an allocation function controlling the relative proportion of extracted resources to increasing quantity versus elevating quality. Since lower quality individuals senescence more rapidly than higher quality individuals, an optimal allocation proportion exists and we derive an expression for how this proportion depends on population parameters that determine the senescence rate, the per-capita mortality rate, and the effects of these rates on the dynamics of the quality variable. We demonstrate that oscillations do not arise in our model from quantity-quality interactions alone, but require consumer-resource interactions across trophic levels that can be stabilized through judicious resource allocation strategies. Analysis and simulations provide compelling arguments for the necessity of populations to evolve quality-related dynamics in the form of maternal effects, storage or other appropriate structures. They also indicate that resource allocation switching between investments in abundance versus quality provide a powerful mechanism for promoting the stability of consumer-resource interactions in seasonally forcing environments.

CONCLUSIONS/SIGNIFICANCE

Our simulations show that physiological inefficiencies associated with this switching can be favored by selection due to the diminished exposure of inefficient consumers to strong oscillations associated with the well-known paradox of enrichment. Also our results demonstrate how allocation switching can explain observed growth patterns in experimental microbial cultures and discuss how our formulation can address questions that cannot be answered using the quantity-only paradigms that currently predominate.