A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment

In this paper, a mathematical model of a prey-predator system is proposed to resolve the paradox of enrichment in ecosystems. The model is based on the natural strategy that a predator takes, i.e, it produces resting eggs in harsh environment. Our result gives a criterion for a functional response, which ensures that entering dormancy stabilizes the population dynamics. It is also shown that the hatching of resting eggs can stabilize the population dynamics when the switching between non-resting and resting eggs is sharp. Furthermore, the bifurcation structure of our model suggests the simultaneous existence of a stable equilibrium and a large amplitude cycle in natural enriched environments.      

Egg viability of the rotifer Brachionus urceolaris after ingestion by the predatory cladoceran Leptodora kindtii

Egg resistance against the digestive process of a predator is an effective strategy for zooplankton to compensate population loss due to predation. Parthenogenetic eggs of the rotiferan Brachionus urceolaris, which were ingested by the predatory cladoceran Leptodora kindtii, were expelled from the feeding basket of the predator without digestion. We found a negative correlation between the unconsumed ratio of eggs after ingestion and body length of the predator. As high as 75% of the unconsumed eggs successfully hatched and the hatch ratio was independent of body length of L. kindtii. Our results indicate that the rotifer has an effective strategy to maintain its population in the environment with abundant invertebrate predators.     

Egg-eating age-structured predators in interaction with age-structured prey

In this paper, we consider a system of integrodifferential equations which models a predator-prey system with both species (predator and prey) age-structured and predators living only on the eggs of prey. The present model is a generalization of the model given in [20]. The existence, stability, and instability of nonnegative equilibria is studied assuming a general fecundity rate function for the prey. With a special choice of fecundity rate function for the predator it is shown here that a large maturation period m of the predator leads to stability. This seems to be contrary to the usual rule of thumb that increasing delays in growth rate responses cause instabilities.     

Functional response of Euseius concordis to densities of different developmental stages of the cassava green mite

Both prey density and developmental stage of pests and natural enemies are known to influence the effectiveness of biological control. However, little is known about the interaction between prey density and population structure on predation and fecundity of generalist predatory mites. Here, we evaluated the functional response (number of prey eaten by predator in relation to prey density) of adult females and nymphs of the generalist predatory mite Euseius concordis to densities of different developmental stages of the cassava green mite Mononychellus tanajoa, as well as the fecundity of adult females of the predator. We further assessed the instantaneous rate of increase, based on fecundity and mortality, of E. concordis fed on eggs, immatures and adults of M. tanajoa. Overall, nymphs and adults of E. concordis feeding on eggs, immatures and females of M. tanajoa had a type III functional response curve suggesting that the predator increased prey consumption rate as prey density increased. Both nymphs and adult females of the predator consumed more eggs than immatures of M. tanajoa from the density of 20 items per leaf disc onwards, revealing an interaction between prey density and developmental stage in the predatory activity of E. concordis. In addition, population growth rate was higher when the predator fed on eggs and immatures in comparison with females. Altogether our results suggest that E. concordis may be a good candidate for the biological control of M. tanajoa populations. However, the efficiency of E. concordis as a biological control agent of M. tanajoa is contingent on prey density and population structure.     

Revisiting the Role of Individual Variability in Population Persistence and Stability

Populations often exhibit a pronounced degree of individual variability and this can be important when constructing ecological models. In this paper, we revisit the role of inter-individual variability in population persistence and stability under predation pressure. As a case study, we consider interactions between a structured population of zooplankton grazers and their predators. Unlike previous structured population models, which only consider variability of individuals according to the age or body size, we focus on physiological and behavioural structuring. We first experimentally demonstrate a high degree of variation of individual consumption rates in three dominant species of herbivorous copepods (Calanus finmarchicus, Calanus glacialis, Calanus euxinus) and show that this disparity implies a pronounced variation in the consumption capacities of individuals. Then we construct a parsimonious predator-prey model which takes into account the intra-population variability of prey individuals according to behavioural traits: effectively, each organism has a ‘personality’ of its own. Our modelling results show that structuring of prey according to their growth rate and vulnerability to predation can dampen predator-prey cycles and enhance persistence of a species, even if the resource stock for prey is unlimited. The main mechanism of efficient top-down regulation is shown to work by letting the prey population become dominated by less vulnerable individuals when predator densities are high, while the trait distribution recovers when the predator densities are low.     

Adaptive evolution of foraging-related traits in a predator-prey community

In this paper, with the method of adaptive dynamics and geometric technique, we investigate the adaptive evolution of foraging-related phenotypic traits in a predator-prey community with trade-off structure. Specialization on one prey type is assumed to go at the expense of specialization on another. First, we identify the ecological and evolutionary conditions that allow for evolutionary branching in predator phenotype. Generally, if there is a small switching cost near the singular strategy, then this singular strategy is an evolutionary branching point, in which predator population will change from monomorphism to dimorphism. Second, we find that if the trade-off curve is globally convex, predator population eventually branches into two extreme specialists, each completely specializing on a particular prey species. However, if the trade-off curve is concave-convex-concave, after branching in predator phenotype, the two predator species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist. The analysis reveals that an attractive dimorphism will always be evolutionarily stable and that no further branching is possible under this model.     

Breeding biology of ostriches (Struthio camelus) in the Serengeti ecosystem, Tanzania

Ostrich breeding behaviour in the Serengeti ecosystem, Tanzania was investigated for differences in laying dates between low altitude western area (WA) and high altitude eastern area (EA) populations. Ostriches in WA laid eggs significantly earlier than in EA. The differences could be attributed to topography and rainfall pattern. Reliable rains in lower altitudes ensure availability of food that in turn influences the whole process of the reproductive cycle. Clutches were contributed by several females with a nest having up to 38 eggs. We also compared the frequency of observation of predators, ostriches, nests, 'singletons' (single eggs laid randomly) and broods between the two areas. There was no significant difference between WA and EA in 1) ostrich/nest ratio, indicating similar breeding densities; 2) ostrich/predator and predator/nest ratios, indicating that predation pressure was equally high; 3) nest/singleton and predator/singleton ratios, indicating that loss of nests did not vary between areas. However, there were significantly more predators, nests and ostriches compared to broods in EA than in WA, indicating a significantly lower reproductive success in EA. Using metapopulation terminology, ostriches in EA could be regarded as a 'sink' population and those in WA as a 'source' population, but investigations over longer time-periods are needed to further resolve if this is the case.     

Assessing the viability of tri-trophic food chain model in designing a conservation plan: The case of dwindling Quokka population

The extinction and persistence dynamics of quokka (Setonix brachyurus) population at northern jarrah forest of Australia is investigated using mathematical modelling. Predator's management demands a comprehensive understanding of the ecological circumstances associated with predation. Predation by red foxes (Vulpes vulpes) has a significant role in reducing the native animal population. This paper mainly focuses on the extinction dynamics of quokka population and its reduction by red foxes, by qualitative and quantitative analyses of a designed tri-trophic food-chain model composing a prey (quokka), a mesopredator (red fox) and apex predator (dingo). Existence of solution are analysed and shown to be uniformly bounded. We applied the concept of basic reproduction number from epidemiology to the food chain model, to derive a condition for extinction and persistence of predator population. Global stability of the predator-free equilibrium is established by geometric approach. We use Partial Rank Correlation Coefficient (PRCC) for performing global sensitivity analysis to identify most influential model parameter responsible for quokkas prevalence and mortality. Results of numerical simulation for both deterministic and stochastic model confirms the analytical finding and support those of previous studies. The outcome of this work shows that persistence and existence of quokka depend on the demographic impacts of environmental stochasticity on its own population. Based on our results, many conservation strategies are suggested to improve the overall growth of the species. We believe that declination of red fox and the presence of dingoes are important for preserving the uniform occurrence of quokkas.     

Host-plant species modifies the diet of an omnivore feeding on three trophic levels

The diet choice of omnivores feeding on two adjacent trophic levels (either plants and herbivores or herbivores and predators) has been studied extensively. However, omnivores usually feed on more than two trophic levels, and this diet choice and its consequences for population dynamics have hardly been studied. We report how host-plant quality affects the diet choice of western flower thrips feeding on three trophic levels: plants (cucumber or sweet pepper), eggs of spider mites and eggs of a predatory mite that attacks spider mites. Spider mites feed on the same host plants as thrips and produce a web that hampers predator mobility. To assess the indirect effects of spider mites on predation by thrips, the thrips were offered spider-mite eggs and predatory-mite eggs on cucumber or sweet pepper leaf discs that were either clean, damaged by spider mites but without spider-mite web, or damaged and webbed. We show that, overall, thrips consumed more eggs on sweet pepper, a plant of low quality, than on cucumber, a high quality host plant. On damaged and webbed leaf discs (mimicking the natural situation), thrips killed more predator eggs than spider-mite eggs on sweet pepper, but they killed equal numbers of eggs of each species on cucumber. This is because web hampered predation on spider-mite eggs by thrips on sweet pepper, but not on cucumber, whereas it did not affect predation on predatory-mite eggs. We used the data obtained to parameterize a model of the local dynamics of this system. The model predicts that total predation by the omnivore has little effects on population dynamics, whereas differential attack of predator eggs and spider-mite eggs by the omnivore has large effects on the dynamics of both mite species on the two host plants.     

Interspecific infanticide deters predators

It is well known that young, small predator stages are vulnerable to predation by conspecifics, intra-guild competitors or hyperpredators. It is less known that prey can also kill vulnerable predator stages that present no danger to the prey. Since adult predators are expected to avoid places where their offspring would run a high predation risk, this opens the way for potential prey to deter dangerous predator stages by killing vulnerable predator stages. We present an example of such a complex predator–prey interaction. We show that (1) the vulnerable stage of an omnivorous arthropod prey discriminates between eggs of a harmless predator species and eggs of a dangerous species, killing more eggs of the latter; (2) prey suffer a minor predation risk from newly hatched predators; (3) adult predators avoid ovipositing near killed predator eggs, and (4) vulnerable prey near killed predator eggs experience an almost fourfold reduction of predation. Hence, by attacking the vulnerable stage of their predator, prey deter adult predators and thus reduce their own predation risk. This provides a novel explanation for the killing of vulnerable stages of predators by prey and adds a new dimension to anti-predator behaviour.     

FLUCTUATING SELECTION AND RESPONSE IN A POPULATION OF FRESHWATER COPEPODS

The timing of springtime production of diapausing eggs by a population of the freshwater copepod, Diaptomus sanguineus, has been shown previously to be consistent with avoidance of seasonally intense fish predation. Natural selection acting on the timing of diapause fluctuates between years depending upon the population density of fish. Here we show that, in the field, the mean timing of diapause shifts between years in response to fluctuations in selection. Diapause is earlier in years following high predator density, and is later in years following low predator density. Although selection intensity in individual years may be large, the mean intensity over the decade of fluctuating selection investigated here is close to zero. Photoperiod sensitivity of the diapausetiming trait is heritable in the laboratory. The combination of fluctuating selection and multi-generation storage of genotypes as diapausing eggs in lake sediments may contribute to the maintenance of the genetic variation that permits the rapid selection response seen in the field.     

Functional equivalence of non-lethal effects: generalized fish avoidance determines distribution of gray treefrog, Hyla chrysoscelis, larvae

How patterns of prey abundance are generated determines how predation influences population and community level dynamics. We investigated how a natural population of ovipositing treefrogs, Hyla chrysoscelis , partitioned their eggs amongst experimental ponds differing in the non-lethal presence of five fish predators, each representing a distinct family. Four fish predators were functionally equivalent in terms of the behavioral response they induced in H. chrysoscelis females and hence the distribution of larval H. chrysoscelis . Mean number of H. chrysoscelis eggs deposited was significantly decreased by the mere presence of these predators relative to controls, with three species eliciting a complete avoidance (e.g. no eggs deposited). One fish predator, Aphredoderus sayanus , was statistically indistinguishable from the control treatment. These data mimic patterns of species distribution observed in nature in response to the presence of fish, but suggest an alternative mechanism for generating patterns of prey abundance amongst habitats differing in their predator composition. Furthermore, our results expand the importance of predator induced non-lethal effects as a process that could dramatically affect population and community level dynamics.     

A Test of the Multi-Predator Hypothesis: Rapid Loss of Antipredator Behavior after 130 years of Isolation

Many species find themselves isolated from the predators with which they evolved. Isolation often leads to the loss of costly antipredator behavior, which may have adverse consequences if the population should later come into contact with predators. An understanding of both the mechanism (i.e. the degree to which antipredator behavior depends on experience), and of the time course of loss is important to be able to predict how a population will respond to future contact. We studied ‘group‐size effects’– the way in which animals change the time they allocate to antipredator vigilance as a function of group size – and visual and acoustic predator recognition in a population of tammar wallabies (Macropus eugenii), a cat‐sized (6–10 kg) macropodid marsupial. To study group size effects we observed wallabies foraging in four populations – three with some sort of predator and a New Zealand population that was isolated from all predators for about 130 yr. To study predator recognition, we observed the response of New Zealand wallabies to the presentation of a model or taxidermic mount of mammalian predators, and to the broadcast sounds of mammalian and avian predators. We compare these predator recognition experiments with results from a previous study of Kangaroo Island (South Australia) tammars. Complete isolation from all predators for as few as 130 yr led to the loss of group size effects and a rapid breakdown in visual predator recognition abilities. Our results are consistent with a key prediction of the multi‐predator hypothesis – namely, that the isolation from all predators may lead to a rapid loss of antipredator behavior.     

The meta-Allee effect: A generalization from intermittent metapopulations

Intermittent population trajectories are likely to emerge in almost any population that faces a predator yet has a refuge from that predator. Using the well-known model of Pomeau and Manneville for intermittent populations, a collection of a group of inherently unstable subpopulations can survive through the balance of extinction and migration rates, which is a metapopulation. This formulation also generates a meta-Allee point, which is to say a minimal number of subpopulations that must exist to sustain the population over the long term.     

Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation

Interplay between predator and prey is a complex process in ecosystems due to its nature. The population dynamics can be affected by many extrinsic and intrinsic factors. In this paper, we make an attempt to uncover the effects from environmental disturbances when populations are subject to habitat complexity and aggregation effect. We firstly propose a stochastic predator-prey model with habitat complexity and aggregation efficiency for prey. We then mathematically analyze the model, to demonstrate the existence, uniqueness and the stochastically ultimately boundedness of the global positive solution, and to establish sufficient conditions for the existence of ergodic stationary distribution of the solution. We also establish sufficient conditions under which either only predator population dies out or the entire predator-prey model becomes extinct. Our theoretical and numerical results indicate that: (1) the environmental noises are disadvantage for the survival of biological populations; (2) when the density of prey is greater than one, prey aggregation can heighten the capability of predator species to capture prey and reduce the effect of environmental fluctuations, while when the density of prey is less than one, the results are opposite; (3) habitat complexity is propitious to the survival of prey population and may seriously threaten the persistence of the predator population.     

A mechanistic model for interference and Allee effect in the predator population

We present the results of simulations in an individual-based model describing spatial movement and predator-prey interaction within a closed rectangular habitat. Movement of each individual animal is determined by local conditions only, so any collective behavior emerges owing to self-organization. It is shown that the pursuit of prey by predators entails predator interference, manifesting itself at the population level as the dependency of the trophic function (individual ration) on predator abundance. The stabilizing effect of predator interference on the dynamics of a predator-prey system is discussed. Inclusion of prey evasion induces apparent cooperation of predators and further alters the functional response, giving rise to a strong Allee effect, with extinction of the predator population upon dropping below critical numbers. Thus, we propose a simple mechanistic interpretation of important but still poorly understood behavioral phenomena that underlie the functioning of natural trophic systems.     

Prey Selection,Vertical Migrations and the Impacts of Harvesting Upon the Population Dynamics of a Predator-Prey System

A model is developed to describe the interaction between a predator and two prey types located in different regions. Conditions for stability and persistence are analysed. The effects of harvesting the predators are investigated by making the predator mortality rate habitat dependent. Results demonstrate that for any given set of parameter values there is a value of the intrinsic preference of the predator for each prey type at which the system undergoes a Hopf bifurcation. Above this critical value the system evolves towards a stable equilibrium, whereas below it, stable limit cycles arise by Hopf bifurcations. Simulations demonstrate that the presence of demographic stochasticity may destabilise oscillatory populations, thereby causing population extinctions. An application of the model to the foraging behaviour of North Sea cod is described. It is shown that if the preferred prey is more productive, it is likely that the equilibrium will be stable, whereas if the less preferred prey is more productive, populations are likely to display cycles and in the stochastic case become extinct. As cod fishing mortality is increased, the point of bifurcation and region of parameter space for which the system is unstable decreases. An increased understanding of how cod behave may enable fish stocks to be managed more successfully, for example by indicating where marine reserves should be placed.     

Prey-stage preferences and functional and numerical responses of Amblyseius largoensis (Acari: Phytoseiidae) to Raoiella indica (Acari: Tenuipalpidae)

Raoiella indica Hirst (Acari: Tenuipalpidae) is a phytophagous mite that recently invaded the Western Hemisphere. This mite is a multivoltine and gregarious species that can reach very high population densities and cause significant damage to various palm species (Arecaceae). The predatory mite Amblyseius largoensis (Muma) (Acari: Phytoseiidae) has been found associated with R. indica in Florida. This study evaluated A. largoensis for potential to control R. indica by (1) determining predator preferences among developmental stages of R. indica, and (2) estimating predator functional and numerical responses to varying densities of its most preferred prey-stage. Under no-choice conditions A. largoensis consumed significantly more eggs than other stages of R. indica. In choice tests A. largoensis showed a significant preference for R. indica eggs over all other prey stages. Amblyseius largoensis displayed a type II functional response showing an increase in number of prey killed with an increase in prey population density. Consumption of prey stabilized at approximately 45 eggs/day, the level at which oviposition by the predator was maximized (2.36?±?0.11 eggs/day; mean?±?SEM). Results of this study suggest that A. largoensis can play a role in controlling R. indica populations, particularly when prey densities are low.     

Evolutionary branching and evolutionarily stable coexistence of predator species: Critical function analysis

On the ecological timescale, two predator species with linear functional responses can stably coexist on two competing prey species. In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate under what conditions such a coexistence is also evolutionarily stable, and whether the two predator species may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in capture rates and a predator with a high capture rate for one prey has a low capture rate for the other and vice versa. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly convex in the vicinity of the singular strategy and the interspecific prey competition is not strong, then this singular strategy is an evolutionary branching point, near which the resident and mutant predator populations can coexist and diverge in their strategies. Second, we find that after branching has occurred in the predator phenotype, if the trade-off curve is globally convex, the predator population will eventually branch into two extreme specialists, each completely specializing on a particular prey species. However, in the case of smoothed step function-like trade-off, an interior dimorphic singular coalition becomes possible, the predator population will eventually evolve into two generalist species, each feeding on both of the two prey species. The algebraical analysis reveals that an evolutionarily stable dimorphism will always be attractive and that no further branching is possible under this model.     

The feeding behaviour of Phytoseiulus persimilis (Acarina: Phytoseiidae), particularly as affected by certain pesticides

Detailed observations were made of the behaviour of Phytoseiulus persimilis while searching for, identifying and feeding on eggs of Tetranychus urticae. A theory is proposed to explain how P. persimilis may identify prey eggs and distinguish them from non-prey objects. The existence of a water-soluble feeding stimulant on prey eggs is postulated. The effect of residues of captan, dinocap and malathion on the feeding behaviour of P. persimilis was investigated. Residues of the fungicide dinocap on the eggs of the prey did not affect acceptance by the predator, but captan had a marked repellent effect. Malathion had an even stronger repellent effect. It is suggested that, by making the prey eggs less acceptable to the predator, the use of certain fungicides could render more difficult the prediction of population interactions on which biological control depends. We wish to thank Dr N. W. Hussey of the Glasshouse Crops Research Institute for helpful comments and for supplying predatory mites. Mr Jackson wishes to thank the Overseas Development Administration for financial support during this work.