The effect of long time delays in predator-prey systems

Past studies have indicated that a time delay longer than the natural period of a system will generally cause instability; however here it is shown that including long maturational time delays in a general predator-prey model need not have this effect. In each of the three cases studied (a predator delay, a prey delay, and both), local stability can persevere despite the presence of arbitrarily long time delays. This perseverence depends upon an interaction between delayed and undelayed features of the model. Delayed processes always act to destabilize the model. For example, prey self-regulation, usually a source of stability, becomes destabilizing if subject to a long delay. However, the effect of such a delay is offset by undelayed regulatory processes, such as a stabilizing functional reponse. In addition, the adverse effects of delayed predator recruitment can be reduced by the nonreproductive component of the numerical reponse, a feature not usually involved in determining stability. Finally, it is shown that long time delays are not necessarily more disruptive than short delays; it cannot be assumed that lengthening a time delay progessively reduces stability.     

Absolute stability in predator-prey models

An equilibrium of a time-lagged population model is said to be absolutely stable if it remains locally stable regardless of the length of the time delay, and it is argued that the criteria for absolute stability provide a valuable guide to the behavior of population models. For example, it is sometimes assumed that time delays have a limited impact until they exceed the natural time scale of a system; here it is stressed that under some conditions very short time delays can have a marked (and often maximal) destabilizing effect. Consequently it is important that our understanding of population dynamics is robust to the inclusion of the short time delays present in all biological systems. The absolute stability criteria are ideally suited for this role. Another important reason for using the criteria for absolute stability rather than using criteria which depend upon the details of a time delay is that biological time delays are unlikely to be constant. For example, a time delay due to maturation inevitably varies between individuals and the mean may itself vary over time. Here it is shown that the criteria for absolute stability are generally robust in the presence of distributed delays and of varying delays. The analysis presented is based upon a general predator-prey model and it is shown that absolute stability can be expected under a broad range of parameter values whenever the time delay is due to the maturation time of either the predator or the prey or of both. This stability occurs because of the interaction between delayed and undelayed dynamic features of the model. A time-delayed process, when viewed across all possible delays, always reduces stability and this effect occurs regardless of whether the process would act to stabilize or destabilize an undelayed system. Opposing the destabilization due to a time delay and making absolute stability a possibility are a number of processes which act without delay. Some of these processes can be identified as stabilizing from the analysis of undelayed models (for example, the type 3 functional response) but other cannot (for example, the nonreproductive numerical response of predators).     

Dispersal delays, predator-prey stability, and the paradox of enrichment

It takes time for individuals to move from place to place. This travel time can be incorporated into metapopulation models via a delay in the interpatch migration term. Such a term has been shown to stabilize the positive equilibrium of the classical Lotka-Volterra predator-prey system with one species (either the predator or the prey) dispersing. We study a more realistic, Rosenzweig-MacArthur, model that includes a carrying capacity for the prey, and saturating functional response for the predator. We show that dispersal delays can stabilize the predator-prey equilibrium point despite the presence of a Type II functional response that is known to be destabilizing. We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment.     

Scales of dispersal and the biogeography of marine predator-prey interactions

Striking differences in the dispersal of coexisting species have fascinated marine ecologists for decades. Despite widespread attention to the impact of dispersal on individual species dynamics, its role in species interactions has received comparatively little attention. Here, we approach the issue by combining analyses of simple heuristic predator-prey models with different dispersal patterns and data from several predator-prey systems from the Pacific coasts of North and South America. In agreement with model predictions, differences in predator dispersal generated characteristic biogeographic patterns. Predators lacking pelagic larvae tracked geographic variation in prey recruitment but not prey abundance. Prey recruitment rate alone explained more than 80% of the biogeographic variation in predator abundance. In contrast, predators with broadcasting larvae were uncorrelated with prey recruitment or adult prey abundance. Our findings reconcile perplexing results from previous studies and suggest that simple models can capture some of the complexity of life-history diversity in marine communities.     

The Effect of Food Size and Dispersion Pattern on Retrieval Rate by the Argentine Ant, Linepithema humile (Hymenoptera: Formicidae)

Food acquisition in central-place foraging animals demands efficient detection and retrieval of resources. Most ant species rely on a mass recruitment foraging strategy, which requires that some potential foragers remain at the nest where they can be recruited to food once resources are found. Because this strategy reduces the number of workers initially looking for food, it may reduce the food detection rate while increasing the postdiscovery food retrieval rate. In previous studies this tradeoff has been analyzed by computer simulation and mathematical models. Both kinds of models show that food acquisition rate is greatly influenced by food distribution and resource patch size: as food is condensed into fewer patches, the maximal acquisition rate is achieved by a shift to fewer initial searchers and more potential recruits. In general, these models show that a mass recruitment strategy is most effective when resources are clumped. We tested this prediction in two experiments by letting laboratory colonies of the Argentine ant (Linepithema humile) forage for resources placed in different distributions. When all prey were small, retrieval rate increased with increasing resource patch size, in support of foraging models. When prey were large, however, the mass of prey returned to the colony over time was much lower than when prey were small and widely distributed. As more ants reached a large prey item, the distance the prey item was transported decreased due to a greater emphasis on feeding rather than transport. Because Argentine ants can transport more biomass externally than they can ingest, food retrieval that depends only on ingestion can depress the biomass retrieval rate. Thus, our results generally support theoretical foraging models, but we show how prey size, through differential prey-handling behavior, can produce an outcome greatly different from that predicted only on the distribution of resources.     

The food and feeding relationships of larval and 0+ year juvenile fishes in lowland rivers and connected waterbodies. II. Prey selection and the influence of gape

The relative importance of taxa- and size-specific prey selection, and the influence of gape on the prey consumed by the larvae and 0+ year juveniles of four fish species were investigated in 'main river', 'marina' and 'pond' macrohabitats in the lower River Trent, England. A general sequence of ontogenetic shifts in food consumption was reflected in the electivity indices of particular prey taxa, partly due to the restrictions imposed by the gape of 0+ year fishes. Certain taxa, however, were consistently selected over others, irrespective of size, suggesting that taxa-specific, as well as size-specific, prey characteristics may be important in the selection process. There were significant, positive relationships between maximum prey (zooplankton) length and maximum gape height for larvae, but not for 0+ year juveniles. The majority of fishes, however, consumed prey substantially smaller than the maximum theoretically possible inferred from their gape. The greater size ranges of zooplankton in connected waterbodies compared with main river channels provide suitable prey for a range of developmental steps and fish species, and may, thus, enhance recruitment success.     

Oceanographic coupling across three trophic levels shapes source–sink dynamics in marine metacommunities

A central goal of metapopulation ecology is to determine which subpopulations have the greatest value to the larger metapopulation. That is, where are the ‘sources’ that are most essential to persistence? This question is especially relevant to benthic marine systems, where dispersal and recruitment are greatly affected by oceanographic processes. In a single‐species context, theoretical models typically identify ‘hotspots’ with high recruitment, especially high self‐recruitment, as having the highest value. However, the oceanographic forces affecting larval delivery of a given species may also influence the recruitment of that species’ predators, prey, and competitors.We present evidence from the Virgin Islands and Bahamas that oceanographic forces produce spatial coupling between the recruitment of planktivorous fishes, the recruitment of their predators, and the productivity of their zooplankton prey. We examined the consequences of this type of multi‐trophic coupling using a simple analytical population model and a multispecies numerical simulation model with parameter values based on the Virgin Islands system. In both analyses, strong coupling caused planktivores at the highest recruitment sites to experience higher mortality (a consequence of higher predator densities) but faster growth and higher fecundity (a consequence of higher zooplankton densities) than planktivores at low recruitment sites. As such, the relative strength of oceanographic coupling between the three trophic levels strongly determined whether a particular reef acted as a source or sink. In the simulation model, density‐dependent competition for zooplankton limited overall metapopulation biomass more severely than predation, so oceanographic coupling between planktivore larval supply and zooplankton productivity had a stronger effect on the metapopulation value of a patch. We argue that the potential for such tri‐trophic coupling should be incorporated into future metacommunity models and has considerable implications for the design and evaluation of marine reserves.     

Spatially correlated recruitment of a marine predator and its prey shapes the large-scale pattern of density-dependent prey mortality

Patterns of predator dispersal can be critical to the dynamics of prey metapopulations. In marine systems, oceanic currents may shape the dispersal of planktonic larvae of both predators and prey, producing spatial correlations in the recruitment of both species and distinctive geographic patterns of prey mortality. I examined the potential for this phenomenon in two fishes, a wrasse and its grouper predator, at a Caribbean island where the near-shore oceanographic regime produces a temporally consistent spatial pattern of fish recruitment. I found that recruitment and adult abundance of groupers were spatially correlated with recruitment of wrasse prey. Furthermore, the local abundance of predators strongly affected the nature of density-dependent prey mortality. At sites with few predators, wrasse mortality was inversely density-dependent, while mortality was positively density-dependent at sites with higher predator densities. This phenomenon could be important to the dynamics of any metacommunity in which physical forces produce correlated dispersal.     

Avian interaural canal enhances interaural delay

Summary Using a simple model of the birds' binaural pressure difference acoustic receivers it was predicted that the interaural delay achieved by birds at low frequencies is far greater than that of mammals with a similar head-size. This was upheld when interaural delay was recorded, between the cochlear microphonics, for six species. Stimulus positions were varied over the azimuthal range from the frontal midline to the interaural axis. Predicted delays were frequency dependent (higher frequency, smaller delay), as were the actual delays, and the magnitude of the measured delays were comparable with predictions. Delays measured at high frequencies were close to those expected from pathlength around the head, but delays measured at low frequencies could be more than three times this expectation. This finding raises the possibility that interaural delay may be a useful localization cue in birds, even for those species with very small heads, since the large delays at low frequencies are sufficient to provide a physiological cue to azimuth.     

Altered predator/prey behavior in polluted environments: implications for fish conservation

Predator/prey behavior has important consequences for individual survival and recruitment into fish populations, both of which can be affected by stressors such as environmental contaminants. The degree to which prey capture or predator avoidance abilities of a predator or prey species are affected will determine the direction in which the balance will be shifted. In a contaminated estuary we have studied, prey capure and predator avoidance of resident mummichogs, Fundulus heteroclitus, are impaired, which may account for individuals in that estuary having reduced growth and longevity compared with those from uncontaminated sites. Exposure to sediments, water, and grass shrimp from the contaminated site can impair the predatory abilities of mummichogs from a clean site. An important prey species, the grass shrimp, Palaemonetes pugio, has a greater population density and a greater proportion of large individuals at the polluted site, apparently because of reduced predation pressure. Mummichog larvae at the polluted site are initially more active and better at prey capture and predator avoidance than larvae from clean sites, but later they become poorer at both. Differences in predator vulnerability among larvae appear to be due to population differences in behavior, which may be due in part to both genetic and environmentally-caused factors. Conservation of fish populations should consider fish behavior and its interaction with contaminants.     

Prey selection and the impact of the starfish Marthasterias glacialis (L.) and other predators on the mussel Choromytilus Meridionalis (Krauss)

The diet of the starfish, Marthasterias glacialis (L.), consists of a variety of mollusc species, as well as ascidians and barnacles. Starfish densities are maximal where mussels, Choromytilus meridionalis (Krauss), are abundant and in such areas mussels form the bulk of the diet. Laboratory feeding experiments indicate that Marthasterias glacialis select mussels of particular sizes and that the length of prey taken is an increasing function of predator arm length. The time taken to consume each mussel is determined by the ratio of shell length to starfish size. The number of mussels consumed per day increases only slightly with starfish size, but because the prey taken increase in size, energy consumption is maintained at a relatively consistent 1% of predator body energy per day. Using prey selection and feeding rate data for different sized starfish, predictive three dimensional predation surfaces are developed for a natural starfish population feeding on either one or two cohort Choromytilus meridionalis populations. The models indicate that predatory effort should be concentrated on the smallest mussels when a single adult cohort is present, but on recruiting mussels just above the minimum prey size limit where two cohorts are present. Other major predators of mussels, the rock lobster, Jasus lalandii (Milne Edwards), and the whelk, Natica tecta Anton, appear to select similar size-ranges of prey to starfish, despite their differing body forms and feeding methods. Since the juveniles of all three predators can only take small mussels, predator recruitment may well depend upon the successful settlement of strong mussel cohorts. Evidence for such entrainment of predator cohorts to settlements of mussels is presented.     

Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays

This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.     

Prey vulnerability to a gape-size limited predator: behavioural and morphological impacts on northern pike piscivory

The northern pike ( Esox lucius ) is a selective and important predator in lake ecosystems. Prey size in pike is limited by pike gape size, which is a linear function of pike body length. Here we show that the absolute gape-size limit in pike is greater than previously considered, and that maximum ingestible prey size is limited by prey body depth. Further, we experimentally show that pike prefer shallow-bodied roach before deeper-bodied common bream, and small prey sizes within each prey species. Handling time in pike increases with prey body depth, and since common bream are deeper-bodied than roach, handling time is longer for bream than for roach of the same length, but equal considering body depth. Prey handling time is suggested to be a major cost to the pike, since it increases the risk of losing the prey, as well as exposure to predation, kleptoparasitism and cannibalism. Consequently, prey vulnerability is determined by risk of predation and intraspecific interactions, and behavioural preferences in the pike, and not by pike gape-size limits. The consequences for natural populations is evaluated by analysing size structures of predator and prey fish populations in a eutrophic lake.     

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.     

Delayed reproduction in Arabidopsis thaliana improves fitness in soil with suboptimal phosphorus availability

Low phosphorus availability (low P) often delays flowering and maturity in annual plants, while abiotic stress generally accelerates flowering and maturity. The utility of this response is unknown. We hypothesize that phenological delay in low P is beneficial by permitting more time for phosphorus acquisition and utilization. We grew seven genotypes of Arabidopsis thaliana with contrasting phenology in high and low P. Low P delayed bolting and maturity in all genotypes. Low P decreased root length, but not root-length duration (the integral of root length over time), because phenological delay allowed low-P plants to compensate for shorter root length. Root-length duration was correlated with phosphorus accumulation. Leaf phosphorus duration (the integral of leaf phosphorus over time) was correlated with reproductive biomass, indicating the utility of increased phosphorus utilization. Phenological delays accounted for up to 30% of biomass production when low-P plants were compared to models of plants with no delays. These results support the hypothesis that phenological delay in low P is adaptive and leads to increased phosphorus acquisition and utilization. Because low P conditions are prevalent, understanding the utility of this response could be useful in crop breeding and in predicting plant responses to global climate change.     

食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响

建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移,且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度,可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明,在一定条件下,存在唯一的正平衡点,并且此平衡点全局稳定。进一步,捕食者的数量随着食饵庇护所数量增加而降低;在一定条件下,食饵的数量随着食饵庇护所数量增加先增加后降低,在足够强的庇护所强度下,两物种出现灭绝。对比以往研究,利用显式含有和隐含空间庇护所的数学模型所得结论不一致,这意味着在研究庇护所对捕食系统种群动态影响时,空间结构可能起着重要作用。     

Feeding behavior of yellowfin tuna around two insular regions of the western Atlantic Ocean

The yellowfin tuna is a very abundant tropical tuna species in the western equatorial Atlantic Ocean and an important fishery resource for the Brazilian tuna fleet. In this study we performed stable isotope analysis to better understand the spatial trophodynamics and dietary changes in yellowfin tuna around two insular marine protected areas in Brazil. A total of 65 yellowfin tuna specimens measuring between 47 and 138 cm LT (total length) were sampled around the archipelagos of Fernando de Noronha (FNA; n = 34) and Saint Peter and Saint Paul (SPSPA; n = 31) between July 2018 and September 2019. Bayesian mixing models and generalized additive models were used to investigate the contributions of four different prey items (zooplankton, cephalopods, fish larvae, and flying fish) to yellowfin tuna diet in each area and their potential changes in relation to predator growth. The four prey items were found to have different overall contributions between the two studied areas, with zooplankton being the most important prey in FNA, whereas flying fish was the most relevant prey to the species' diet in SPSPA. Significant changes in the species diet by size were also found, with fish smaller than 90 cm (TL) having a more generalist diet and larger animals relying more on consuming larger and more nutritious prey (i.e., flying fish). Our results suggest that these two marine protected areas play an important role in ocean dynamics, providing important and different foraging grounds for the development of this predator species.     

Predatory behavior of the praying mantis,Tenodera aridifolia II. Combined effect of prey size and predator size on the prey recognition

Predatory behavior of the praying mantis,Tenodera aridifolia, as a function of the combined effect of its size and the size of the prey was investigated by using prey models. Behavioral responses were almost identical through the nymphal development in the predator. As the mantis grew, it attacked larger prey models, suggesting that it recognizes the prey's size in accordance with its own body size. Regression analyses demonstrate that the ratio of the prey's volume to the cube and the square of the predator's length is a more important parameter for prey recognition than are the one-dimensional parameters of the prey's and the predator's sizes.     

Growth,Grazing, and Starvation Survival in Three Heterotrophic Dinoflagellate Species

To assess the effects of fluctuating prey availability on predator population dynamics and grazing impact on phytoplankton, we measured growth and grazing rates of three heterotrophic dinoflagellate species—Oxyrrhis marina, Gyrodinium dominans and Gyrodinium spirale—before and after depriving them of phytoplankton prey. All three dinoflagellate species survived long periods (> 10 d) without algal prey, coincident with decreases in predator abundance and cell size. After 1–3 wks, starvation led to a 17–57% decrease in predator cell volume and some cells became deformed and transparent. When re‐exposed to phytoplankton prey, heterotrophs ingested prey within minutes and increased cell volumes by 4–17%. At an equivalent prey concentration, continuously fed predators had ~2‐fold higher specific growth rates (0.18 to 0.55 d^?1) than after starvation (?0.16 to 0.25 d^?1). Maximum specific predator growth rates would be achievable only after a time lag of at least 3 d. A delay in predator growth poststarvation delays predator‐induced phytoplankton mortality when prey re‐emerges at the onset of a bloom event or in patchy prey distributions. These altered predator‐prey population dynamics have implications for the formation of phytoplankton blooms, trophic transfer rates, and potential export of carbon.     

Community regulation: the relative importance of recruitment and predation intensity of an intertidal community dominant in a seascape context

Predicting the strength and context-dependency of species interactions across multiple scales is a core area in ecology. This is especially challenging in the marine environment, where populations of most predators and prey are generally open, because of their pelagic larval phase, and recruitment of both is highly variable. In this study we use a comparative-experimental approach on small and large spatial scales to test the relationship between predation intensity and prey recruitment and their relative importance in shaping populations of a dominant rocky intertidal space occupier, mussels, in the context of seascape (availability of nearby subtidal reef habitat). Predation intensity on transplanted mussels was tested inside and outside cages and recruitment was measured with standard larval settlement collectors. We found that on intertidal rocky benches with contiguous subtidal reefs in New Zealand, mussel larval recruitment is usually low but predation on recruits by subtidal consumers (fish, crabs) is intense during high tide. On nearby intertidal rocky benches with adjacent sandy subtidal habitats, larval recruitment is usually greater but subtidal predators are typically rare and predation is weaker. Multiple regression analysis showed that predation intensity accounts for most of the variability in the abundance of adult mussels compared to recruitment. This seascape-dependent, predation-recruitment relationship could scale up to explain regional community variability. We argue that community ecology models should include seascape context-dependency and its effects on recruitment and species interactions for better predictions of coastal community dynamics and structure.