Whole-system nutrient enrichment increases secondary production in a detritus-based ecosystem

Although the effects of nutrient enrichment on consumer-resource dynamics are relatively well studied in ecosystems based on living plants, little is known about the manner in which enrichment influences the dynamics and productivity of consumers and resources in detritus-based ecosystems. Because nutrients can stimulate loss of carbon at the base of detrital food webs, effects on higher consumers may be fundamentally different than what is expected for living-plant-based food webs in which nutrients typically increase basal carbon. We experimentally enriched a detritus-based headwater stream for two years to examine the effects of nutrient-induced changes at the base of the food web on higher metazoan (predominantly invertebrate) consumers. Our paired-catchment design was aimed at quantifying organic matter and invertebrate dynamics in the enriched stream and an adjacent reference stream for two years prior to enrichment and two years during enrichment. Enrichment had a strong negative effect on standing crop of leaf litter, but no apparent effect on that of fine benthic organic matter. Despite large nutrient-induced reductions in the quantity of leaf litter, invertebrate secondary production during the enrichment was the highest ever reported for headwater streams at this Long Term Ecological Research site and was 1.2-3.3 times higher than predicted based on 15 years of data from these streams. Abundance, biomass, and secondary production of invertebrate consumers increased significantly in response to enrichment, and the response was greater among taxa with larval life spans < or = 1 yr than among those with larval life spans >1 yr. Production of invertebrate predators closely tracked the increased production of their prey. The response of invertebrates was largely habitat-specific with little effect of enrichment on food webs inhabiting bedrock outcrops. Our results demonstrate that positive nutrient-induced changes to food quality likely override negative changes to food quantity for consumers during the initial years of enrichment of detritus-based stream ecosystems. Longer-term enrichment may impact consumers through eventual reductions in the quantity of detritus.     

Transient dynamics and the destabilizing effects of prey heterogeneity

The presence of prey heterogeneity and weakly interacting prey species is frequently viewed as a stabilizer of predator-prey dynamics, countering the destabilizing effects of enrichment and reducing the amplitude of population cycles. However, prior model explorations have largely focused on long-term, dynamic attractors rather than transient dynamics. Recent theoretical work shows that the presence of prey that are defended from predation can have strongly divergent effects on dynamics depending on time scale: prey heterogeneity can counteract the destabilizing effects of enrichment on predator-prey dynamics at long time scales but strongly destabilize systems during transient phases by creating long periods of low predator/prey abundance and increasing extinction probability (an effect that is amplified with increasing enrichment). We tested these general predictions using a planktonic system composed of a zooplankton predator and multiple algal prey. We first parameterized a model of our system to generate predictions and tested these experimentally. Our results qualitatively supported several model predictions. During transient phases, presence of defended algal prey increased predator extinctions at low and high enrichment levels compared to systems with only a single edible prey. This destabilizing effect was moderated at higher dilution rates, as predicted by our model. When examining dynamics beyond initial oscillations, presence of the defended prey increased predator-prey temporal variability at high nutrient enrichment but had no effect at low nutrient levels. Our results highlight the importance of considering transient dynamics when assessing the role of stabilizing factors on the dynamics of food webs.     

Allee Effect and the Uncertainty of Population Recovery

Recovery of depleted populations is fundamentally important for conservation biology and sustainable resource harvesting. At low abundance, population growth rate, a primary determinant of population recovery, is generally assumed to be relatively fast because competition is low (i.e., negative density dependence). But population growth can be limited in small populations by an Allee effect. This is particularly relevant for collapsed populations or species that have not recovered despite large reductions in, or elimination of, threats. We investigated how an Allee effect can influence the dynamics of recovery. We used Atlantic cod (Gadus morhua) as the study organism and an empirically quantified Allee effect for the species to parameterize our simulations. We simulated recovery through an individual‐based mechanistic simulation model and then compared recovery among scenarios incorporating an Allee effect, negative density dependence, and an intermediate scenario. Although an Allee effect significantly slowed recovery, such that population increase could be negligible even after 100 years or more, it also made the time required for biomass rebuilding much less predictable. Our finding that an Allee effect greatly increased the uncertainty in recovery time frames provides an empirically based explanation for why the removal of threat does not always result in the recovery of depleted populations or species. El Efecto Allee y la Incertidumbre de la Recuperación de Poblaciones     

Modulation of predator-prey interactions by the Allee effect

An Allee effect arising from density-dependent mating success can have significant impacts at the ecosystem level when considered in the context of predator-prey interactions. These are captured by a mathematical model for the exchange of biomass between a structured predator population (continuous weight distribution) and a resource. Because the predator’s mating success affects the amount of resources required for the production of offsprings and their future growth into mature organisms, it influences the flux of biomass between trophic levels. Under simple assumptions, the equations can be reduced to an equivalent unstructured predator-prey model in which the Allee effect modulates the predation rate: the mating probability multiplies the rate of predator growth as well as the rate of resource depletion. Implications of the Allee effect for the bifurcation structure and equilibrium densities are examined. The model is compared to a modified version in which the Allee effect instead modulates the assimilation efficiency, hence the mating probability does not appear in the dynamical equation for the resource density. Both models exhibit qualitatively similar dynamics. However, compared to the model in which the Allee effect modulates predation, the model in which the Allee effect modulates assimilation efficiency predicts (i) unrealistically inefficient resource assimilation when predator density is low, (ii) a higher risk of catastrophic extinction resulting from a change in the parameter controlling the strength of the Allee effect, and (iii) no possibility of an increase in population size when the density dependence is enhanced.     

Predators, prey, and transient states in the assembly of spatially structured communities

Ecological theory suggests that both dispersal limitation and resource limitation can exert strong effects on community assembly. However, empirical studies of community assembly have focused almost exclusively on communities with a single trophic level. Thus, little is known about the combined effects of dispersal and resource limitation on assembly of communities with multiple trophic levels. We performed a landscape-scale experiment using spatially arranged mesocosms to study effects of dispersal and resource limitation on the assembly dynamics of aquatic invertebrate communities with two trophic levels. We found that interplay between dispersal and resource limitation regulated the assembly of predator and prey trophic levels in these pond communities. Early in assembly, predators and prey were strongly dispersal limited, and resource (i.e., prey) availability did not influence predator colonization. Later in assembly, after predators colonized, resource limitation was the strongest driver of predator abundance, and dispersal limitation played a negligible role. Thus, habitat isolation affected predators directly by reducing predator colonization rate, and indirectly through the effect of distance on prey availability. Dispersal and resource limitation of predators resulted in a transient period in which predators were absent or rare in isolated habitats. This period may be important for understanding population dynamics of vulnerable prey species. Our findings demonstrate that dispersal and resource limitation can jointly regulate assembly dynamics in multi-trophic systems. They also highlight the need to develop a temporal picture of the assembly process in multi-trophic communities because the availability and spatial distribution of limiting resources (i.e., prey) and the distribution of predators can shift radically over time.     

The interaction of cannibalism and omnivory: consequences for community dynamics

Although cannibalism is ubiquitous in food webs and frequent in systems where a predator and its prey also share a common resource (intraguild predation, IGP), its impacts on species interactions and the dynamics and structure of communities are still poorly understood. In addition, the few existing studies on cannibalism have generally focused on cannibalism in the top-predator, ignoring that it is frequent at intermediate trophic levels. A set of structured models shows that cannibalism can completely alter the dynamics and structure of three-species IGP systems depending on the trophic position where cannibalism occurs. Contrary to the expectations of simple models, the IG predator can exploit the resources more efficiently when it is cannibalistic, enabling the predator to persist at lower resource densities than the IG prey. Cannibalism in the IG predator can also alter the effect of enrichment, preventing predator-mediated extinction of the IG prey at high productivities predicted by simple models. Cannibalism in the IG prey can reverse the effect of top-down cascades, leading to an increase in the resource with decreasing IG predator density. These predictions are consistent with current data. Overall, cannibalism promotes the coexistence of the IG predator and IG prey. These results indicate that including cannibalism in current models can overcome the discrepancy between theory and empirical data. Thus, we need to measure and account for cannibalistic interactions to reliably predict the structure and dynamics of communities.     

Flooding impacts on responses of a riparian consumer to cross-ecosystem subsidies

Landscape-driven processes impact the magnitude and direction of cross-ecosystem resource subsidies, but they may also control consumers' numerical and functional responses by altering habitat availability. We investigated effects of the interaction between habitat availability and subsidy level on populations of a riparian fishing spider, Dolomedes aquaticus, using a flood disturbance gradient in the Waimakariri River catchment, New Zealand. D. aquaticus predominantly eat aquatic prey as they hunt from the water surface. However, D. aquaticus biomass peaked at rivers with intermediate flood disturbance, rather than at less flood-prone rivers where the biomass of aquatic insect prey was markedly higher. Flooding positively influenced spider habitat quality, and an experimental manipulation at stable rivers indicated that unembedded cobbles, preferred D. aquaticus habitat, were a limiting factor, preventing response to the increased prey resource at stable sites. Potential terrestrial prey abundance was low, did not vary across the disturbance gradient, and is likely to have been a much smaller component of the fishing spiders' diet than aquatic insect prey. Thus landscape-driven factors not only controlled the magnitude of resource subsidies, but also influenced the ability of consumers to respond to them by altering the physical nature of the ecosystem boundary.     

Consequences of stage-structured predators: cannibalism, behavioral effects, and trophic cascades

Cannibalistic and asymmetrical behavioral interactions between stages are common within stage-structured predator populations. Such direct interactions between predator stages can result in density- and trait-mediated indirect interactions between a predator and its prey. A set of structured predator-prey models is used to explore how such indirect interactions affect the dynamics and structure of communities. Analyses of the separate and combined effects of stage-structured cannibalism and behavior-mediated avoidance of cannibals under different ecological scenarios show that both cannibalism and behavioral avoidance of cannibalism can result in short- and long-term positive indirect connections between predator stages and the prey, including "apparent mutualism." These positive interactions alter the strength of trophic cascades such that the system's dynamics are determined by the interaction between bottom-up and top-down effects. Contrary to the expectation of simpler models, enrichment increases both predator and prey abundance in systems with cannibalism or behavioral avoidance of cannibalism. The effect of behavioral avoidance of cannibalism, however, depends on how strongly it affects the maturation rate of the predator. Behavioral interactions between predator stages reduce the short-term positive effect of cannibalism on the prey density, but can enhance its positive long-term effects. Both interaction types reduce the destabilizing effect of enrichment. These results suggest that inconsistencies between data and simple models can be resolved by accounting for stage-structured interactions within and among species.     

Pre-encounter versus post-encounter inducible defenses in predator–prey model systems

It has been reported that, in order to reduce mortality, prey are able to change their phenotype in response to cues released from predators. These short-time responses constitute effective antipredator strategies in variable environments, and involve changes in morphology, behavior, physiology or life-history traits of prey individuals belonging to a wide spectrum of taxa. Defenses can be classified into pre-encounter and post-encounter, depending on the phase of the predation process in which they take place. Also, inducible defenses should be costly.Despite the current knowledge of inducible defenses at the individual level, our understanding of their dynamic consequences at the population and community level is limited. In this work we construct and analyze numerically a predator–prey system, parameterized from published experimental data, in which prey exhibit inducible defenses of the type pre-encounter (affecting attack rate) or post-encounter (affecting handling time) and entailing either metabolic or feeding costs. The above assumptions were analyzed over a gradient of resource availability.Our results indicated that both types of cost have a similar effect on the dynamics of the model system, but we expect that different costs will produce different outcomes in a more complex model community. Conversely, pre-encounter and post-encounter IDs define domains of attraction with different size and shape within the studied sections of the multidimensional parameter space. Roughly speaking, post-encounter IDs determine a more rich dynamics when plausible parameter values are chosen, and the effect of resource density is different if the ID is handling-time based or attack-rate based. In agreement with previous works, our analyses indicate that IDs can damp population oscillations and prevent the paradox of enrichment.     

Food resource partitioning in a Mediterranean demersal fish assemblage: the effect of body size and niche width

We investigated the effects of body size, feeding strategy and depth distribution on the trophic resource partitioning among the 26 dominant fish consumers in a fish assemblage on the central Mediterranean shelf-break. The fish assemblage was structured in two major trophic guilds: epibenthic and zooplanktonic feeders, according to the position of each predator along the benthos–plankton gradient. Within each main guild, the species were segregated along a prey-size or fish-size gradient into five further guilds. Fish size and prey size were strongly correlated, indicating that the prey-size niche can be well explained by predator size. Fish consumers showed a significant negative correlation between the similarity in prey type and the similarity in depth distribution; most species with similar trophic preferences segregated along the depth dimension. The only predators overlapping in both food and depth preferences were those with a more specialist trophic behavior. These results suggest that fish body size and depth preferences are the two main niche dimensions, explaining a large part of the coexistence between the Mediterranean shelf-break fish consumers.     

Nutrient enrichment reduces constraints on material flows in a detritus-based food web

Most aquatic and terrestrial ecosystems are experiencing increased nutrient availability, which is affecting their structure and function. By altering community composition and productivity of consumers, enrichment can indirectly cause changes in the pathways and magnitude of material flows in food webs. These changes, in turn, have major consequences for material storage and cycling in the ecosystem. Understanding mechanisms and predicting consequences of nutrient-induced changes in material flows requires a quantitative food web approach that combines information on consumer energetics and consumer-resource stoichiometry. We examined effects of a whole-system experimental nutrient enrichment on the trophic basis of production and the magnitude and pathways of carbon (C), nitrogen (N), and phosphorus (P) flows in a detritus-based stream food web. We compared the response of the treated stream to an adjacent reference stream throughout the study. Dietary composition and elemental flows varied considerably among invertebrate functional feeding groups. During nutrient enrichment, increased flows of leaf litter and amorphous detritus to shredders and gatherers accounted for most of the altered flows of C from basal resources to consumers. Nutrient enrichment had little effect on patterns of material flows but had large positive effects on the magnitude of C, N, and P flows to consumers (mean increase of 97% for all elements). Nutrient-specific food webs revealed similar flows of N and P to multiple functional groups despite an order of magnitude difference among groups in consumption of C. Secondary production was more strongly related to consumption of nutrients than C, and increased material flows were positively related to the degree of consumer-resource C:P and C:N imbalances. Nutrient enrichment resulted in an increased proportion of detrital C inputs consumed by primary consumers (from -15% to 35%) and a decreased proportion of invertebrate prey consumed by predators (from -80% to 55%). Our results demonstrate that nutrient enrichment of detritus-based systems may reduce stoichiometric constraints on material flows, increase the contribution of consumers to C, N, and P cycling, alter the proportion of C inputs metabolized by consumers, and potentially lead to reduced ecosystem-level storage of C.     

Intraguild predation and mesopredator release effect on long-lived prey

Complete extirpation of a species can generate cascading effects throughout an ecosystem, yet are precisely the goal of island eradications of pest species. “Mesopredator release effect”, an asymmetrical special case of intraguild predation, has been hypothesised as a possible indirect effect from eradications, where superpredator removal can generate a mesopredator increase which may increase the impact on their shared prey. Theoretically this suggests that for intraguild predators, the superpredator may protect the shared prey from mesopredation, and removal of superpredators alone is not recommended. We create a model of long-lived age-structured shared prey and explore the non-equilibrium dynamics of this system. The superpredator can impact all prey life-stages (adult survival and reproductive success) whereas the smaller mesopredator can only impact early life-stages (reproductive success). This model is independently tested with data from a closed oceanic island system where eradication of introduced intraguild predators is possible for conservation of threatened birds. Mesopredator release only occurs in strongly top-down moderated (resource-abundant) systems. Even when mesopredator release can occur, the negative impact of more mesopredators is outweighed by the benefit of superpredator removal, allowing recovery of the prey population. Results are robust to 10% variation in model parameters. The consideration of age-structured prey contradicts previous theoretical results for mesopredator release effect and intraguild predation. Superpredator eradication is vital for population recovery of long-lived insular species. Nonetheless island conservation must retain a whole-ecosystem perspective given the complex trophic relationships among multiple species on islands.     

Sensitivity to assumptions in models of generalist predation on a cyclic prey

Ecological theory predicts that generalist predators should damp or suppress long-term periodic fluctuations (cycles) in their prey populations and depress their average densities. However, the magnitude of these impacts is likely to vary depending on the availability of alternative prey species and the nature of ecological mechanisms driving the prey cycles. These multispecies effects can be modeled explicitly if parameterized functions relating prey consumption to prey abundance, and realistic population dynamical models for the prey, are available. These requirements are met by the interaction between the Hen Harrier (Circus cyaneus) and three of its prey species in the United Kingdom, the Meadow Pipit (Anthus pratensis), the field vole (Microtus agrestis), and the Red Grouse (Lagopus lagopus scoticus). We used this system to investigate how the availability of alternative prey and the way in which prey dynamics are modeled might affect the behavior of simple trophic networks. We generated cycles in one of the prey species (Red Grouse) in three different ways: through (1) the interaction between grouse density and macroparasites, (2) the interaction between grouse density and male grouse aggressiveness, and (3) a generic, delayed density-dependent mechanism. Our results confirm that generalist predation can damp or suppress grouse cycles, but only when the densities of alternative prey are low. They also demonstrate that diametrically opposite indirect effects between pairs of prey species can occur together in simple systems. In this case, pipits and grouse are apparent competitors, whereas voles and grouse are apparent facilitators. Finally, we found that the quantitative impacts of the predator on prey density differed among the three models of prey dynamics, and these differences were robust to uncertainty in parameter estimation and environmental stochasticity.     

Measuring the impact of dynamic antipredator traits on predator-prey-resource interactions

This article analyzes the limitations of the most widely used method for quantifying the impact of dynamic antipredator traits on food chain dynamics and discusses alternative approaches. The standard method for a predator-prey-resource chain estimates the effects of the prey's defensive behavior by comparing population densities or fitness measures in a "predator cue" treatment to those in a no-predator treatment. This design has been interpreted as providing a measure of the "nonconsumptive effect" of the predator on the prey and the "trait-mediated indirect effect" of the predator on the resource. Other approaches involve measurements of the impact of the behavior in the presence of functional predators. The questions addressed here are: (1) How consistent are the results of different approaches? (2) How time-dependent are their results? (3) How well do they correspond to theoretical measures of effect size? (4) How useful are the measurements in understanding system dynamics? A model of a tritrophic system in which the prey species adjusts a defensive trait adaptively is used to evaluate the experimental designs. Measures of changes in prey fitness or population density in a cue treatment generally include offsetting effects of the cost of the behavior and the benefit of more resources. This means that the sign of the effect, as well as its magnitude, may change depending on when the experiment is terminated. Because predation is not present in the cue treatment, few conclusions can be drawn about the impact of the behavior on population densities or fitness of the prey in a natural setting with predators. Cue experiments often do not accurately separate trait-mediated from density-mediated effects on the resource. Most scalar measures of effects are sensitive to experimental duration and initial densities. Use of a wider range of experimental designs to measure trait-related effects is called for.     

Adaptive prey behavior and the dynamics of intraguild predation systems

Intraguild predation constitutes a widespread interaction occurring across different taxa, trophic positions and ecosystems, and its endogenous dynamical properties have been shown to affect the abundance and persistence of the involved populations as well as those connected with them within food webs. Although optimal foraging decisions displayed by predators are known to exert a stabilizing influence on the dynamics of intraguild predation systems, few is known about the corresponding influence of adaptive prey decisions in spite of its commonness in nature. In this study, we analyze the effect that adaptive antipredator behavior exerts on the stability and persistence of the populations involved in intraguild predation systems. Our results indicate that adaptive prey behavior in the form of inducible defenses act as a stabilizing mechanism and show that, in the same direction that adaptive foraging, enhances the parameter space in which species can coexist through promoting persistence of the IG-prey. At high levels of enrichment, the intraguild predation system exhibits unstable dynamics and zones of multiples attractors. In addition, we show that the equilibrium density of the IG-predator could be increased at intermediate values of defense effectiveness. Finally we conclude that adaptive prey behavior is an important mechanism leading to species coexistence in intraguild predation systems and consequently enhancing stability of food webs.     

The influence of size-specific indirect interactions in predator-prey systems

Nonlethal indirect interactions between predators often lead to nonadditive effects of predator number on prey survival and growth. Previous studies have focused on systems with at least two different predator species and one prey species. However, most predators undergo extreme ontological changes in phenotype such that interactions between different-sized cohorts of a predator and its prey could lead to nonadditive effects in systems with only two species. This may be important since different-sized individuals of the same species can differ more in their ecology than similar-sized individuals of different species. This study examined trait-mediated indirect effects in a two-species system including a cannibalistic predator with different-sized cohorts and its prey. I tested for these effects using larvae of two stream salamanders, Gyrinophilus porphyriticus (predator) and Eurycea cirrigera (prey), by altering the densities and combinations of predator size classes in experimental streams. Results showed that the presence of large individuals can significantly reduce the impact of density changes of smaller conspecifics on prey survival through nonlethal means. In the absence of large conspecifics, an increase in the relative frequency of small predators significantly increased predation rates, thereby reducing prey survival. However, with large conspecifics present, increasing the density of small predators did not decrease prey survival, resulting in a 14.3% lower prey mortality than predicted from the independent effects of both predator size classes. Small predators changed their microhabitat use in the presence of larger conspecifics. Prey individuals reduced activity in response to large predators but did not respond to small predators. Both predators reduced prey growth. These results demonstrate that the impact of a predator can be significantly altered by two different types of trait-mediated indirect effects in two-species systems: between different-sized cohorts and between different cohorts and prey. This study demonstrates that predictions based on simple numerical changes that assume independent effects of different size classes or ignore size structure can be strongly misleading. We need to account for the size structure within predator populations in order to predict how changes in predator abundance will affect predator-prey dynamics.     

Incorporating consumer–resource spatial interactions in reserve design

The persistence of species in reserves depends in large part on the persistence of functional ecological interactions. Despite their importance, however, ecological interactions have not yet been explicitly incorporated into conservation prioritization methods. We develop here a general method for incorporating consumer–resource interactions into spatial reserve design. This method protects spatial consumer–resource interactions by protecting areas that maintain the connectivity between the distribution of consumers and resources. We illustrate our method with a conservation planning case study of a mammalian predator, American marten (Martes americana), and its two primary prey species, Red-backed vole (Clethrionomys rutilus) and Deer mouse (Peromyscus maniculatus). The conservation goal was to identify a reserve for marten that comprised 12% of a forest management unit in the boreal forest in Québec, Canada. We compared reserves developed using analysis variants that utilized different levels of information about predator and prey habitat distributions, species-specific connectivity requirements, and interaction connectivity requirements. The inclusion of consumer–resource interactions in reserve-selection resulted in spatially aggregated reserves that maintained local habitat quality for the species. This spatial aggregation was not induced by applying a qualitative penalty for the boundary length of the reserve, but rather was a direct consequence of modelling the spatial needs of the interacting consumer and resources. Our method for maintaining connectivity between consumers and their resources within reserves can be applied even under the most extreme cases of either complete spatial overlap or complete spatial segregation of consumer–resource distributions. The method has been made available via public software.     

Four Factors Modifying the Effect of Competition on Carnivore Population Dynamics as Illustrated by African Wild Dogs

Abstract: Limitation of predator populations by prey availability and the effects of predators on prey populations are widely recognized as important ecological processes that affect carnivore conservation. Interspecific competition can also be a strong limiting factor for carnivore populations, and the effects of competition help explain why some carnivore species are prone to extinction. Competition among carnivores is unusual in some ways, so some predictions from traditional models of competition do not hold. For example, an increase in the density of prey can increase the effect of competition among carnivores, rather than weakening it. I used published data from African wild dogs (    Lycaon pictus ) to highlight four complexities that can modify the effects of competition on the population dynamics of carnivores: habitat fragmentation, counterintuitive effects of prey density, predator-prey size ratios, and habitat type.     

Invading parasitoids suffer no Allee effect: a manipulative field experiment

One frequent explanation for the failure of biological invasions is the Allee effect: due to positive density dependence, initially small invading populations may fail to establish and spread. Populations released for biological control are similar to fortuitous invading populations and may therefore suffer from Allee effects. However, unlike fortuitous invasions, biological control allows the experimental manipulation of initial population size and, thus, offers a unique opportunity to test for the occurrence of Allee effects. We manipulated the initial size of 45 populations of a parasitoid wasp introduced for the biological control of a phytophagous insect and followed the population dynamics of both parasitoids and hosts during three years. Our results suggest an absence of Allee effects but clear negative density dependence instead: (1) the probability of establishment after three years was not affected by initial population size; (2) net reproductive rate was highest at low parasitoid density and high host density; (3) the sex ratio, reflecting the proportion of virgin females, did not increase at low density, suggesting that low densities did not impede mate-finding; (4) the depression of host populations did not depend upon the number of parasitoids introduced. This is, to our knowledge, the first experimental test of the Allee effect in an invading parasitoid. It leads us to propose that a number of behavioral and life-history features of many parasitoids could protect them from Allee effects.     

A simple population theory for mutualism by the use of lattice gas model

The population dynamics of species interactions provides valuable information for life sciences. Lotka-Volterra equations (LVEs) are known to be the most popular model, and they are mainly applied to the systems of predation and competition. However, LVEs often fail to catch the population dynamics of mutualism; the population sizes of species increase infinitely under certain condition (divergence problem). Furthermore, LVEs never predicts the Allee effect in the systems of obligate mutualism. Instead of LVEs, several models have been presented for mutualism; unfortunately, they are rather complicated. It is, therefore, necessary to introduce a simpler theory for mutualism. In the present paper, we apply the lattice gas model which corresponds to the mean-field theory of the usual lattice model. The derived equations are cubic and contain only essential features for mutualism. In the case of obligate mutualism, the dynamics exhibits the Allee effect, and it is almost the same as in the male-female systems. In our model, the population sizes never increase infinitely, because our model contains not only intra- but also interspecific competitions. If the density of one species increases disproportionately in respect of its mutual partners, then this might imply downward pressure on the population abundance of the mutual partner species and such feedback would eventually act as a controlling influence on the population abundance of either species. We discuss several assumptions in our model; in particular, if both species can occupy in each cell simultaneously, then the interspecific competition disappears.