A trait-based approach for downscaling complexity in plankton ecosystem models

Although predator–prey cycles can be easily predicted with mathematical models it is only since recently that oscillations observed in a chemostat predator–prey (rotifer–algal) experiment offer an interesting workbench for testing model soundness. These new observations have highlighted the limitations of the conventional modelling approach in correctly reproducing some unexpected characteristics of the cycles. Simulations are improved when changes in algal community structure, resulting from natural selection operating on an assemblage of algal clones differing in competitive ability and defence against rotifer predation, is considered in multi-prey models. This approach, however, leads to extra complexity in terms of state variables and parameters. We show here that multi-prey models with one predator can be effectively approximated with a simpler (only a few differential equations) model derived in the context of adaptive dynamics and obtained with a moment-based approximation. The moment-based approximation has been already discussed in the literature but mostly in a theoretical context, therefore we focus on the strength of this approach in downscaling model complexity by relating it to the chemostat predator–prey experiment. Being based on mechanistic concepts, our modelling framework can be applied to any community of competing species for which a trade-off between competitive ability and resistance to predators can be appropriately defined. We suggest that this approach can be of great benefit for reducing complexity in biogeochemical modelling studies at the basin or global ocean scale.     

Predation affects the susceptibility of hard clam Meretrix lusoria to Hg-stressed birnavirus

Predator–prey interaction in aquatic ecosystem is one of the simplest drivers affecting the species population dynamics. Predation controls are recognized as important aspects of ecosystem husbandry and management. In this paper we investigated how predation control cause an increase in host growth in the abundance of hard clam (Meretrix lusoria) populations subject to mercury (Hg)-stressed birnavirus. Here we linked predator–prey relationships with a bioenergetic matrix population model (MPM) associated with a susceptible–infectious–mortality (SIM) model based on a host–pathogen–predator framework to quantify the predator effects on population dynamics of disease in hard clam populations. Our results indicated that relative high predation rates could promote the hard clam abundances in relation to predators that selectively captured the infected hard clam, by which the disease transmission was suppressed. The results also demonstrated that predator-induced modifications in host behavior could have potential negative or positive effects on host growth depending on relative species density and resource dynamics. The most immediate implication of this study for the management of aquatic ecosystem is that, beyond the potential for causing a growth in abundance, predation might provoke greater predictability in aquatic ecosystem species populations and thereby increase the safety of ecosystem production from stochastic environmental events.     

Food web structure affects the extinction risk of species in ecological communities

This paper studies the effect of food web structure on the extinction risk of species. We examine 793 different six-species food web structures with different number, position and strength of trophic links and expose them to stochasticity in a model with Lotka–Volterra predator–prey dynamics. The characteristics of species (intrinsic rates of increase as well as intraspecific density dependence) are held constant, but the interactions with other species and characteristics of the food web are varied.     

Pattern formation and individual-based models: The importance of understanding individual-based movement

This paper demonstrates that while pattern formation can stabilize individual-based models of predator–prey systems, the same individual-based models also allow for stabilization by alternate mechanisms, particularly localized consumption or diffusion limitation. The movement rules of the simulation are the critical feature which determines which of these mechanisms stabilizes any particular predator–prey individual-based model. In particular, systems from well-connected subpopulations, in each of which a predator can attack any prey, generally exhibit stabilization by pattern formation. In contrast, when restricted movement within a (sub-)population limits the ability of predators to consume prey, localized consumption or diffusion limitation can stabilize the system. Thus while the conclusions from differential equations on the role of pattern formation for stability may apply to discrete and noisy systems, it will take a detailed understanding of movement and scales of interaction to examine the role of pattern formation in real systems. Additionally, it will be important to link an understanding of both foraging and inter-patch movement, since by analogy to the models, both would be critical for understanding how real systems are stabilized by being discrete and spatial.     

Predator–prey fuzzy model

In this work we have used fuzzy rule-based systems to elaborate a predator–prey type of model to study the interaction between aphids (preys) and ladybugs (predators) in citriculture, where the aphids are considered as transmitter agents of the Citrus Sudden Death (CSD). Simulations were performed and a graph was drawn to show the prey population, the potentiality of the predators, and a phase-plane. From this phase-plane, a classic model of the Holling–Tanner type is fitted and its parameters were found. Finally, we have studied the stability of the critical points of the Holling–Tanner model.     

Chaos and pattern formation in a spatial tritrophic food chain

The model of Hastings and Powell describes a tritrophic food chain that exhibits chaotic dynamics. The model assumes that the populations are homogeneously mixed, so that the probability that any two individuals interact is uniform and space can be ignored. In this paper we propose a spatial version of the Hastings and Powell model in which predators seek their preys only in a finite neighborhood of their home location, breaking the mixing hypothesis. Treating both space and time as discrete variables we derive a set of coupled equations that describe the evolution of the populations at each site of the spatial domain. We show that the introduction of local predator–prey interactions result in qualitatively distinct dynamics of predator and prey populations. The evolution equations for the predators involve averages over the local density of preys, whereas the equations for the preys involve double averages, where the local density of both preys and predators appear. Our numerical simulations show that local predation also leads to spontaneous pattern formation and to qualitative changes in the global dynamics of the system. In particular, depending on the size of the predation neighborhoods, the chaotic strange attractor present in the original model of Hastings and Powell can be replaced by a stable fixed point or by an attractor of simpler topology.     

A resource-based approach to modelling the dynamics of interacting populations

The procedure for modelling the growth of single-species populations [Sakanoue, S., 2007. Extended logistic model for growth of single-species populations. Ecol. Model. 205, 159–168] is improved to be applicable to the study of the dynamics of interacting populations. The improved procedure is based on three assumptions: resource availability changes with population size as a variable, resource supply to populations and population demand for resources are defined as functions of resource availability and population size, and the variables of resource availability and population size shift in the supply function attracted to the demand function. These assumptions are organized into three equations. The equations can generate the dynamics models of plant, herbivore, and detritivore populations, and their own resources. The models can be used to describe prey–predator dynamics. They naturally contain nonlinear terms for the predator’s numerical and functional responses. Depending on the terms, the fluctuations in resource availability and population size stabilize. The three equations can also generate the dynamics models of different populations consuming the same resources. The analysis of zero isoclines of the models shows that a superior population can be simply defined as one with a higher intrinsic rate of natural increase, that a stable coexistence may be realized with the intraspecific interference or the interspecific facilitation of superiors, and that the interspecific interference or the intraspecific facilitation of inferiors may make the coexistence unstable and the inferiors winners depending on their initial population size.     

Predator–prey models: an application for the plankton dynamics of lake Geneva

In this paper we present a hierarchical Bayesian analysis for a predator–prey model applied to ecology considering the use of Markov Chain Monte Carlo methods. We consider the introduction of a random effect in the model and the presence of a covariate vector. An application to ecology is considered using a data set related to the plankton dynamics of lake Geneva for the year 1990. We also discuss some aspects of discrimination of the proposed models.     

Simple predator–prey interactions control dynamics in a plankton food web model

A plankton food web model is analysed using interaction parameter values appropriate to the upper mixed layer of the high latitude oceans. The dynamics of this four-variable system are analysed in terms of the dynamics of much simpler two-variable predator–prey subsystems. Thus, the food web's robust, periodic, four-dimensional dynamics are explained by means of two-dimensional spirals and limit cycles. These dynamical subsystems are coupled by means of an omnivore that transfers control of the dynamics between the two predator–prey subsystems. The food web may substantially decouple the predator–prey subsystems so that the oscillating phytoplankton/zooplankton blooms exhibit population collapses when bacterial ‘breathers’ briefly dominate after growing dramatically from low background levels. This regular bloom/breather behaviour becomes benignly chaotic when the system is mildly forced by the annual cycle of the sun's irradiance.     

Mean free-path length theory of predator–prey interactions: Application to juvenile salmon migration

Ecological theory traditionally describes predator–prey interactions in terms of a law of mass action in which the prey mortality rate depends on the density of predators and prey. This simplifying assumption makes population-based models more tractable but ignores potentially important behaviors that characterize predator–prey dynamics. Here, we expand traditional predator–prey models by incorporating directed and random movements of both predators and prey. The model is based on theory originally developed to predict collision rates of molecules. The temporal and spatial dimensions of predators–prey encounters are determined by defining movement rules and the predator's field of vision. These biologically meaningful parameters can accommodate a broad range of behaviors within an analytically tractable framework suitable for population-based models. We apply the model to prey (juvenile salmon) migrating through a field of predators (piscivores) and find that traditional predator–prey models were not adequate to describe observations. Model parameters estimated from the survival of juvenile chinook salmon migrating through the Snake River in the northwestern United States are similar to estimates derived from independent approaches and data. For this system, we conclude that survival depends more on travel distance than travel time or migration velocity.     

Transient dynamics and the destabilizing effects of prey heterogeneity

The presence of prey heterogeneity and weakly interacting prey species is frequently viewed as a stabilizer of predator-prey dynamics, countering the destabilizing effects of enrichment and reducing the amplitude of population cycles. However, prior model explorations have largely focused on long-term, dynamic attractors rather than transient dynamics. Recent theoretical work shows that the presence of prey that are defended from predation can have strongly divergent effects on dynamics depending on time scale: prey heterogeneity can counteract the destabilizing effects of enrichment on predator-prey dynamics at long time scales but strongly destabilize systems during transient phases by creating long periods of low predator/prey abundance and increasing extinction probability (an effect that is amplified with increasing enrichment). We tested these general predictions using a planktonic system composed of a zooplankton predator and multiple algal prey. We first parameterized a model of our system to generate predictions and tested these experimentally. Our results qualitatively supported several model predictions. During transient phases, presence of defended algal prey increased predator extinctions at low and high enrichment levels compared to systems with only a single edible prey. This destabilizing effect was moderated at higher dilution rates, as predicted by our model. When examining dynamics beyond initial oscillations, presence of the defended prey increased predator-prey temporal variability at high nutrient enrichment but had no effect at low nutrient levels. Our results highlight the importance of considering transient dynamics when assessing the role of stabilizing factors on the dynamics of food webs.     

Modeling inverted biomass pyramids and refuges in ecosystems

Although the existence of robust inverted biomass pyramids (IBPs) seems paradoxical, they are well known to exist in planktonic communities, and have recently been discovered in pristine coral reefs and in a reef off the North Carolina coast. Understanding the underlying mechanisms which produce inverted biomass pyramids provides new ecological insights. Some ecologists hypothesize that “the high growth rate of prey and low death rate of predators” causes IBPs. However, we show this is not always the case (see Sections 3.1 and 4). We devise predator–prey models to describe three mechanisms that can lead to IBPs: (1) well-mixed populations with large prey turn-over rate, (2) well-mixed populations with prey immigration, and (3) non-mixed populations where the prey can hide in refuges. The three models are motivated by the three ecosystems where IBPs have been observed. We also devise three refuge mediated models, with explicit refuge size, which incorporate different prey responses in the refuge, and we discuss how these lead to IBPs.     

Vulnerability of the copepod Acartia tonsa to predation by the scyphomedusa Chrysaora quinquecirrha : effect of prey size and behavior

Although scyphomedusae have received increased attention in recent years as important predators in coastal and estuarine environments, the factors affecting zooplankton prey vulnerability to these jellyfish remain poorly understood. Current models predicting feeding patterns of cruising entangling predators, such as Chrysaora quinquecirrha (Desor, 1948), fail to account for the selection of fast-escaping prey such as copepods. Nevertheless, our analysis of gastric contents of field-collected medusae showed that this scyphomedusa fed selectively on the calanoid copepod Acartia tonsa (Dana, 1846) and preferentially ingested adult over copepodite stages. We measured feeding rates in a planktonkreisel while simultaneously videotaping predator–prey interactions. C. quinquecirrha consumed adult A. tonsa ten times faster than copepodites. Differences in prey behavior, in the form of predator–prey encounter rates or post-encounter escape responses, could not account for the elevated feeding rates on adults. Prey size, however, had a dramatic impact on the vulnerability of copepods. In experiments using heat-killed prey, feeding rates on adults (1.5 times longer than copepodites) were 11 times higher than on copepodites. In comparison, medusae ingested heat-killed prey at only two to three times the rate of live prey. These results suggest that during scyphomedusan–copepod interactions, prey escape ability is important, but ultimately small size is a more effective refuge from predation. Received: 26 September 1997 / Accepted: 20 May 1998     

Deterministic approach to the study of the interaction predator-prey in a chemostat with predator mutual interference. Implications for the paradox of enrichment

Our understanding of predator-prey systems has progressed in recent decades mainly due to the ability to test models in chemostats. This study aimed to develop a deterministic model using differential equations to reproduce the dynamics of the interaction of a predator and a prey in a two stage chemostat focusing in the proposed previous prey dependent model of Fussmann et al. (2000) [Fussmann, G.F., Ellner, S.P., Shertzer, K.W., Hairston Jr., N.G., 2000. Crossing the Hopf bifurcation in a live predator-prey system. Science 290, 1358-1360]. The main problem with that model, but parameterized with the values obtained in this study (particularly the concentration of nutrient), was that the temporal trajectory of both the prey and the predator showed very high peaks that eventually led to the extinction of predator in all cases. In the same way the experimental time series obtained in this study does not exhibit the behavior predicted by the model of Fussman et al. On the contrary, as prey density increases, the system actually becomes more stable. Finally, the model that best explained the behavior of the predator and prey in the chemostat, at medium to high dilution rates, was the ratio dependent (algae-nitrogen) model with mutual interference measured in the chemostat (rotifer-alga) and that incorporated the age structure of the predator. Qualitative analysis of the dynamic behavior enabled evaluation of coexistence at equilibrium, coexistence on limit cycles, extinction of the predator or extinction of both populations.     

Modelling predation by transient leopard seals for an ecosystem-based management of Southern Ocean fisheries

Correctly quantifying the impacts of rare apex marine predators is essential to ecosystem-based approaches to fisheries management, where harvesting must be sustainable for targeted species and their dependent predators. This requires modelling the uncertainty in such processes as predator life history, seasonal abundance and movement, size-based predation, energetic requirements, and prey vulnerability. We combined these uncertainties to evaluate the predatory impact of transient leopard seals on a community of mesopredators (seals and penguins) and their prey at South Georgia, and assess the implications for an ecosystem-based management. The mesopredators are highly dependent on Antarctic krill and icefish, which are targeted by regional fisheries. We used a state-space formulation to combine (1) a mark-recapture open-population model and individual identification data to assess seasonally variable leopard seal arrival and departure dates, numbers, and residency times; (2) a size-based bioenergetic model; and (3) a size-based prey choice model from a diet analysis. Our models indicated that prey choice and consumption reflected seasonal changes in leopard seal population size and structure, size-selective predation and prey vulnerability. A population of 104 (90–125) leopard seals, of which 64% were juveniles, consumed less than 2% of the Antarctic fur seal pup production of the area (50% of total ingested energy, IE), but ca. 12–16% of the local gentoo penguin population (20% IE). Antarctic krill (28% IE) were the only observed food of leopard seal pups and supplemented the diet of older individuals. Direct impacts on krill and fish were negligible, but the “escapement” due to leopard seal predation on fur seal pups and penguins could be significant for the mackerel icefish fishery at South Georgia. These results suggest that: (1) rare apex predators like leopard seals may control, and may depend on, populations of mesopredators dependent on prey species targeted by fisheries; and (2) predatory impacts and community control may vary throughout the predator's geographic range, and differ across ecosystems and management areas, depending on the seasonal abundance of the prey and the predator's dispersal movements. This understanding is important to integrate the predator needs as natural mortality of its prey in models to set prey catch limits for fisheries. Reliable estimates of the variability of these needs are essential for a precautionary interpretation in the context of an ecosystem-based management.     

Urban expansion and its contribution to the regional carbon emissions: Using the model based on the population density distribution

The method is used for calculating regional urban area dynamics and the resulting carbon emissions (from the land-conversion) for the period of 1980 till 2050 for the eight world regions. This approach is based on the fact that the spatial distribution of population density is close to the two-parametric Γ-distribution [Kendall, M.G., Stuart, A., 1958. The Advanced Theory of Statistics, vol. 1.2. Academic Press, New York; Vaughn, R., 1987. Urban Spatial Traffic Patterns, Pion, London]. The developed model provides us with the scenario of urbanisation, based on which the regional and world dynamics of carbon emissions and export from cities, and the annual total urban carbon balance are estimated. According to our estimations, world annual emissions of carbon as a result of urbanisation increase up to 1.25 GtC in 2005 and begin to decrease afterwards. If we compare the emission maximum with the annual emission caused by deforestation, 1.36 GtC per year, then we can say that the role of urbanised territories (UT) in the global carbon balance is of a comparable magnitude. Regarding the world annual export of carbon from UT, we observe its monotonous growth by three times, reaching 505 MtC. The latter, is comparable to the amount of carbon transported by rivers into the ocean (196–537 MtC). The current model shows that urbanisation is inhibited in the interval 2020–2030, and by 2050 the growth of urbanised areas would almost stop. Hence, the total balance, being almost constant until 2000, then starts to decrease at an almost constant rate. By the end of the XXI century, the total carbon balance will be equal to zero, with the exchange flows fully balanced, and may even be negative, with the system beginning to take up carbon from the atmosphere, i.e., becomes a “sink”. The regional dynamics is somewhat more complex, i.e., some regions, like China, Asia and Pacific are being active sources of Carbon through the studied period, while others are changing from source to sink or continue to be neutral in respect the GCC.     

Structural changes in lake functioning induced from nutrient loading and climate variability

Climate variability is increasingly recognized as an important regulatory factor, capable of influencing the structural properties of aquatic ecosystems. Lakes appear to be particularly sensitive to the ecological impacts of climate variability, and several long time series have shown a close coupling between climate, lake thermal properties and individual organism physiology, population abundance, community structure, and food web dynamics. Thus, understanding the complex interplay among meteorological forcing, hydrological variability, and ecosystem functioning is essential for improving the credibility of model-based water resources/fisheries management. Our objective herein is to examine the relative importance of the ecological mechanisms underlying plankton seasonal variability in Lake Washington, Washington State (USA), over a 35-year period (1964–1998). Our analysis is founded upon an intermediate complexity plankton model that is used to reproduce the limiting nutrient (phosphate)–phytoplankton–zooplankton–detritus (particulate phosphorus) dynamics in the lake. Model parameterization is based on a Bayesian calibration scheme that offers insights into the degree of information the data contain about model inputs and allows obtaining predictions along with uncertainty bounds for modeled output variables. The model accurately reproduces the key seasonal planktonic patterns in Lake Washington and provides realistic estimates of predictive uncertainty for water quality variables of environmental management interest. A principal component analysis of the annual estimates of the underlying ecological processes highlighted the significant role of the phosphorus recycling stemming from the zooplankton excretion on the planktonic food web variability. We also identified a moderately significant signature of the local climatic conditions (air temperature) on phytoplankton growth (r = 0.41), herbivorous grazing (r = 0.38), and detritus mineralization (r = 0.39). Our study seeks linkages with the conceptual food web model proposed by Hampton et al. [Hampton, S.E., Scheuerell, M.D., Schindler, D.E., 2006b. Coalescence in the Lake Washington story: interaction strengths in a planktonic food web. Limnol. Oceanogr. 51, 2042–2051.] to emphasize the “bottom-up” control of the Lake Washington plankton phenology. The posterior predictive distributions of the plankton model are also used to assess the exceedance frequency and confidence of compliance with total phosphorus (15 μg L⁻¹) and chlorophyll a (4 μg L⁻¹) threshold levels during the summer-stratified period in Lake Washington. Finally, we conclude by underscoring the importance of explicitly acknowledging the uncertainty in ecological forecasts to the management of freshwater ecosystems under a changing global environment.     

A simulation model to explore the response of the Gulf of Maine food web to large-scale environmental and ecological changes

A dynamic simulation model was constructed using outputs from a balanced Gulf of Maine (GOM) energy budget model as the initial parameter set. The model was structured to provide a recipient control set of dynamics, largely based off of flows to and from different biological groups. The model was used to produce Monte Carlo simulations that were compared (percent change in biomass) with basecase simulations for a variety of scenarios. Changes in primary production, large increases in pelagic and demersal fish biomass, increases in fishing mortality, and large increases in top predators such as baleen whales and pinnepids were simulated. These scenarios roughly simulated the potential impacts of climate change, altered fishing pressure, additional protected species mitigations, and combinations thereof. Results suggest that the GOM system is primarily influenced by bottom-up processes involving phytoplankton, zooplankton, and bacterial biomass. Pelagic and demersal fish were important in determining trends in some of the scenarios. Marine mammals, large pelagic fish, and seabirds have a minor role in the GOM system in terms of biomass flows among the ecosystem components. The system is resilient to large-scale change due, in part to many predator–prey linkages. However, major alterations could occur from sustained climate change, high fishing rates, and by combinations of these types of external forcing mechanisms.     

Zooplankton population model coupled to a biogeochemical model of the North Western Mediterranean Sea ecosystem

A stage structured population (SSP) model based on Fennel's [Fennel, W., 2001. Modelling copepods with links to circulation models. Journal of Plankton Research, 23, 1217–1232] equations is applied to Centropages typicus (Kröyer), a dominant copepod species of the North Western Mediterranean Sea (NWMS) and a prey of small pelagic fish. The model considers five groups of stages and development rates are represented by a mechanistic formulation depending on individual specific growth in each stage. Individual growth is calculated from the individual energy budget depending on food availability and temperature.     

Intraguild predation and mesopredator release effect on long-lived prey

Complete extirpation of a species can generate cascading effects throughout an ecosystem, yet are precisely the goal of island eradications of pest species. “Mesopredator release effect”, an asymmetrical special case of intraguild predation, has been hypothesised as a possible indirect effect from eradications, where superpredator removal can generate a mesopredator increase which may increase the impact on their shared prey. Theoretically this suggests that for intraguild predators, the superpredator may protect the shared prey from mesopredation, and removal of superpredators alone is not recommended. We create a model of long-lived age-structured shared prey and explore the non-equilibrium dynamics of this system. The superpredator can impact all prey life-stages (adult survival and reproductive success) whereas the smaller mesopredator can only impact early life-stages (reproductive success). This model is independently tested with data from a closed oceanic island system where eradication of introduced intraguild predators is possible for conservation of threatened birds. Mesopredator release only occurs in strongly top-down moderated (resource-abundant) systems. Even when mesopredator release can occur, the negative impact of more mesopredators is outweighed by the benefit of superpredator removal, allowing recovery of the prey population. Results are robust to 10% variation in model parameters. The consideration of age-structured prey contradicts previous theoretical results for mesopredator release effect and intraguild predation. Superpredator eradication is vital for population recovery of long-lived insular species. Nonetheless island conservation must retain a whole-ecosystem perspective given the complex trophic relationships among multiple species on islands.