Prey Growth Research Articles

Maturation delay for the predators can enhance stable coexistence for a class of prey–predator models

Maturation time delay for the predators is introduced in prey–predator models to implicitly model the stage-structure of predators. Most of the prey–predator models with maturation delay are known to exhibit destabilization of coexistence steady-state. Discrete time delay induced destabilization is a common finding, however, this is due to the introduction of time delay with lack of ecological justification. The main objective of the present work is to show the stabilizing role of maturation delay for a class of delayed prey–predator model. To be specific, we consider prey–predator models with strong and weak Allee effects in prey growth and Michaelis–Menten type functional response. We provide ecological justification for the introduction of maturation delay parameter in predator's growth equation. We obtain the conditions for stable and oscillatory coexistence of prey and their specialist predator in case of strong as well as weak Allee effect for non-delayed and delayed models. Apart from the analytical results for the models under consideration, we perform extensive numerical simulations to construct the relevant bifurcation diagrams. Our analytical and supportive numerical findings reveal that delay is not always a destabilizing factor rather the stable coexistence in the presence of time delay depends upon the formulation of the delayed model. The biological implications of the current investigation are provided in the conclusion section. We also explain the validity of obtained results for other types of prey–predator models with a specialist predator.

Complex dynamics generated by negative and positive feedback delays of a prey–predator system with prey refuge: Hopf bifurcation to Chaos

Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey–predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than its non-delayed counterpart. In this paper, we study a multi-delayed prey–predator model with prey refuge. We consider modified Holling Type II response function that incorporates the effect of prey refuge and then introduce two discrete delays in the model system. A negative feedback delay is considered in the logistic prey growth rate to represent density dependent feedback mechanism and a positive feedback delay is considered to represent the gestation time of the predator. Our study reveals that the system exhibits different dynamical behaviors, viz., stable coexistence, periodic coexistence or chaos depending on the values of the delay parameters and degree of prey refuge. The interplay between two delays for a fixed value of prey refuge has also been determined. It is noticed that these delays work in a complementary fashion. In addition, using the normal form theory and center manifold argument, we derive the explicit formulae for determining the direction of the bifurcation, the stability and other properties of the bifurcating periodic solutions.

Seasonal Patterns of Intraguild Predation and Size Variation among Larval Salamanders in Ephemeral Ponds

Abstract Predation among potential competitors, or intraguild predation (IGP), is dependent on size disparities between competing predators and prey and strongly influences the ecology of larval amphibians in ephemeral ponds. Although intraguild prey are hypothesized to exhibit faster growth rates than intraguild predators and, therefore, outgrow predation risk through time, intraguild predation also is associated with significant increases in predator growth rates that are hypothesized to increase the potential for future predation. Given these conflicting hypotheses, how predation among amphibian larvae early in development should influence size disparities and ontogenetic shifts in predation risk is unclear. To clarify the effects of intraguild predation on predator and prey growth, we quantified size variation among larval salamanders (Ambystomatidae) in forested ephemeral ponds while concurrently monitoring seasonal patterns of intraguild predation through gut content analyses. Intraguild predation h...

Spatial degeneracy vs functional response

In this paper, we are concerned with a predator-prey model with Beddington-DeAngelis functional response in heterogeneous environment. By the bifurcation theory and some estimates, the global bifurcation of positive stationary solution is shown. Our result shows that new stationary patterns are produced by the spatial degeneracy and the Beddington-DeAngelis functional response. Essentially different from the known results, the two factors generate two critical values for the prey growth rate $\lambda.$ As $\lambda$ crosses each critical value, the positive stationary solution set undergoes a drastic change. In particular, when $\lambda$ is suitably large, the interaction between the two factors yields nonexistence of positive stationary solutions for any $\mu,$ which is in strong contrast to the existence for suitable ranges of $\mu$ corresponding to the Lotka-Volterra or Holling-II functional response. Moreover, which one of the two factors plays a dominating role in the stationary patterns is shown. In addition, we give the asymptotic behavior of the positive stationary solutions as $\mu\rightarrow\infty$. Finally, both uniqueness and multiplicity of the positive stationary solutions are shown as well as their stability.

Allometric growth and development of organs in ballan wrasse (Labrus bergylta Ascanius, 1767) larvae in relation to different live prey diets and growth rates.

ABSTRACTSmall fish larvae grow allometrically, but little is known about how this growth pattern may be affected by different growth rates and early diet quality. The present study investigates how different growth rates, caused by start-feeding with copepods or rotifers the first 30 days post-hatch (dph), affect allometric growth and development of nine major organs in ballan wrasse (Labrus bergylta) larvae up to experimental end at 60 dph. Feeding with cultivated copepod nauplii led to both increased larval somatic growth and faster development and growth of organ systems than feeding with rotifers. Of the organs studied, the digestive and respiratory organs increased the most in size between 4 and 8 dph, having a daily specific growth rate (SGR) between 30 and 40% in larvae fed copepods compared with 20% or less for rotifer-fed larvae. Muscle growth was prioritised from flexion stage and onwards, with a daily SGR close to 30% between 21 and 33 dph regardless of treatment. All larvae demonstrated a positive linear correlation between larval standard length (SL) and increase in total tissue volume, and no difference in allometric growth pattern was found between the larval treatments. A change from positive allometric to isometric growth was observed at a SL close to 6.0 mm, a sign associated with the start of metamorphosis. This was also where the larvae reached postflexion stage, and was accompanied by a change in growth pattern for most of the major organ systems. The first sign of a developing hepatopancreas was, however, first observed in the largest larva (17.4 mm SL, 55 dph), indicating that the metamorphosis in ballan wrasse is a gradual process lasting from 6.0 to at least 15-17 mm SL.

Comparing nearshore benthic and pelagic prey as mercury sources to lake fish: the importance of prey quality and mercury content

Mercury (Hg) bioaccumulation in fish poses well-known health risks to wildlife and humans through fish consumption. Yet fish Hg concentrations are highly variable, and key factors driving this variability remain unclear. One little studied source of variation is the influence of habitat-specific feeding on Hg accumulation in lake fish. However, this is likely important because most lake fish feed in multiple habitats during their lives, and the Hg and caloric content of prey from different habitats can differ. This study used a three-pronged approach to investigate the extent to which habitat-specific prey determine differences in Hg bioaccumulation in fish. This study first compared Hg concentrations in common nearshore benthic invertebrates and pelagic zooplankton across five lakes and over the summer season in one lake, and found that pelagic zooplankton generally had higher Hg concentrations than most benthic taxa across lakes, and over a season in one lake. Second, using a bioenergetics model, the effects of prey caloric content from habitat-specific diets on fish growth and Hg accumulation were calculated. This model predicted that the consumption of benthic prey results in lower fish Hg concentrations due to higher prey caloric content and growth dilution (high weight gain relative to Hg from food), in addition to lower prey Hg levels. Third, using data from the literature, links between fish Hg content and the degree of benthivory, were examined, and showed that benthivory was associated with reduced Hg concentrations in lake fish. Taken together, these findings support the hypothesis that higher Hg content and lower caloric content make pelagic zooplankton prey greater sources of Hg for fish than nearshore benthic prey in lakes. Hence, habitat-specific foraging is likely to be a strong driver of variation in Hg levels within and between fish species.

Spatiotemporal Patterns of a Predator–Prey System with an Allee Effect and Holling Type III Functional Response

A diffusive Gause type predator–prey system with Allee effect in prey growth and Holling type III response subject to Neumann boundary conditions is investigated. Existence of nonconstant positive steady state solutions is proved by Leray–Schauder degree theory and bifurcation theory. Global stability of the positive equilibrium of the system is also investigated. Moreover, bifurcations of spatially homogeneous and nonhomogeneous periodic solutions are analyzed. Our rigorous results justify some recent ecological observations.

Effects of water-soluble fraction of petroleum on growth and prey consumption of juvenile Hoplias aff. malabaricus (Osteichthyes: Erythrinidae).

The influence of the water-soluble fraction of petroleum (WSF) on prey consumption and growth of juvenile trahira Hoplias aff. malabaricus was investigated. Juveniles were submitted to either WSF or Control treatment over 28 days, and jewel tetra Hyphessobrycon eques adults were offered daily as prey for each predator. Total prey consumption ranged from 16 to 86 individuals. Despite the initially lower prey consumption under WSF exposure, there were no significant differences in overall feeding rates between the two treatments. Water-soluble fraction of petroleum had a negative effect on the growth in length of H. aff. malabaricus juveniles. Although unaffected, prey consumption suggested a relative resistance in H. aff. malabaricus to WSF exposition and the lower growth of individuals exposed to WSF than the Control possibly reflects metabolic costs. The implications of the main findings for the individual and the food chain are discussed, including behavioral aspects and the role played by this predator in shallow aquatic systems.

On certain exact solutions of diffusive predator-prey system of fractional order

Partial differential equations are used to model the variety of ecological phenomena and also extensively applied to elucidate the effects of spatial variation on populations. This paper investigates the issue of exact solutions for some important population growth dynamic models of fractional order. More precisely, a system of equations for description of the predator-prey relations and reaction-diffusion invasion model is considered. In particular, the predator-prey model corresponds to the modified Lotka-Volterra system with logistic growth of predator and prey. Exact traveling wave solutions of the considered models are found by means of the Q-function method. Moreover, graphical illustrations of some of the obtained solutions in two and three dimensional are also provided to predict their behavior dependence on the parameter values. The results reveal that the Q-function method is very simple, reliable and effective for finding exact solutions of complex nonlinear evolution equations.

Dynamics of predator–prey models with a strong Allee effect on the prey and predator-dependent trophic functions

The complex dynamics of a two-trophic chain are investigated. The chain is described by a general predator–prey system, in which the prey growth rate and the trophic interaction functions are defined only by some properties determining their shapes. To account for undercrowding phenomena, the prey growth function is assumed to model a strong Allee effect; to simulate the predator interference during the predation process, the trophic function is assumed predator-dependent. A stability analysis of the system is performed, using the predation efficiency and a measure of the predator interference as bifurcation parameters. The admissible scenarios are much richer than in the case of prey-dependent trophic functions, investigated in Buffoni et al. (2011). General conditions for the number of equilibria, for the existence and stability of extinction and coexistence equilibrium states are determined, and the bifurcations exhibited by the system are investigated. Numerical results illustrate the qualitative behaviours of the system, in particular the presence of limit cycles, of global bifurcations and of bistability situations.

ANALISIS KESTABILAN MODEL DUA PEMANGSA DAN SATU MANGSA DENGAN PENERAPAN RACUN

This research discussed prey and predator model showing the interaction between one prey and two predators by using poison. The interaction between prey and predator used response function of Holling type II. The growth of prey and predator used logistic function. From the model, it was found five equilibrium points. The local stability of each equilibrium point was analyzed. To make it easier in interpreting the dynamic between prey and two predators and the effect of giving poison, the numeric simulation was done by showing the change of parameter of the level of death due to poison and the efficiency of changing the prey consumption towards the birth of the first and second predators

Stabilizing Role of Nonlocal Interaction on Spatio-temporal Pattern Formation

Here we study a spatio-temporal prey-predator model with ratio-dependent functional response and nonlocal interaction term in the prey growth. For a clear understanding of the effect of nonlocal in ...

Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate

A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.

Impulsive Control on Seasonally Perturbed General Holling Type Two-Prey One-Predator Model

We investigate the dynamical behaviors of two-prey one-predator model with general Holling type functional responses. The effect of seasonal perturbation on the model has been discussed analytically as well as numerically. The periodic fluctuation is considered in prey growth rate and the predator mortality rate of the model. The impulsive effects involving biological and chemical control strategy, periodic releasing of natural enemies, and spraying pesticide at different fixed times are introduced in the model with seasonal perturbation. We derive the conditions of stability for impulsive system using Floquet theory, small amplitude perturbation skills. A local asymptotically stable prey (pest) eradicated periodic solution is obtained when the impulsive period is less than some critical value. Numerical simulations of the model with and without seasonal disturbances exhibit different dynamics. Also we simulate numerically the model involving seasonal perturbations without impulse and with impulse. Finally, concluding remarks are given.

An evidence-based framework for predicting the impact of differing autotroph-heterotroph thermal sensitivities on consumer-prey dynamics.

Increased temperature accelerates vital rates, influencing microbial population and wider ecosystem dynamics, for example, the predicted increases in cyanobacterial blooms associated with global warming. However, heterotrophic and mixotrophic protists, which are dominant grazers of microalgae, may be more thermally sensitive than autotrophs, and thus prey could be suppressed as temperature rises. Theoretical and meta-analyses have begun to address this issue, but an appropriate framework linking experimental data with theory is lacking. Using ecophysiological data to develop a novel model structure, we provide the first validation of this thermal sensitivity hypothesis: increased temperature improves the consumer's ability to control the autotrophic prey. Specifically, the model accounts for temperature effects on auto- and mixotrophs and ingestion, growth and mortality rates, using an ecologically and economically important system (cyanobacteria grazed by a mixotrophic flagellate). Once established, we show the model to be a good predictor of temperature impacts on consumer–prey dynamics by comparing simulations with microcosm observations. Then, through simulations, we indicate our conclusions remain valid, even with large changes in bottom-up factors (prey growth and carrying capacity). In conclusion, we show that rising temperature could, counterintuitively, reduce the propensity for microalgal blooms to occur and, critically, provide a novel model framework for needed, continued assessment.

Warming reinforces nonconsumptive predator effects on prey growth, physiology, and body stoichiometry.

While nonconsumptive effects of predators may strongly affect prey populations, little is known how future warming will modulate these effects. Such information would be especially relevant with regard to prey physiology and resulting changes in prey stoichiometry. We investigated in Enallagma cyathigerum damselfly larvae the effects of a 4°C warming (20°C vs. 24°C) and predation risk on growth rate, physiology and body stoichiometry, for the first time including all key mechanisms suggested by the general stress paradigm (GSP) on how stressors shape changes in body stoichiometry. Growth rate and energy storage were higher at 24°C. Based on thermodynamic principles and the growth rate hypothesis, we could demonstrate predictable reductions in body C:P under warming and link these to the increase in P-rich RNA; the associated warming-induced decrease in C:N may be explained by the increased synthesis of N-rich proteins. Yet, under predation risk, growth rate instead decreased with warming and the warming-induced decreases in C:N and C:P disappeared. As predicted by the GSP, larvae increased body C:N and C:P at 24°C under predation risk. Notably, we did not detect the assumed GSP-mechanisms driving these changes: despite an increased metabolic rate there was neither an increase of C-rich biomolecules (instead fat and sugar contents decreased under predation risk), nor a decrease of N-rich proteins. We hypothesize that the higher C:N and N:P under predation risk are caused by a higher investment in morphological defense. This may also explain the stronger predator-induced increase in C:N under warming. The expected higher C:P under predation risk was only present under warming and matched the observed growth reduction and associated reduction in P-rich RNA. Our integrated mechanistic approach unraveled novel pathways of how warming and predation risk shape body stoichiometry. Key findings that (1) warming effects on elemental stoichiometry were predictable and only present in the absence of predation risk and that (2) warming reinforced the predator-induced effects on C:N:P, are pivotal in understanding how nonconsumptive predator effects under global warming will shape prey populations.

A simple adjustment to test reliability of bacterivory rates derived from the dilution method

AbstractQuantification of grazing losses of marine heterotrophic bacteria is critical for understanding nutrient and carbon pathways in aquatic systems. The dilution method is a commonly used experimental approach for quantifying bacterivory. However, valid estimates of grazing rates obtained using this method depend on several methodological assumptions including that the method does not influence specific growth rates of bacteria. Here, we hypothesize that filtration during the set‐up of a dilution experiment has the potential to release allelochemicals from phytoplankton cells and thereby stimulate or inhibit bacterial growth with the consequence of biased grazing estimates. We tested this hypothesis during a natural Phaeocystis pouchetii bloom at two different locations within an Arctic fjord. Results from the dilution experiments suggest higher gross growth rate and grazing impact for bacteria in the outer fjord compared with the inner fjord. However, specific growth rates estimated by bacterial production cell−1 were significantly elevated in dilutions of water from the outer fjord but not the inner fjord. The analysis of dissolved metabolites in the seawater from both experiments prior and after filtration revealed altered metabolic profiles after filtration at both stations. As unaffected specific growth of prey on dilution is one of three fundamental assumptions of the dilution method, we conclude that it is important that empirically estimated bacterial specific growth rates be routinely included when using the dilution method to quantify bacterivory.

Revisiting the Stability of Spatially Heterogeneous Predator-Prey Systems Under Eutrophication.

We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than on the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator-prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to 'infinity'. We investigate two main scenarios: (1) the spatial gradient of the growth rate is due to abiotic factors only, and (2) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator-prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an 'unlimited' carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism. These results highlight the generality of the stabilization mechanisms we find in spatially structured predator-prey ecological systems in a heterogeneous environment.

Can the halophilic ciliate Fabrea salina be used as a bio-control of microalgae blooms in solar salterns?

The microlage Dunaliella salina, a major producer in salterns, is a serious problem for salt production. In this study we tried to assess if Fabrea salina can control D. salina. By parameterising numerical and functional response (growth and grazing vs prey abundance, respectively) at 90 psu and 30°C, where the ciliate is abundant and grows well, we developed a predator-prey model. The model is used to explore how change in microalga growth rate affect the dynamics, and the functional response is used in combination with field data to assess the potential impact of F. salina on D. salina. Over the 20 d simulation the ciliate controlled the prey population under all prey growth rates; although once D. salina were exhausted below the threshold level, F. salina died due to starvation, allowing the alga to increase in abundance, resulting in one or two predatorprey cycle, depending on prey growth rate. In general, the model predicted trends observed by others in the field, suggesting that it provided a good prediction of what may occur under the conditions we examined. Likewise we show that the ciliate can have a high impact on microalgal populations in the field. Finally, a literature review indicated that F. salina could be a good competitor with other protozoa and metazoan in salterns, depending on salinity and temperature, which requires further study and attention. In summary, we encourage continued studies on this unique ciliate on solar salterns and suggest that it may be useful in the bio-control of micoalgae.

Role of dissolved nitrate and phosphate in isolates of Mesodinium rubrum and toxin-producing Dinophysis acuminata.

Dinophysis acuminata, a producer of toxins associated with diarrhetic shellfish poisoning (DSP) and/or pectenotoxins (PTXs), is a mixotrophic species that requires both ciliate prey and light for growth. Linkages have been described in the literature between natural abundances of the predator Dinophysis and its prey, Mesodinium rubrum, and culture experiments have demonstrated that prey, in addition to light, is required for toxin production by Dinophysis acuminata; together these suggest Mesodinium is a critical component for Dinophysis growth and toxicity. However, little is known about the role of dissolved inorganic nutrients on Mesodinium growth or that of toxin-producing Dinophysis. Accordingly, a series of experiments were conducted to investigate the possible uptake of dissolved nitrate and phosphate by 1) Dinophysis starved of prey, 2) Dinophysis feeding on Mesodinium rubrum, and 3) M. rubrum grown in nutritionally-modified media. All single-clone or mixed cultures were monitored for dissolved and particulate nutrient levels over the growth cycle, as well as growth rate, biomass, and toxin production when appropriate. D. acuminata did not utilize dissolved nitrate or phosphate in the medium under any nutrient regime tested, i.e., nutrient-enriched and nutrient-reduced, in the absence or presence of prey, or during any growth phase monitored, i.e., exponential and plateau phases. Changes in particulate phosphorus and nitrogen in D. acuminata, were instead, strongly influenced by the consumption of M. rubrum prey, and these levels quickly stabilized once prey were no longer available. M. rubrum, on the other hand, rapidly assimilated dissolved nitrate and phosphate into its particulate nutrient fraction, with maximum uptake rates of 1.38 pmol N/cell/day and 1.63 pmol P/cell/day. While D. acuminata did not benefit directly from the dissolved nitrate and phosphate, its growth (0.37±0.01 day-1) and toxin production rates for okadaic acid (OA), dinophysistoxin-1 (DTX1) or pectenotoxin-2 (PTX2), 0.1, 0.9 and 2.6 pg /cell/day, respectively, were directly coupled to prey availability. These results suggest that while dissolved nitrate and phosphate do not have a direct effect on toxin production or retention by D. acuminata, these nutrient pools contribute to prey growth and biomass, thereby indirectly influencing D. acuminata blooms and overall toxin in the system.