Dynamics of a plant-herbivore-predator system with plant-toxicity

A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.     

Effects of aboveground herbivory on plants with long-term belowground biomass storage

Plant tolerance to herbivory is contingent on multiple traits and adaptive mechanisms, which makes it a complex response with ecological implications. In plants with long-term belowground storage, allocation of biomass to inaccessible parts belowground in response to folivory is a well-recognized tolerance mechanism. In temperate regions, spring growth from buried rootstock is common among winter deciduous plants and is often followed by regrowth after defoliation, both of which draws resources from the stored reserves. We developed a mathematical model to analyze this tolerance response in a winter deciduous plant with long-term belowground biomass when it is defoliated by a specialist insect folivore. The model explores how three closely associated traits—(1) belowground biomass allocation to roots, (2) spring utilization of stored reserves, and (3) post-defoliation regrowth capacity—modulate the persistence and dynamics of the plant and herbivore populations. Model results show that allocation to belowground storage is not only a critical component of tolerance but also influences the herbivore population dynamics in ways that depend on how and when plant biomass is allocated and used. Low belowground biomass allocation and high storage utilization combined with poor photosynthetic growth caused extirpation of the plant population by the defoliating insects. Stable coexistence of the plant at low biomass along with its specialist insect required a moderate amount of post-herbivory belowground allocation. High values of belowground biomass allocation, storage utilization, and photosynthetic growth resulted in sustained cycles of the herbivore and plant populations. Interestingly, utilization of stored reserves had conflicting influence on above and belowground biomass, and strongly affected herbivore population dynamics. Our model thus highlights the complexity of tolerance response when it involves multiple traits and mechanisms as evinced by winter deciduous plants. We close by discussing the implications of our findings for the contributions of defoliating insects to biocontrol programs.     

Dynamics of herbivores and resources on a landscape with interspersed resources and refuges

A tradeoff between energy gain from foraging and safety from predation in refuges is a common situation for many herbivores that are vulnerable to predation while foraging. This tradeoff affects the population dynamics of the plant–herbivore–predator interaction. A new functional response is derived based on the Holling type 2 functional response and the assumption that the herbivore can forage at a rate that maximizes its fitness. The predation rate on the herbivore is assumed to be proportional to the product of the time that the herbivore spends foraging and a risk factor that reflects the habitat complexity; where greater complexity means greater interspersion of high food quality habitat and refuge habitat, which increases the amount of the edge zone between refuge and foraging areas, making foraging safer. The snowshoe hare is chosen as an example to demonstrate the resulting dynamics of an herbivore that has been intensely studied and that undergoes well-known cycling. Two models are studied in which the optimal foraging by hares is assumed, a vegetation–hare–generalist predator model and a vegetation–hare–specialist predator model. In both cases, the results suggest that the cycling of the snowshoe hare population will be greatly moderated by optimal foraging in a habitat consisting of interspersed high quality foraging habitat and refuge habitat. However, there are also large differences in the dynamics produced by the two models as a function of predation pressure.     

Searching for Spatial Patterns in a Pollinator–Plant–Herbivore Mathematical Model

This paper deals with the spatio-temporal dynamics of a pollinator–plant–herbivore mathematical model. The full model consists of three nonlinear reaction–diffusion–advection equations defined on a rectangular region. In view of analyzing the full model, we firstly consider the temporal dynamics of three homogeneous cases. The first one is a model for a mutualistic interaction (pollinator–plant), later on a sort of predator–prey (plant–herbivore) interaction model is studied. In both cases, the interaction term is described by a Holling response of type II. Finally, by considering that the plant population is the unique feeding source for the herbivores, a mathematical model for the three interacting populations is considered. By incorporating a constant diffusion term into the equations for the pollinators and herbivores, we numerically study the spatiotemporal dynamics of the first two mentioned models. For the full model, a constant diffusion and advection terms are included in the equation for the pollinators. For the resulting model, we sketch the proof of the existence, positiveness, and boundedness of solution for an initial and boundary values problem. In order to see the separated effect of the diffusion and advection terms on the final population distributions, a set of numerical simulations are included. We used homogeneous Dirichlet and Neumann boundary conditions.     

Exploitation ecosystems and trophic cascades in non‐equilibrium systems: pasture – red kangaroo – dingo interactions in arid Australia

The exploitation ecosystems hypothesis (EEH) proposes that 1) plant biomass reflects the primary productivity of an ecosystem modified by the regulating effect of herbivory, and 2) herbivore abundance reflects the productivity of plants modified by the regulating effect of predation. Primary productivity thus determines the number of trophic levels in an ecosystem and the extent to which bottom–up and top–down regulation influence the biomass ratios of adjacent and non‐adjacent trophic levels (i.e. trophic cascading). We constructed an interactive model of plant (pasture), herbivore (red kangaroo Macropus rufus) and predator (dingo Canis lupus dingo), a system in which trophic cascades have been suggested to occur, and used it to test the effects of increasing stochastic variation in primary productivity and dingo culling on predictions of the EEH. The model contained four feedback loops: the predator–herbivore and herbivore–plant feedback loops, and the predator and plant density‐dependent feedback loops. The equilibrium conditions along the primary productivity gradient reproduced the three zones of trophic dynamics predicted by the EEH, plus an additional zone at productivities above which the maximum density of a predator is achieved due to social regulation: that zone is characterized by increasing herbivore density and decreasing plant biomass. Culling dingoes produced trophic cascades that were strongly attenuated at primary productivities below which the maximum density of dingoes was attained. Results were robust to uncertainty in kangaroo off‐take by dingoes and to the efficacy of dingo culling, but prey switching by dingoes from red kangaroos to reptiles would weaken trophic cascades. We conclude that social regulation of carnivores has important implications for expression of the EEH and trophic cascades, and that attenuation of trophic cascades increases with increasing stochasticity in primary productivity. Our model also provides a framework for understanding the conditions in which dingo‐mediated trophic cascades might be expected to occur, and generates testable predictions about the effects of higher dingo densities (e.g. by stopping culling or reintroduction to former range) on kangaroo and pasture dynamics.     

Interactions of herbivore exclusion with warming and N addition in a grass-dominated temperate old field

Field experiments used to explore the effects of global change drivers, such as warming and nitrogen deposition on plant productivity and species composition, have typically focused on bottom-up processes. However, both direct and indirect responses of herbivores to the treatments could result in important interactions between top-down and bottom-up effects. These interactions may be complicated by the simultaneous effects of multiple herbivore taxa. We used rodent and mollusc exclosures in the plots of a warming and N addition field experiment to examine how herbivore removal would influence plant biomass responses to the treatments. The effect of rodent exclusion on grass biomass more than doubled in response to nitrogen addition, but did not respond to warming, whereas the effect of mollusc exclusion on grass biomass increased in response to warming, but not nitrogen. In contrast, the effect of rodent exclusion on total biomass (grasses and forbs combined) increased in response to both nitrogen and warming, while the effect of mollusc exclusion on total biomass was insensitive to nitrogen and warming. In no cases were there interactions between nitrogen and warming with respect to their influence on exclosure effects. Overall, our results demonstrated substantial and variable effects of multiple herbivore taxa on plant biomass responses to warming and N addition, despite the absence of conspicuous damage to the plant canopy. These results therefore highlight the potential importance of interactions between top-down and bottom-up factors in global change field experiments.     

Transient spatio-temporal dynamics of a diffusive plant–herbivore system with Neumann boundary conditions

In many existing predator–prey or plant–herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant–herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations. A large variety of different types of transient behaviours including oscillations in one or both of space and time are observed.     

Effects of nitrogen deposition on the interaction between an aphid and its host plant

Abstract 1. Anthropogenic increases in nitrogen deposition are impacting terrestrial ecosystems worldwide. While some of the direct ecosystem‐level effects of nitrogen deposition are understood, the effects of nitrogen deposition on plant–insect interactions and on herbivore population dynamics have received less attention. 2. Nitrogen deposition will potentially influence both plant resource availability and herbivore population growth. If increases in herbivore population growth outstrip increases in resource availability, then increases in the strength of density dependence expressed within the herbivore population would be predicted. Alternatively, if plant resources respond more vigorously to nitrogen deposition than do herbivore populations, a decline in the strength of density dependence would be expected. No change in the strength of density dependence acting upon the herbivore population would suggest equivalent responses by herbivores and plants. 3. A density manipulation experiment was performed to examine the effect of nitrogen deposition on the interaction between a host plant, Asclepias tuberosa, and its herbivore, Aphis nerii. Aphid maximum per capita growth rate (R_max), carrying capacity (K), and the strength of density dependence were measured under three nitrogen deposition treatments. The effect of nitrogen deposition on the relationship among these three measures of insect population dynamics was explored. 4. Simulated nitrogen deposition increased aphid per capita population growth, plant foliar nitrogen concentrations, and plant biomass. Nitrogen deposition caused R_max and K to increase proportionally, leading to no overall change in the strength of density dependence. In this system, potential changes in the negative feedback processes operating on herbivore populations following nitrogen deposition appear to be buffered by concomitant changes in resource availability.     

Dynamical analysis of a prey-predator model incorporating a prey refuge with variable carrying capacity

A prey-predator model incorporating prey refuge with variable carrying capacity and Holling type-II functional response is proposed and analyzed. The model includes a case of increasing carrying capacity as well as a decreasing carrying capacity case. Sufficient conditions are derived to ensure the existence and local stability of the equilibrium points of the proposed model. Moreover, the occurrence of transcritical bifurcation as well as Hopf bifurcation are investigated. The effect of some model parameter related to the prey refuge and the variable carrying capacity on the prey-predator dynamics has been examined. Numerical simulations are presented to demonstrate the theoretical results and to illustrate the effect of these parameters on the model dynamics. Moreover, a comparison with the constant carrying case has been presented.     

Dynamics of a plant-herbivore model

We formulate a simple host-parasite type model to study the interaction of certain plants and herbivores. Our two-dimensional discrete-time model utilizes leaf and herbivore biomass as state variables. The parameter space consists of the growth rate of the host population and a parameter describing the damage inflicted by herbivores. We present insightful bifurcation diagrams in that parameter space. Bistability and a crisis of a strange attractor suggest two control strategies: reducing the population of the herbivore under some threshold or increasing the growth rate of the plant leaves.     

Plant genetic diversity yields increased plant productivity and herbivore performance

1.  Plant genotypic diversity has important consequences for a variety of ecosystem processes, yet empirical evidence for its effects on productivity, one of the most fundamental of these processes, is lacking. In addition, the performance of insect herbivores in response to high genotypic diversity is unknown, despite previous work demonstrating differential herbivore performance among plant genotypes.
2.  We manipulated genotypic diversity of the annual plant Arabidopsis thaliana in both the presence and absence of the generalist herbivore Trichoplusia ni under semi-natural growth conditions. We used nine genotypes (eight ecotypes and one mutant) of A. thaliana known to differ widely in functional traits. Productivity and insect biomass were measured in monocultures and mixtures of all nine genotypes grown at multiple fertilization levels and planting densities.
3.  In both the absence and presence of herbivores, genotypic diversity increased plant productivity and survival. This effect was, for the most part, independent of fertility or density. Sampling or selection effects did not appear to be wholly responsible for these results as all genotypes were maintained in equal proportion and no single genotype became dominant for the duration of the experiment.
4.  High diversity increased T. ni biomass and survival in all treatments. Insect biomass was positively, but not tightly, correlated to plant biomass, indicating that the higher herbivore performance observed in genotypic mixtures was only partially due to higher productivity.
5. Synthesis. Our data support the idea that even within a single plant species, genotypic diversity can exert strong influences on both the producer and herbivore communities. The exact mechanisms responsible for these effects and the relative importance of genotypic diversity in natural communities warrant further investigation.     

Comparing the consequences of induced and constitutive plant resistance for herbivore population dynamics

Although it has been suggested that induced and constitutive plant resistance should have different effects on insect herbivore population dynamics, there is little experimental evidence that plant resistance can influence herbivore populations longer than one season. We used a density-manipulation experiment and model fitting to examine the effects of constitutive and induced resistance on herbivore dynamics over both the short and long term. We used likelihood methods to fit population dynamic models to recruitment data for populations of Mexican bean beetles on soybean varieties with no resistance, constitutive resistance, or induced resistance. We compared model configurations that fit parameters for resistance types separately to models that did not account for resistance type. Models representing the hypothesis that the three resistance types differed in their effects on beetle dynamics received the most support. Induced resistance resulted in lower population growth rates and stronger density dependence than no resistance. Constitutive resistance resulted in lower population growth rates and stronger density dependence than induced resistance. Constitutive resistance had a stronger effect on both short-term beetle recruitment and predicted beetle population dynamics than induced resistance. The results of this study suggest that induced and constitutive resistance can differ in their effects on herbivore populations even in a relatively complex system.     

Plant compensatory growth: a conquering strategy in plant–herbivore interactions?

We present a theoretical analysis that considers the phenotypic trait of compensatory growth ability in a context of population dynamics. Our model depicts a system of three interactors: herbivores and two different plant types referred to as ordinary and compensating. The compensating plant type has the ability to increase its intrinsic rate of biomass increase as a response to damage. This compensatory growth ability is maintained at the expense of a reduced growth rate in the absence of damage, where the ordinary plant type has the higher growth rate. Analysis of this system suggests that, even though a compensatory capacity of this kind will not imply an increase in equilibrium plant density, it will give a competitive advantage in relation to other plants, in the presence of a sufficiently efficient herbivore. Invasion of compensating plants into a population of non-compensating plants is facilitated by a high compensatory growth ability and a high intrinsic rate of plant biomass increase. Conversely, an ordinary plant can invade and outcompete a compensating plant when the herbivore is characterised by a relatively low attack rate, and/or when plant intrinsic growth rate is decreased.     

Physical and chemical response of juvenile Acacia tortilis trees to browsing. Experimental evidence

1. Changes in nutritional value and accessibility of leaves following browsing are important in the dynamics of plant–herbivore interactions because they influence the fitness of the plant attacked and the future utilization of it by the herbivore.
2. Hand pruning of Acacia tortilis , a spinescent tree common in savanna ecosystems of eastern Africa, resulted in higher biomass of spines and new shoots in pruned trees than in unpruned controls.
3. Pruned trees allocated a higher proportion of shoot biomass to spines than unpruned ones, whereas the proportion of leaf biomass in new shoots was slightly reduced. Because increases in spine biomass and density following pruning are coupled with an increase in shoot production, it is concluded that higher production of spines is an inducible response of Acacia tortilis to pruning.
4. No significant changes in the concentration of total phenolics, condensed tannins or leaf nitrogen were induced by pruning.
5. Irrespective of treatment, high foliar concentrations of nitrogen were correlated with an increase in twig production for a given leaf biomass and a reduction in the concentration of secondary substances in leaves. This relation may lead to a conflict between foraging efficiency and nutrition for browsers of A. tortilis.     

Modeling herbivore competition mediated by inducible changes in plant quality

Competition between herbivorous insects often occurs as a trait mediated indirect effect mediated by inducible changes in plant quality rather than a direct effect mediated by plant biomass. While plant-mediated competition likely influences many herbivores, progress linking studies of plant-mediated competition in terrestrial phytophagous insects to longer-term consequences for herbivore communities has been elusive, and there is little relevant theory to guide this effort. We present simple models describing plant-mediated interactions between two herbivorous insects or other functionally equivalent organisms. These models consider general features of plant-mediated competition including specificity of elicitation by and effects on herbivores, positive and negative interactions among herbivores, competition independent of changes in plant biomass, and the existence of multiple relevant plant traits. Our analyses generate four important conclusions. First, herbivores competing strongly via only one plant quality phenotype exhibit a limited range of outcomes. These include coexistence and competitive exclusion of either herbivore, but do not include initial condition dependence. Second, when the outcome of competition is competitive exclusion, the herbivore that persists is the one that can do so under the highest inducible reductions in plant quality. Third, competition via more than one inducible phenotype can exhibit a wider range of outcomes including multiple equilibria and initial condition dependence. Finally, transient dynamics may not predict the eventual outcome of competition when changes in plant quality are slow relative to herbivore population growth, especially when herbivores compete through multiple phenotypes. We interpret our results in terms of competition outcomes reported in the literature, and suggest directions for the future empirical study of herbivore competition mediated by inducible changes in plant quality.     

Biomass and biodiversity in species-rich tritrophic communities

We consider a tritrophic system with one basal and one top species and a large number of primary consumers, and derive upper and lower bounds for the total biomass of the middle trophic level. These estimates do not depend on dynamical regime, holding for fixed point, periodic, or chaotic dynamics. We have two kinds of estimates, depending on whether the predator abundance is zero. All these results are uniform in a self-limitation parameter, which regulates prey diversity in the system. For strong self-limitation, diversity is large; for weak self-limitation, it is small. Diversity depends on the variance of species’ parameter values. The larger this variance, the lower the diversity, and vice versa. Moreover, variation in the parameters of the Holling type II functional response changes the bifurcation character, with the equilibrium state with nonzero predator abundance losing stability. If that variation is small then the bifurcation can lead to oscillations (the Hopf bifurcation). Under certain conditions, there exists a supercritical Hopf bifurcation. We then find a connection between diversity and Hopf bifurcations. We also show that the system exhibits top-down regulation and a hump-shaped diversity-productivity curve.We then extend the model by allowing species to experience self-regulation. For this extended model, explicit estimates of prey diversity are obtained. We study the dynamics of this system and find the following. First, diversity and system dynamics crucially depend on variation in species parameters. We show that under certain conditions, the system undergoes a supercritical Hopf bifurcation. We also establish a connection between diversity and Hopf bifurcations. For strong self-limitation, diversity is large and complex dynamics are absent. For weak self-limitation, diversity is small and the equilibrium with non-zero predator abundance is unstable.     

How do two specialist butterflies determine growth and biomass of a shared host plant?

Although insect herbivory can modify subsequent quantity and quality of their host plants, change in plant quantity following herbivory has received less attention than plant quality. In particular, little is known about how previous herbivore damage determines plant growth and biomass in an insect species-specific manner. We explored whether herbivore species-specific food demand influences plant growth and biomass. To do this, we conducted a series of experiments and field survey using two specialist butterflies, Sericinus montela and Atrophaneura alcinous, and their host plant, Aristolochia debilis. It is known that A. alcinous larva requires four times more food resources to fulfill its development than S. montela larva. Despite that A. alcinous larvae imposed greater damage on plants than S. montela larvae, plant growth did not differ due to herbivory by these species both in single and multiple herbivory events. On the other hand, total aboveground biomass of the plants was reduced more by A. alcinous than S. montela feeding regardless of the number of herbivory events. Feeding on plants with a history of previous herbivory neither decreased nor increased larval growth. Our results suggest that food demand of the two butterfly species determined subsequent plant biomass, although the plant response may depend on tolerance of the host plant (i.e., ability to compensate for herbivore damage). Such difference in the effects of different herbivore species on host plant biomass is more likely to occur than previously thought, because food demand differs in most herbivore species sharing a host plant.     

Tracking sucking herbivory with nitrogen isotope labelling: Lessons from an individual trait-based approach

Response and effect traits help to understand how changes in ecological communities (e.g. in response to land use) relate to changes in ecosystem functioning. In grasslands, plants and insect herbivores are involved in many ecosystem processes such as herbivory and plant biomass production. Simultaneous changes in the trait composition of both plants and herbivores should affect herbivory rates, with consequences for plant growth and potentially biomass production. The mechanisms underlying these links are little understood for grasses and sucking insects, which build a major part of grassland communities. In a mesocosm experiment, we manipulated the composition of grasses and sucking herbivores (Hemiptera) to study the role of plant traits, herbivore traits and their interaction on herbivory and plant growth. Because sucking herbivory is generally difficult to quantify, we developed a novel experimental setting, in which we labelled plants with ¹⁵N isotope. This allowed to quantify ¹⁵N uptake and thus sucking rates of individuals. We found that herbivory and simultaneous plant growth reduction are most strongly linked to herbivore species identity. Unexpectedly, herbivory did not increase with herbivore size, but was highest for small species and for thin-bodied Heteroptera. Additionally, herbivory and plant growth reduction depended on the interacting herbivore and plant species, indicating trait matching, which could, however, not be explained with commonly used traits. This indicates that mechanisms linking ecological communities and ecosystem processes are highly context-specific. To understand how global change affects ecosystem functioning, studies need to cover all functionally relevant groups, including plant sap suckers.     

Fish fauna and fisheries of large European rivers: examples from the Volga and the Danube

The role of herbivores in regulating aquatic plant dynamics has received growing recognition from researchers and managers. However, the evidence for herbivore impacts on aquatic plants is largely based on short-term exclosure studies conducted within a single plant growing season. Thus, it is unclear how long herbivore impacts on aquatic plant abundance can persist for. We addressed this knowledge gap by testing whether mute swan (Cygnus olor) grazing on lowland river macrophytes could be detected in the following growing season. Furthermore, we investigated the role of seasonal changes in water current speed in limiting the temporal extent of grazing. We found no relationship between swan biomass density in 1 year and aquatic plant cover or biomass in the following spring. No such carry-over effects were detected despite observing high swan biomass densities in the previous year from which we inferred grazing impacts on macrophytes. Seasonal increases in water velocity were associated with reduced grazing pressure as swans abandoned river habitat. Furthermore, our study highlights the role of seasonal changes in water velocity in determining the length of the mute swan grazing season in shallow lowland rivers and thus in limiting the temporal extent of herbivore impacts on aquatic plant abundance.