Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Ten years after the Prestige Oil Spill: seabird trophic ecology as indicator of long-term effects on the coastal marine ecosystem

Major oil spills can have long-term impacts since oil pollution does not only result in acute mortality of marine organisms, but also affects productivity levels, predator-prey dynamics, and damages habitats that support marine communities. However, despite the conservation implications of oil accidents, the monitoring and assessment of its lasting impacts still remains a difficult and daunting task. Here, we used European shags to evaluate the overall, lasting effects of the Prestige oil spill (2002) on the affected marine ecosystem. Using δ15N and Hg analysis, we trace temporal changes in feeding ecology potentially related to alterations of the food web due to the spill. Using climatic and oceanic data, we also investigate the influence of North Atlantic Oscillation (NAO) index, the sea surface temperature (SST) and the chlorophyll a (Chl a) on the observed changes. Analysis of δ15N and Hg concentrations revealed that after the Prestige oil spill, shag chicks abruptly switched their trophic level from a diet based on a high percentage of demersal-benthic fish to a higher proportion of pelagic/semi-pelagic species. There was no evidence that Chl a, SST and NAO reflected any particular changes or severity in environmental conditions for any year or season that may explain the sudden change observed in trophic level. Thus, this study highlighted an impact on the marine food web for at least three years. Our results provide the best evidence to date of the long-term consequences of the Prestige oil spill. They also show how, regardless of wider oceanographic variability, lasting impacts on predator-prey dynamics can be assessed using biochemical markers. This is particularly useful if larger scale and longer term monitoring of all trophic levels is unfeasible due to limited funding or high ecosystem complexity.

Relationship between diet and reproductive success in the Israeli barn owl

The effect of diet on barn owl (Tyto alba) breeding biology has been well studied in the temperate regions but not in the more arid Middle East. In temperate regions, barn owls are darker colored and mainly prey upon Cricetidae rodents, whereas in arid regions, they are lighter colored and prey to a larger degree upon Muridae rodents. In this study we analyzed the diet and breeding success of 261 barn owl pairs nesting in Israel. The reproductive success of barn owls declined from March to August, and fledged more young when they consumed a larger proportion of social voles (Microtus socialis guentheri). Although the diet of the lighter colored barn owls in Israel comprises more Muridae than that of the darker morphs in temperate regions, in both regions the number of barn owl young increases with an increased proportion of voles in the diet.

Predation of Bradysia sp (Diptera: Sciaridae), Liriomyza trifolii (Diptera: Agromyzidae) and Bemisia tabaci (Hemiptera: Aleyrodidae) by Coenosia attenuata (Diptera: Muscidae) in greenhouse crops

We studied the predation behaviour of the "hunter fly" (Coenosia attenuata Stein) in the laboratory and greenhouse. In the laboratory, which was conducted at 25 degrees C at 60-80% RH, with a 16L : 8D photoperiod, we examined the functional response of this species to three different pests, namely the sciarid fly (Bradysia sp.), the tobacco whitefly (Bemisia tabaci) and the leaf miner Liriomyza trifolii. In the greenhouse, we studied the population dynamics of the predator and its prey on pepper and water melon crops grown in southern Spain. Adult hunter flies were found to exhibit a type I functional response to adult sciarid flies and whiteflies, but a type II response to adult leaf miners. The type II response was a result of the greater difficulty in capturing and handling leaf miners compared to the other two species. The dynamics of the predator-prey interaction in the greenhouse revealed that the predator specializes mainly on adult sciarids and that the presence of the other prey can be supplemental, but is never essential for survival of the predator; this, however, is crop-dependent. The results oil the dynamics of the predator-prey systems were obtained through a known population dynamics model with modifications.

Ant semiochemicals limit apterous aphid dispersal

Some organisms can manipulate the nervous systems of others or alter their physiology in order to obtain benefit. Ants are known to limit alate aphid dispersal by physically removing wings and also through chemical manipulation of the alate developmental pathway. This results in reduced dispersal and higher local densities of aphids, which benefit ants in terms of increased honeydew and prey availability. Here, we show that the walking movement of mutualistic apterous aphids is also reduced by ant semiochemicals. Aphids walk slower and their dispersal from an unsuitable patch is hampered by ants. If aphid walking dispersal has evolved as a means of natural enemy escape, then ant chemicals may act as a signal indicating protection; hence, reduced dispersal could be adaptive for aphids. If, however, dispersal is primarily a means to reduce competition or to maintain persistent metapopulations, then manipulation by ants could be detrimental. Such manipulation strategies, common in host-parasite and predator-prey interactions, may be more common in mutualism than expected.

The costs and consequences of parasitoid attack for the predatory hoverfly, Episyrphus balteatus

Question: What are the life-history costs for a predatory insect of surviving parasitoid attack, and can parasitoid attack alter predator-prey interactions? Hypotheses: Survivorship is influenced by host age. Hosts that suffer parasitoid attack grow more slowly and consume fewer prey. Those that survive attack are smaller as adults and show reduced survivorship. Organisms: The aphidophagous hoverfly Episyrphus balteatus, its endoparasitoid wasp Diplazon laetatorius and its prey, the pea aphid, Acyrthosiphon pisum. Site of experiments: All experiments were conducted in controlled temperature rooms and chambers in the laboratory. Methods: Episyrphus balteatus larvae of each instar were exposed to attack by Diplazon laetatorius, then dissected to measure the encapsulation response (a measure of immunity). Second instar larvae were either attacked or not attacked by D. laetatorius. Their development rates and numbers of prey consumed were noted. The size and survivorship of surviving (immune) and control hoverflies were compared following eclosion. Conclusions: Successful immune response increased with larval age (first instar 0%, second instar 40%, third instar 100% survival). Second instar larvae that successfully resisted parasitoid attack were larger as pupae (but not as adults) and showed reduced adult survivorship. Female adult survivors were more likely than male survivors to have died within 16 days of eclosion, but there was no difference between unattacked male and female control hoverflies. Attacked larvae, irrespective of immune status, consumed fewer aphids than unattacked individuals. Episyrphus balteatus suffers significant costs of resisting parasitoid attack, and parasitoid attack can reduce the top-down effects of an insect predator, irrespective of whether the host mounts an immune response or not.

How predation and landscape fragmentation affect vole population dynamics

Background: Microtine species in Fennoscandia display a distinct north-south gradient from regular cycles to stable populations. The gradient has often been attributed to changes in the interactions between microtines and their predators. Although the spatial structure of the environment is known to influence predator-prey dynamics of a wide range of species, it has scarcely been considered in relation to the Fennoscandian gradient. Furthermore, the length of microtine breeding season also displays a north-south gradient. However, little consideration has been given to its role in shaping or generating population cycles. Because these factors covary along the gradient it is difficult to distinguish their effects experimentally in the field. The distinction is here attempted using realistic agent-based modelling. Methodology/Principal Findings: By using a spatially explicit computer simulation model based on behavioural and ecological data from the field vole (Microtus agrestis), we generated a number of repeated time series of vole densities whose mean population size and amplitude were measured. Subsequently, these time series were subjected to statistical autoregressive modelling, to investigate the effects on vole population dynamics of making predators more specialised, of altering the breeding season, and increasing the level of habitat fragmentation. We found that fragmentation as well as the presence of specialist predators are necessary for the occurrence of population cycles. Habitat fragmentation and predator assembly jointly determined cycle length and amplitude. Length of vole breeding season had little impact on the oscillations. Significance: There is good agreement between our results and the experimental work from Fennoscandia, but our results allow distinction of causation that is hard to unravel in field experiments. We hope our results will help understand the reasons for cycle gradients observed in other areas. Our results clearly demonstrate the importance of landscape fragmentation for population cycling and we recommend that the degree of fragmentation be more fully considered in future analyses of vole dynamics.

The stability of ecosystems: a brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system, thereby collapsing the trophic interaction, a phenomenon referred to as "the paradox of enrichment". After it was first proposed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator-prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form, inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that, although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms, which may differ among systems, need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models.

Size matters: body size determines functional responses of ground beetle interactions

Understanding patterns in predator:prey systems and the mechanisms that underlie trophic interactions provides a basis for predicting community structure and the delivery of natural pest control services. The functional response of predators to prey density is a fundamental measure of interaction strength and its characterisation is essential to understanding these processes. We used mesocosm experiments to quantify the functional responses of five ground beetle species that represent common generalist predators of north-west European arable agriculture. We investigated two mechanisms predicted to be key drivers of trophic interactions in natural communities: predator:prey body size ratio and multiple predator effects. Our results show regularities in foraging patterns characteristic of similarly sized predators. Ground beetle attack rates increased and handling times decreased as the predator:prey body-mass ratio rose. Multiple predator effects on total prey consumption rates were sensitive to the identity of the interacting species but not prey density. The extent of interspecific interactions may be a result of differences in body mass between competing beetle species. Overall these results add to the growing evidence for the importance of size in determining trophic interactions and suggest that body mass could offer a focus on which to base the management of natural enemy assemblages.

Potencial de alimentação de Chrysoperla externa (Hagen, 1861) (Neuroptera, Chrysopidae) em diferentes densidades de Uroleucon ambrosiae (Thomas, 1878) (Hemiptera, Aphididae)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Relação predador: presa de Chrysoperla externa (Hagen) (Neuroptera: Chrysopidae) para o controle do pulgão-verde em genótipos de sorgo

O uso da resistência de plantas associado a agentes de controle biológico pode ser uma alternativa viável no controle de Schizaphis graminum (Rondani) em sorgo. Objetivou-se estudar diferentes relações predador:presa em genótipos de sorgo resistente (TX 430 x GR 111), moderadamente resistente (GB 3B) e suscetível (BR 007B) para o controle do pulgão-verde por Chrysoperla externa (Hagen). Para isso foram realizadas, em condições de casa-de-vegetação, liberações do crisopídeo nas relações predador:presa de 1:5; 1:10; 1:25 e 1:50. O genótipo TX 430 x GR 111 foi o mais eficiente no controle do pulgão-verde, S. graminum, assim como as relações predador:presa de 1:5 e de 1:10 nos três genótipos. A interação resistência de plantas e controle biológico foi positiva e permitiu controle acima de 80% nas relações predador:presa de 1:5 e 1:10 no material resistente TX 430 x GR 111; no genótipo GB 3B o melhor controle foi obtido com 1 predador: 5 presas.

The effect of hunger level on predation dynamics in the spider Nesticodes rufipes: a functional response study

It is well known that a predator has the potential to regulate a prey population only if the predator responds to increases in prey density and inflicts greater mortality rates. Predators may cause such density-dependent mortality depending on the nature of the functional and numerical responses. As spiders are usually faced with a shortage of prey, the killing behavior of the spider Nesticodes rufipes at varying densities of Musca domestica was examined here through laboratory functional response experiments where spiders were deprived of food for 5 (well-fed) or 20 days (hungry). An additional laboratory experiment was also carried out to assess handling time of spiders. The number of prey killed by spiders over 24- and 168-h periods of predator-prey interaction was recorded. Logistic regression analyses revealed the type II functional response for both well-fed and hungry spiders. We found that the lower predation of hungry spiders during the first hours of experimentation was offset later by an increase in predation ( explained by estimated handling times), resulting in similarity of functional response curves for well-fed and hungry spiders. It was also observed that the higher number of prey killed by well-fed spiders over a 24- h period of spider-prey interaction probably occurred due to their greater weights than hungry spiders. We concluded that hungry spiders may be more voracious than well-fed spiders only over longer time periods, since hungry spiders may spend more time handling their first prey items than well-fed spiders.

The role of habitat heterogeneity for the functional response of the spider Nesticodes rufipes (Araneae : Theridiidae) to houseflies

We investigated whether or not different degrees of refuge for prey influence the characteristic of functional response exhibited by the spider Nesticodes rufipes on Musca domestica, comparing the inherent ability of N. rufipes to kill individual houseflies in such environments at two distinct time intervals. To investigate these questions, two artificial habitats were elaborated in the laboratory. For 168 h of predator-prey interaction, logistic regression analyses revealed a type 11 functional response, and a significant decrease in prey capture in the highest prey density was observed when habitat complexity was increased. Data from habitat 1 (less complex) presented a greater coefficient of determination than those from habitat 2 (more complex), indicating a higher variation of predation of the latter. For a 24 h period of predator-prey interaction, spiders killed significantly fewer prey in habitat 2 than in habitat 1. Although prey capture did not enable data to fit properly in the random predator equation in this case, predation data from habitat 2 presented a higher variation than data from habitat 1, corroborating results from 168 h of interaction. The high variability observed on data from habitat 2 (more complex habitat) is an interesting result because it reinforces the importance of refuge in promoting spatial heterogeneity, which can affect the extent of predator-prey interactions.

Chemical cues related to conspecific size in pintado catfish, Pseudoplatystoma coruscans

The pintado (Pseudoplatystoma coruscans) is a ferocious carnivorous catfish with evident cannibalistic behaviour; its nocturnal habits are related to its ability to use predominately chemical sensorial modalities. This study investigated whether the pintado distinguishes conspecifics of different body sizes using chemical cues, which may reflect different physiological conditions such as hunger or stress. Pintados were observed when receiving water conditioned by either larger or similar-size conspecifics. A control group consisted of pintados receiving unconditioned water. Twelve repetitions were used for each condition. Feeding-like behaviours were investigated in the receiver fish and showed that they responded only to the conditioned water. Furthermore, a higher frequency of responses occurred when the water was conditioned by a similar-size conspecific. Thus, it is concluded that pintados are able to recognize conspecific size by chemical cues related to size and that this ability contributes to the individual's decision making on whether to approach or to avoid the conspecific.

Effects of Food Deprivation on the Development of Coleomegilla maculata (De Geer) (Coleoptera: Coccinellidae)

The lady beetle Coleomegilla maculata (De Geer) is a natural enemy of several insect pests and feeds on pollen and nectar to survive periods when prey is scarce. The effect of the feeding interval on the development, survival, fecundity, and longevity of C. maculata was determined. Newly hatched larvae of C. maculata were reared individually and fed with eggs of the Mediterranean flour moth Anagasta kuehniella (Zeller) at intervals of one, two, and three days under controlled conditions (23 ± 1ºC; 60 ± 10% RH; 12 h phtophase). The duration of larval instars and the total larval stage was prolonged as the feeding interval increased. The larval period lasted on average 9.2 ± 0.19 days when the larvae were fed daily with prey, and 14.6 ± 0.48 days when food was offered at three-day intervals. There was an inverse relationship between food intervals, survival, and weight of larvae and adults of the coccinellid. Survival rate of larvae fed daily was 76.8%, while the rate was 50.0% and 23.4% for larvae fed every two and three days, respectively. Coleomegilla maculata showed fecundity of 781.1 ± 149.02, 563.4 ± 80.81 and 109.0 ± 103.0 eggs when fed daily and at intervals of two and three days, respectively.