Invasion of an intermediate predator: Fish population dynamics in a mathematical model of a trophic chain (As applied to Syamozero lake)

A mathematical model is presented for the dynamics of a spatially heterogeneous predator-prey population system; a prototype is the Syamozero lake fish community. We show that the invasion of an intermediate predator can evoke chaotic oscillations in the population densities. We also show that different dynamic regimes (stationary, nonchaotic oscillatory, and chaotic) can coexist. The “choice” of a particular regime depends on the initial invader density. Analysis of the model solutions shows that invasion of an alien species is successful only in the absence of competition between the juvenile invaders and the native species.     

Modelling invasibility in endogenously oscillating tree populations: timing of invasion matters

The timing of introduction of a new species into an ecosystem can be critical in determining the invasibility (i.e. the sensitivity to invasion) of a resident population. Here, we use an individual-based model to test how (1) the type of competition (symmetric versus asymmetric) and (2) seed masting influence the success of invasion by producing oscillatory dynamics in resident tree populations. We focus on a case where two species (one resident, one invader introduced at low density) do not differ in terms of competitive abilities. By varying the time of introduction of the invader, we show that oscillations in the resident population favour invasion, by creating “invasibility windows” during which resource is available for the invader due to transiently depressed resident population density. We discuss this result in the context of current knowledge on forest dynamics and invasions, emphasizing the importance of variability in population dynamics.     

A conceptual model of the dynamics of the Syamozero lake community

We have developed a conceptual mathematical model of the dynamics of a spatially heterogeneous population system, the prototype of which is the Syamozero lake fish community. Based on the analysis of solutions of the model, we show that interrelations between prey and predator populations in two neighboring habitats (pelagic and offshore zones) can lead to both undamped oscillations and stationary values of the population size. The population density was found to be close to the values oblained in the course of long-term observations of the biota of the Syamozero lake. Besides, we showed that the transition to the stationary states can be accompanied by long-term (dozens and hundreds of years) damped oscillations of the prey and predator population size. In natural waters, long-term transition periods can prevent the attainment of stationary regimes of fish community functioning.     

Species diversity reduces invasion success in pathogen‐regulated communities

The loss of natural enemies is thought to explain why certain invasive species are so spectacularly successful in their introduced range. However, if losing natural enemies leads to unregulated population growth, this implies that native species are themselves normally subject to natural enemy regulation. One possible widespread mechanism of natural enemy regulation is negative soil feedbacks, in which resident species growing on home soils are disadvantaged because of a build‐up of species‐specific soil pathogens. Here we construct simple models in which pathogens cause resident species to suffer reduced competitive ability on home soils and consider the consequences of such pathogen regulation for potential invading species. We show that the probability of successful invasion and its timescale depend strongly on the competitive ability of the invader on resident soils, but are unaffected by whether or not the invader also suffers reduced competitive ability on home soils (i.e. pathogen regulation). This is because, at the start of an invasion, the invader is rare and hence mostly encounters resident soils. However, the lack of pathogen regulation does allow the invader to achieve an unusually high population density. We also show that increasing resident species diversity in a pathogen‐regulated community increases invasion resistance by reducing the frequency of home‐site encounters. Diverse communities are more resistant to invasion than monocultures of the component species: they preclude a greater range of potential invaders, slow the timescale of invasion and reduce invader population size. Thus, widespread pathogen regulation of resident species is a potential explanation for the empirical observation that diverse communities are more invasion resistant.     

A theorem for the invasion triangle and its applicability for invasion biology

The triangle conceptual model is a construct that is foundational across several fields of the natural sciences including the study of diseases, invasive species, and fire. The invasion triangle incorporates the complex ecological and evolutionary interactions between the qualities of the abiotic environment, the invader, and the biotic interactions that describes or predicts the impacts of the invasive species. Although the triangle concept is widely used among fields, to date there has not been an analytical implementation of the model. Current modelling in invasion biology often only considers the effects of one or two factors on the outcomes of species introductions. A mathematical implementation of the triangle model will allow a more comprehensive consideration of the various ecological factors. Here, we provide the first mathematical theorem for an interpretation of the invasion triangle that allows for the consideration of time. This new analytical development of the triangle is flexible, and can be used to model the spatial and temporal population dynamics observed in invasions. We also describe the conditions under which invasion is maintained when factors change with opposing effects. In this interpretation, the lower limits for invasion are explicitly defined and each component can move independently. The complexity of the interactions between factors contributing to invasions is integrated into the single model, such as those suggested by major invasion hypotheses. We briefly describe how the theorem can be applied to account for various phenomena in range dynamics using rapid range expansion and the time lag in invasions as examples. Future work can explicitly define the interdependence among components to suit more specific questions.     

Mathematical model of invasion of mysids (Mysidacea) into the Naroch Lake system

We present a mathematical model of the invasion of mysid into the Naroch Lake system. The model is parameterized with the use of field observation data. We show that the mysid invasion can lead to an increase in the time-averaged fish population size, and to a decrease in the time-averaged rotifer population size.     

A mathematical model of the invasion of mysid (Mysidacea) into Narochan Lakes

We present a mathematical model of the invasion of mysid into the Narochan Lakes system. The model is parameterized with the use of field observation data. We show that the mysid invasion can lead to an increase in the time-averaged fish population size, and to a decrease in the time-averaged rotifer population size.     

Long-period endogenous oscillations in fish population size: Mathematical modeling

We present a mathematical model of an aquatic community, where the size-and-age structure of hydrobiont populations is taken into account and the corresponding trophic interactions between zooplankton, peaceful fish, and predatory fish are described. We show that interactions between separate components of the aquatic community can give rise to long-period oscillations in fish population size. The period of these oscillations is on the order of decades. With this model we also show that an increase in the zooplankton growth rate may entail a sequence of bifurcations in the fish population dynamics: steady states → regular oscillations → quasicycles → dynamic chaos.     

Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect

Invasion of an exotic species initiated by its local introduction is considered subject to predator-prey interactions and the Allee effect when the prey growth becomes negative for small values of the prey density. Mathematically, the system dynamics is described by two nonlinear diffusion-reaction equations in two spatial dimensions. Regimes of invasion are studied by means of extensive numerical simulations. We show that, in this system, along with well-known scenarios of species spread via propagation of continuous population fronts, there exists an essentially different invasion regime which we call a patchy invasion. In this regime, the species spreads over space via irregular motion and interaction of separate population patches without formation of any continuous front, the population density between the patches being nearly zero. We show that this type of the system dynamics corresponds to spatiotemporal chaos and calculate the dominant Lyapunov exponent. We then show that, surprisingly, in the regime of patchy invasion the spatially average prey density appears to be below the survival threshold. We also show that a variation of parameters can destroy this regime and either restore the usual invasion scenario via propagation of continuous fronts or brings the species to extinction; thus, the patchy spread can be qualified as the invasion at the edge of extinction. Finally, we discuss the implications of this phenomenon for invasive species management and control.     

The impact of interactions on invasion and colonization resistance in microbial communities

In human microbiota, the prevention or promotion of invasions can be crucial to human health. Invasion outcomes, in turn, are impacted by the composition of resident communities and interactions of resident members with the invader. Here we study how interactions influence invasion outcomes in microbial communities, when interactions are primarily mediated by chemicals that are released into or consumed from the environment. We use a previously developed dynamic model which explicitly includes species abundances and the concentrations of chemicals that mediate species interaction. Using this model, we assessed how species interactions impact invasion by simulating a new species being introduced into an existing resident community. We classified invasion outcomes as resistance, augmentation, displacement, or disruption depending on whether the richness of the resident community was maintained or decreased and whether the invader was maintained in the community or went extinct. We found that as the number of invaders introduced into the resident community increased, disruption rather than augmentation became more prevalent. With more facilitation of the invader by the resident community, resistance outcomes were replaced by displacement and augmentation. By contrast, with more facilitation among residents, displacement outcomes shifted to resistance. When facilitation of the resident community by the invader was eliminated, the majority of augmentation outcomes turned into displacement, while when inhibition of residents by invaders was eliminated, invasion outcomes were largely unaffected. Our results suggest that a better understanding of interactions within resident communities and between residents and invaders is crucial to predicting the success of invasions into microbial communities.     

Impacts of a woody invader vary in different vegetation communities

The impact of an exotic species in natural systems may be dependent not only on invader attributes but also on characteristics of the invaded community. We examined impacts of the invader bitou bush, Chrysanthemoides monilifera ssp. rotundata , in fore and hind dune communities of coastal New South Wales, Australia. We compared invader impacts on vegetation structure, richness of both native and exotic growth forms and community variability in fore and hind dunes. We found that impacts of bitou invasion were context specific: in fore dune shrublands, functionally distinct graminoid, herb and climber rather than shrub growth forms had significantly reduced species richness following bitou invasion. However, in forested hind dunes, the functionally similar native shrub growth form had significantly reduced species richness following bitou invasion. Density of vegetation structure increased at the shrub level in both fore and hind dune invaded communities compared with non-invaded communities. Fore dune ground-level vegetation density declined at invaded sites compared with non-invaded sites, reflecting significant reductions in herb and graminoid species richness. Hind dune canopy-level vegetation density was reduced at invaded compared with non-invaded sites. Bitou bush invasion also affected fore dune community variability with significant increases in variability of species abundances observed in invaded compared with non-invaded sites. In contrast, variability among all hind dune sites was similar. The results suggest that effects of bitou bush invasion are mediated by the vegetation community. When bitou bush becomes abundant, community structure and functioning may be compromised.     

Ecological Invasion,Roughened Fronts,and a Competitor’s Extreme Advance: Integrating Stochastic Spatial-Growth Models

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a “roughened” front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner’s relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front’s mean position. We find that a class of models with different assumptions about neighborhood interactions exhibits universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.     

Spatial dynamics of invasion: the geometry of introduced species

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single- and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almost-deterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.     

Resource-dependent dispersal and the speed of biological invasions

Many mobile organisms exhibit resource-dependent movement in which movement rates adjust to changes in local resource densities through changes in either the probability of moving or the distance moved. Such changes may have important consequences for invasions because reductions in resources behind an invasion front may cause higher dispersal while simultaneously reducing population growth behind the front and thus lowering the number of dispersers. Intuiting how the interplay between population growth and dispersal affects invasions is difficult without mathematical models, yet most models assume dispersal rates are constant. Here we present spatial-spread models that allow for consumer-resource interactions and resource-dependent dispersal. Our results show that when resources affect the probability of dispersal, then the invasion dynamics are no different than if resources did not affect dispersal. When resources instead affect the distance dispersed, however, the invasion dynamics are strongly affected by the strength of the consumer-resource interaction, and population cycles behind the wave front lead to fluctuating rates of spread. Our results suggest that for actively dispersing invaders, invasion dynamics can be determined by species interactions. More practically, our work suggests that reducing invader densities behind the front may be a useful method of slowing an invader's rate of spread.     

Evolutionary game theory as a framework for studying biological invasions

Although biological invasions pose serious threats to biodiversity, they also provide the opportunity to better understand interactions between the ecological and evolutionary processes structuring populations and communities. However, ecoevolutionary frameworks for studying species invasions are lacking. We propose using game theory and the concept of an evolutionarily stable strategy (ESS) as a conceptual framework for integrating the ecological and evolutionary dynamics of invasions. We suggest that the pathways by which a recipient community may have no ESS provide mechanistic hypotheses for how such communities may be vulnerable to invasion and how invaders can exploit these vulnerabilities. We distinguish among these pathways by formalizing the evolutionary contexts of the invader relative to the recipient community. We model both the ecological and the adaptive dynamics of the interacting species. We show how the ESS concept provides new mechanistic hypotheses for when invasions result in long- or short-term increases in biodiversity, species replacement, and subsequent evolutionary changes.     

Population density modifies the ecological impacts of invasive species

In assessments of ecological impact in invasion ecology, most studies compare un‐invaded sites with highly invaded sites, representing the ‘worst‐case scenario’, and so there is little information on how impact is modified by the population density of the invader. Here, we assess how ecological impact is modified by population density through the experimental development of density‐impact curves for a model invasive fish. Using replicated mesocosms and the highly invasive Pseudorasbora parva as the model, we quantified how their population density influenced their diet composition and their impacts on invertebrate communities and ecosystem processes. The density–impact curves revealed both linear and non‐linear density–impact relationships. The relationship between P. parva density and zooplankton body mass was represented by a low‐threshold curve, where their impact was higher at low densities than predicted by a linear relationship. In contrast, whilst the relationship between density and zooplankton biomass and abundance was also non‐linear, it was high‐threshold, indicating a lower impact than a linear relationship would predict. Impacts on diversity and phytoplankton standing stock were linear and impacts on benthic invertebrate abundance and decomposition rates were represented by s‐shaped curves. These relationships were underpinned by P. parva dietary analyses that revealed increasing reliance on zooplankton as density increased due to depletion of other resources. We caution against the common assumption that ecological impact increases linearly with invader density and suggest that increased understanding of the relationship between invader population density and ecological impact can avoid under‐investment in the management of invaders that cause severe problems at low densities.     

Estimating the impact of oyster restoration scenarios on transient fish production

Oyster reef restoration projects are increasing in number both to enhance oyster density and to retain valuable ecosystem services provided by oyster reefs. Although some oyster restoration projects have demonstrated success by increasing density and biomass of transient fish, it still remains a challenge to quantify the effects of oyster restoration on transient fish communities. We developed a bioenergetics model to assess the impact of selected oyster reef restoration scenarios on associated transient fish species. We used the model to analyze the impact of changes in (1) oyster population carrying capacity; (2) oyster population growth rate; and (3) diet preference of transient fish on oyster reef development and associated transient fish species. Our model results indicate that resident fish biomass is directly affected by oyster restoration and oyster biomass, and oyster restoration can have cascading impacts on transient fish biomass. Furthermore, the results highlight the importance of a favorable oyster population growth rate during early restoration years, as it can lead to rapid increases in mean oyster biomass and biomass of transient fish species. The model also revealed that a transient fish's diet solely dependent on oyster reef‐derived prey could limit the biomass of transient fish species, emphasizing the importance of habitat connectivity in estuarine areas to enhance transient fish species biomass. Simple bioenergetics models can be developed to understand the dynamics of a system and make qualitative predictions of management and restoration scenarios.     

Biodiversity influences invasion success of a facultative epiphytic seaweed in a marine forest

The biotic resistance hypothesis predicts that more diverse communities should have greater resistance to invasions than species-poor communities. However for facultative and obligate epiphytic invaders a high native species richness, abundance and community complexity might provide more resources for the invader to thrive to. We conducted surveys across space and time to test for the influence of native algal species abundance and richness on the abundance of the invasive facultative epiphytic filamentous alga Lophocladia lallemandii in a Mediterranean Cystoseira balearica seaweed forest. By removing different functional groups of algae, we also tested whether these relationships were dependent on the complexity and abundance of the native algal community. When invasion was first detected, Lophocladia abundance was positively related to species richness, but the correlation became negative after two years of invasion. Similarly, a negative relationship was also observed across sites. The removal experiment revealed that more complex native communities were more heavily invaded, where also a positive relationship was found between native algal richness and Lophocladia, independently of the native algal abundance. Our observational and experimental data show that, at early stages of invasion, species-rich seaweed forests are not more resistant to invasion than species-poor communities. Higher richness of native algal species may increase resource availability (i.e. substrate) for invader establishment, thus facilitating invasion. After the initial invasion stage, native species richness decreases with time since invasion, suggesting negative impacts of invasive species on native biodiversity.     

Coexistence and Spread of Competitors in Heterogeneous Landscapes

Competition between species is ubiquitous in nature and therefore widely studied in ecology through experiment and theory. One of the central questions is under which conditions a (rare) invader can establish itself in a landscape dominated by a resident species at carrying capacity. Applying the same question with the roles of the invader and resident reversed leads to the principle that “mutual invasibility implies coexistence.” A related but different question is how fast a locally introduced invader spreads into a landscape (with or without competing resident), provided it can invade. We explore some aspects of these questions in a deterministic, spatially explicit model for two competing species with discrete non-overlapping generations in a patchy periodic environment. We obtain threshold values for fragmentation levels and dispersal distances that allow for mutual invasion and coexistence even if the non-spatial competition model predicts competitive exclusion. We obtain exact results when dispersal is governed by a Laplace kernel. Using the average dispersal success, we develop a mathematical framework to obtain approximate results that are independent of the exact dispersal patterns, and we show numerically that these approximations are very accurate.