Coexistence in a simple food chain with diffusion

We show the global existence of classical positive solutions in each component of a Lotka-Volterra system with diffusion and logistic growing conditions. We are mainly interested in the search of coexistence states solving the associated elliptic problem under homogeneous Dirichlet boundary conditions.     

Remarks on antipredator behavior and food chain dynamics

When consumers feeding on a resource spend time in avoiding high risks of predation, the predator functional response declines with predator density. While this is well established, less attention has been paid to the dependence of the consumer functional response on predator density. Here we show how the separation of behavioral and ecological timescales allows one to determine both responses starting from an explicit behavioral model. Within the general set-up considered in this paper, the two functional responses can tend toward Holling type II responses when consumers react only weakly to predation. Thus, the main characteristics of the standard Rosenzweig-MacArthur tritrophic food chain (logistic resource and Holling type II consumer and predator) remain valid also when consumers have weak antipredator behavior. Moreover, through numerical analysis, we show that in a particular but interesting case pronounced antipredator behaviors stabilize the system.     

Seasonality directs contrasting food collection behavior and nutrient regulation strategies in ants

Long-lived animals, including social insects, often display seasonal shifts in foraging behavior. Foraging is ultimately a nutrient consumption exercise, but the effect of seasonality per se on changes in foraging behavior, particularly as it relates to nutrient regulation, is poorly understood. Here, we show that field-collected fire ant colonies, returned to the laboratory and maintained under identical photoperiod, temperature, and humidity regimes, and presented with experimental foods that had different protein (p) to carbohydrate (c) ratios, practice summer- and fall-specific foraging behaviors with respect to protein-carbohydrate regulation. Summer colonies increased the amount of food collected as the p:c ratio of their food became increasingly imbalanced, but fall colonies collected similar amounts of food regardless of the p:c ratio of their food. Choice experiments revealed that feeding was non-random, and that both fall and summer ants preferred carbohydrate-biased food. However, ants rarely ate all the food they collected, and their cached or discarded food always contained little carbohydrate relative to protein. From a nutrient regulation strategy, ants consumed most of the carbohydrate they collected, but regulated protein consumption to a similar level, regardless of season. We suggest that varied seasonal food collection behaviors and nutrient regulation strategies may be an adaptation that allows long-lived animals to meet current and future nutrient demands when nutrient-rich foods are abundant (e.g. spring and summer), and to conserve energy and be metabolically more efficient when nutritionally balanced foods are less abundant.     

Response of a solutivory chain to a nutrient pulse

A microbial community model is proposed that accounts for byproducts of one strain being nutrients for another and for cells passing in and out of states of torpor. It is shown that such models can sustain the propagation of a nutrient pulse as observed, for example, in methanogenesis.This work was supported in part by NSF Grant DMS9206677 and in part by NSF STC Center in Microbial Ecology, Michigan State University.     

The food chain dynamics of the oyster,clam, and mussel in an aquaculture food chain

The food chain dynamics of the edible mussel Mytilus edulis L., the American oyster Crassostrea virginica (Gmelin) and the hard clam Mercenaria mercenaria (L.) were investigated in large experimental tanks with flowing, filtered sea water and controlled addition of phytoplankton. The feeding rate of the mussel (5.36 μg carbon removed/l/g C animal was higher than that of the oyster (3.92) and clam (3.03) but the ecological efficiencies (net production/ingested food) × 100 of the clam (23.69 %) and the oyster (18.38 %) were higher than that of the mussel (10.01 %).The food chain efficiencies (net production/available food) were lower than the ecological efficiencies, suggesting under-exploitation of the available food. The clam, although having a lower feeding rate, was more efficient in utilizing the food it filtered and so showed the highest net production.The rates (μg-at/l/g C animal) of regeneration of nutrients, especially total inorganic nitrogen (mussel, 2.1723 × 10^?3; oyster, 7.4270 × 10^?3; and clam, 8.1750 × 10^?3) along with reported high biodeposition rates of bivalves suggest that multi-species aquaculture systems would be more efficient and productive than one-species systems.     

Qualitative behavior of a selectively neutral allelic model

A model of Fleming and Viot for describing frequency distributions for selectively neutral allelic populations and for multidimensional numerical genetic traits is studied, with specific attention given to two qualitative aspects that are derived: the coherence of the random wandering distribution and the tendency to cluster at microscopic scales. A new quantity, called the clustering or occupation index, is introduced to measure relative patchiness of the distribution in terms of a limiting subcell occupation frequency. Results of one- and two-dimensional computer-generated simulations are presented which provide an estimate of the theoretical expected distribution of allelic types. Evidence of the robustness of the model, in the sense that it arises from a variety of assumptions about the reproductive mechanism, is presented in the Appendix.     

Oscillatory coexistence in a food chain model with competing predators

A food chain model with two predators feeding on a single prey in a chemostat is studied. Using a multiparameter bifurcation analysis, we find parameters values for which there is stable oscillatory coexistence of the predators. It is also shown how these coexistent states provide a transition between two possible states of competitive exclusion. It is shown that the competitive exclusion principle need not hold if one or more of the predators has oscillatory behavior in the absence of other predators.This work was partially supported by National Science Foundation Grant MCS 83-01881     

Differential patterns of food appreciation during consumption of a simple food in congenitally anosmic individuals: an explorative study

Food is evaluated for various attributes. One of the key food evaluation domains is hedonicity. As food is consumed, its hedonic valence decreases (due to prolonged sensory stimulation) and hedonic habituation results. The aim of the present study was to investigate changes in food pleasantness ratings during consumption of a simple food by individuals without olfactory experience with food as compared to normosmics. 15 congenital anosmics and 15 normosmic controls were each presented with ten 10 g banana slices. Each was visually inspected, then smelled and chewed for ten seconds and subsequently rated for hedonicity on a 21-point scale. There was a significant difference in pleasantness ratings between congenital anosmics and controls (F(1, 26) = 6.71, p = .02) with the anosmics exhibiting higher ratings than the controls, a significant main repeated-measures effect on the ratings (F(1.85, 48) = 12.15, p<.001), which showed a decreasing trend over the course of consumption, as well as a significant portion*group interaction (F(1.85, 48) = 3.54, p = .04), with the anosmic participants experiencing a less pronounced decline. The results of the present explorative study suggest that over the course of consumption of a simple food, congenitally anosmic individuals experience differential patterns of appreciation of food as compared to normosmics. In this particular case, the decrease of hedonic valence was less pronounced in congenital anosmics.     

Forest fragmentation truncates a food chain based on an old-growth forest bracket fungus

We studied the effect of forest fragmentation on the insect community inhabiting an old-growth forest specialist bracket fungus, Fomitopsis rosea , in eastern Finland. Samples of the fungus from large non-isolated control areas were compared with samples from forest fragments in two isolation time classes; 2–7 yr and 12–32 yr since isolation. Fomitopsis rosea hosted a species-rich community with relatively many specialized old-growth forest insects. The numerically dominant food chain consisted of F. rosea , the tineid moth Agnathosia mendicella and the tachinid fly Elfia cingulata , a specialist parasitoid of A. mendicella . The frequency of F. rosea on suitable fallen spruce logs and the frequency of A. mendicella in fruiting bodies were significantly lower in the forest fragments than in the control areas. The median number of trophic levels decreased from three in the control areas to one in the fragments that had been isolated for the longest period of time. The parasitoid was completely missing from the fragments isolated for 12–32 yr. Our results show that in boreal forests habitat loss and fragmentation truncate food chains of specialized species in the course of time since isolation.     

Qualitative behavior of predator-prey communities

We examine a set of n-species predator-prey models which incorporate functional responses of the predators to their prey and non-linear intraspecific interactions. We review the limitations of a linear analysis around equilibrium states and provide an extension of the Routh-Hurwitz criteria to the non-linear regime by using Birkhoff's normal forms of differential equations. Qualitative properties like the orbit structure around isolated singularities become clear in this method. It is possible to obtain the radius of the torus and the renormalized frequencies when the eigenvalues of the community matrix have small positive real parts, and to classify different topological structures near bifurcation values of a convenient set of control parameters. Examples of two, three, and four species are analyzed in the context of normal forms.We conclude with some suggestions concerning the coupling of a small subsystem to a large community, and the relations between the graphical method of isoclines and normal forms. This correspondence indicates a road to generalize the study of many-dimensional systems when the intuition provided by the graphical method fails.     

Predator–prey interactions in a grassland food chain vary with temperature and food quality

Because species interactions are often context‐dependent, abiotic factors such as temperature and biotic factors such as food quality may alter species interactions with potential consequences to ecosystem structure and function. For example, altered predator–prey interactions may influence the dynamics of trophic cascades, affecting net primary production. In a three‐year field experiment, we manipulated a plant–grasshopper–spider food chain in mesic tallgrass prairie to investigate the effects of temperature and food quality on grasshopper performance, and to understand the direct and indirect tritrophic interactions that contribute to trophic cascades. Because spiders are active at cooler temperatures than grasshoppers in our system, we hypothesized that predator effects would be strongest in cooled treatments, and weakest in warmed treatments. Grasshopper spider interactions were highly context‐dependent and varied significantly with food quality, temperature treatment and year. Spiders most often reduced grasshopper survival in the cooled and ambient temperature treatments, but had little to no effect on grasshopper survival in the warmed treatments, as hypothesized. In some years, plants compensated for grasshopper herbivory and trophic cascades were not observed despite significant effects of predators on grasshopper survival. However, in the year they were observed, trophic cascades only occurred in cooled treatments where predator effects on grasshoppers were strongest. Predicting ecosystem responses to climate change will require an understanding of how temperature influences species interactions. Our results demonstrate that changes in daily temperature regimes can alter predator–prey interactions among arthropods with consequences for ecosystem processes such as primary production and the relative importance of top–down and bottom–up processes.     

Community convergence in a simple microbial food web

Previous studies of communities implicate many potential mechanisms that can create alternate stable states. These include density-dependent foraging behavior, size refuges reached by early colonists, environmental feedback following disturbance, and different initial densities of intraguild predators. Previous work shows that alternate states of varying stability can occur in food webs containing the intraguild predators Blepharisma americanum and Tetrahymena vorax. Differences in colonization history could create the alternate states, consisting of dominance by either Blepharisma or Tetrahymena, but it was unclear whether results depended on effects of initial density or only on changes in the resource base. We manipulated initial densities of both species to determine if density effects alone could create alternate stable states. Convergence of these communities over time indicated that differences in initial density did not create alternate stable states. By default, other factors influenced by colonization history, such as resource availability, may produce alternate states. Models of alternate stable-state phenomena should incorporate differences in resource availability in addition to direct competitive and predatory interactions to provide a more complete depiction of the causes of differences in community composition in otherwise similar habitats.     

一个海洋食物链能流的初步研究

选择我国北方海岸带水域中属于第一、二、三、四营养级的４个经济种,构成一个简单的人工食物链,即金藻→卤虫→玉筋鱼→黑鱼君．测定了各营养级间物质（湿重、干重）、能量的转换效率,求出了食物链各环节的生产量比值．结果表明,在这个食物链运转过程中,生产１ｋｇ湿重的黑鱼君（第四营养级）需要消耗相当于初级生产力２３５．２ｋｇ湿重的金藻（第一营养级）;生产１ｋｇ干重的黑鱼君需要消耗相当于１４８．３ｋｇ干重的金藻;黑鱼君富集１ｋＪ能量需要消耗含有１１０．７ｋＪ的金藻．     

Bi-trophic food chain dynamics with multiple component populations

Food web models describe the patterns of material and energy flow in communities. In classical food web models the state of each population is described by a single variable which represents, for instance, the biomass or the number of individuals that make up the population. However, in a number of models proposed recently in the literature the individual organisms consist of two components. In addition to the structural component there is an internal pool of nutrients, lipids or reserves. Consequently the population model for each trophic level is described by two state variables instead of one. As a result the classical predator-prey interaction formalisms have to be revised. In our model time budgets with actions as searching and handling provide the formulation of the functional response for both components. In the model, assimilation of the ingested two prey components is done in parallel and the extracted energy is added to a predators reserve pool. The reserves are used for vital processes; growth, reproduction and maintenance. We will explore the top-down modelling approach where the perspective is from the community. We will demonstrate that this approach facilitates a check on the balance equations for mass and energy at this level of organization. Here it will be shown that, if the individual is allowed to shrink when the energy reserves are in short to pay the maintenance costs, the growth process has to be 100% effective. This is unrealistic and some alternative model formulations are discussed. The long-term dynamics of a microbial food chain in the chemostat are studied using bifurcation analysis. The dilution rate and the concentration of nutrients in the reservoir are the bifurcation parameters. The studied microbial bi-trophic food chain with two-component populations shows chaotic behaviour.     

Effects of predation and nutrient enrichment on a food web with edible and inedible prey

1. Trophic heterogeneity, or differences in edibility or resource consumption among species within a single trophic level, is widespread in natural food webs. Here, we test simple food web models that incorporate trophic heterogenity and that make robust predictions regarding food web responses to nutrient enrichment. To test these predictions, we assembled simple food webs consisting of an inedible alga, a mixed assemblage of bacteria, and a protist bacterivore in laboratory microcosms of contrasting nutrient concentrations. 2. Several results were consistent with model predictions. First, increasing nutrient concentration caused an increase in the abundance of the inedible alga, but only in the presence of the bacterivore. Secondly, nutrient enrichment increased the abundance of bacteria, but only in the absence of their bacterivore. Last, nutrient enrichment had no effect on abundance of the bacterivore. 3. Two results were not consistent with model predictions. First, at low nutrient concentrations, the presence of the bacterivore increased the abundance of bacteria. Secondly, although the abundances of the bacterivore and bacteria were positively correlated, some of the lowest abundances of both occurred in the high nutrient treatment. Thus, while our results were generally consistent with several simple food web models, additional explanations are required for selected food web responses.