Modeling invasive species spread in Lake Champlain via evolutionary computations

We use a reaction diffusion equation, together with a genetic algorithm approach for model selection to develop a general modeling framework for biological invasions. The diffusion component of the reaction diffusion model is generalized to include dispersal and advection. The reaction component is generalized to include both linear and non-linear density dependence, and Allee effect. A combination of the reaction diffusion and genetic algorithm is able to evolve the most parsimonious model for invasive species spread. Zebra mussel data obtained from Lake Champlain, which demarcates the states of New York and Vermont, is used to test the appropriateness of the model. We estimate the minimum wave spread rate of Zebra mussels to be 22.5 km/year. In particular, the evolved models predict an average northward advection rate of 60.6 km/year (SD ± 1.9), which compares very well with the rate calculated from the known hydrologic residence time of 60 km/year. A combination of a reaction diffusion model and a genetic algorithm is, therefore, able to adequately describe some of the hydrodynamic features of Lake Champlain and the spread of a typical invasive species—Zebra mussels within the lake.     

Developing dynamic mechanistic species distribution models: predicting bird-mediated spread of invasive plants across northeastern North America

Species distribution models are a fundamental tool in ecology, conservation biology, and biogeography and typically identify potential species distributions using static phenomenological models. We demonstrate the importance of complementing these popular models with spatially explicit, dynamic mechanistic models that link potential and realized distributions. We develop general grid-based, pattern-oriented spread models incorporating three mechanisms--plant population growth, local dispersal, and long-distance dispersal--to predict broadscale spread patterns in heterogeneous landscapes. We use the model to examine the spread of the invasive Celastrus orbiculatus (Oriental bittersweet) by Sturnus vulgaris (European starling) across northeastern North America. We find excellent quantitative agreement with historical spread records over the last century that are critically linked to the geometry of heterogeneous landscapes and each of the explanatory mechanisms considered. Spread of bittersweet before 1960 was primarily driven by high growth rates in developed and agricultural landscapes, while subsequent spread was mediated by expansion into deciduous and coniferous forests. Large, continuous patches of coniferous forests may substantially impede invasion. The success of C. orbiculatus and its potential mutualism with S. vulgaris suggest troubling predictions for the spread of other invasive, fleshy-fruited plant species across northeastern North America.     

Population dynamic models of the spread of Wolbachia

Wolbachia are endosymbionts that are found in many insect species and can spread rapidly when introduced into a naive host population. Most Wolbachia spread when their infection frequency exceeds a threshold normally calculated using purely population genetic models. However, spread may also depend on the population dynamics of the insect host. We develop models to explore interactions between host population dynamics and Wolbachia infection frequency for an age-structured insect population regulated by larval density dependence. We first derive a new expression for the threshold frequency that extends existing theory to incorporate important details of the insect's life history. In the presence of immigration and emigration, the threshold also depends on the form of density-dependent regulation. We show how the type of immigration (constant or pulsed) and the temporal dynamics of the host population can strongly affect the spread of Wolbachia. The results help understand the natural dynamics of Wolbachia infections and aid the design of programs to introduce Wolbachia to control insects that are disease vectors or pests.     

Evolutionarily labile species interactions and spatial spread of invasive species

Both exotic and native species have been shown to evolve in response to invasions, yet the impacts of rapidly evolving interactions between novel species pairs have been largely ignored in studies of invasive species spread. Here, I use a mathematical model of an interacting invasive predator and its native prey to determine when and how evolutionary lability in one or both species might impact the dynamics of the invader's spatial advance. The model shows that evolutionarily labile invaders continually evolve better adapted phenotypes along the moving invasion front, offering an explanation for accelerating spread and spatial phenotype clines following invasion. I then analytically derive a formula to estimate the relative change in spread rate due to evolution. Using parameter estimates from the literature, this formula shows that moderate heritabilities and selection strengths are sufficient to account for changes in spread rates observed in historical and ongoing invasions. Evolutionarily labile native species can slow invader spread when genes flow from native populations with exposure to the invader into native populations ahead of the invasion front. This outcome is more likely in systems with highly diffuse native dispersal, net directional movement of natives toward the invasion front, or human inoculation of uninvaded native populations.     

Landscape diversity slows the spread of an invasive forest pest species

According to the associational resistance hypothesis, diverse habitats provide better resistance to biological invasions than monocultures. Host‐plant abundance has been shown to affect the range expansion of invasive pests, but the effect of landscape diversity (i.e. density of host/non‐host patches and diversity of forest habitat patches) on invasions remains largely untested. We used boundary displacement models and boosted regression tree analyses to investigate the effects of landscape diversity on the invasion of Corsica by the maritime pine bast scale Matsucoccus feytaudi over an 18‐yr period. Taking the passive wind dispersal of the scale into account, we showed that open habitats and connectivity between host patches accelerated spread by up to 13%, whereas landscapes with high tree diversity and a high density of non‐host trees decreased scale spread by up to 14%. We suggest a new mechanism for such associational resistance to pest invasion at the landscape level, which we term ‘the pitfall effect’.     

Modeling the spread of invasive nutrias (Myocastor coypus) over Iran

Nutria (Myocastor coypus) is a native aquatic rodent to South America, and was introduced to Europe, Asia, Africa and North America for fur farming. The South American nutria or coypu is now considered a pest in the area of introduction, because of its negative impact on biological diversity and ecological relationships. Having information on the invasion range of exotic species is crucial for understanding the ecology of invasive spread and for making good conservation and management planning to address this problem. At the beginning of the 20th century, nutria was introduced into Asia. Nutria was recorded for the first time in Iran in 1995. In the present study we proposed a multiple spatial scale approach to predict the invasion trends of the nutria in Iran, and to define up the “suitable scale” for predicting the invasion trends of this species. Our results highlighted the importance of environmental variables including vegetation density (for food and nesting) and water resource (streams, rivers, and lakes) in distribution of the nutria. Potential areas for the presence of the nutria are located near the Caspian Sea, west and central Iran which receive more precipitation than other parts of the country. Therefore, these parts of Iran may face a much greater risk of invasion risk in the future. Moreover, these results can show the possible risk of nutria invasion to the northern and western neighbors of Iran.     

Social personality polymorphism and the spread of invasive species: a model

Ecological invasions are a major worldwide problem exacting tremendous economic and ecological costs. Efforts to explain variability in invasion speed and impact by searching for combinations of ecological conditions and species traits associated with invasions have met with mixed success. We use a simulation model that integrates insights from life-history theory, animal personalities, network theory, and spatial ecology to derive a new mechanism for explaining variation in animal invasion success. We show that spread occurs most rapidly when (1) a species includes a mix of life-history or personality types that differ in density-dependent performance and dispersal tendencies, (2) the differences between types are of intermediate magnitude, and (3) patch connections are intermediate in number and widely spread. Within-species polymorphism in phenotype (e.g., life-history strategies or personality), a feature not included in previous models, is important for overcoming the fact that different traits are associated with success in different stages of the invasion process. Polymorphism in sociability (a personality type) increases the speed of the invasion front, since asocial individuals colonize empty patches and facilitate the local growth of social types that, in turn, induce faster dispersal by asocials at the invasion edge. The results hold implications for the prediction of invasion impacts and the classification of traits associated with invasiveness.     

Modeling species dispersal with occupancy urn models

Models for species dispersal make various simplifications to facilitate analysis, such as ignoring spatial correlations or assuming equal probability of colonization among all sites within a dispersal neighborhood. Here we introduce a variation of the basic contact process (BCP) which allows us to separate the number of offspring produced from the neighborhood size, which are confounded in the original BCP. We then use classical results arising from probability models involving placing balls in urns to study our modified BCP, obtaining bounds for the critical value of the survival probability needed for the population to persist. We also use the probability urn calculations with a local-dispersal mean-field approximation to estimate equilibrium population density. These methods are able to include features such as unequal dispersal probabilities to different sites in the neighborhood, e.g., as would arise when dispersers have a fixed rate of mortality per distance traveled from the parent site. We also show how urn models allow one to generalize these results to two species competing for space.     

Modeling the presence probability of invasive plant species with nonlocal dispersal

Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by Mollison (J R Stat Soc 39(3):283, 1977). We derive the deterministic integro-differential equation of a more general contact model and show that the quantity of interest may be interpreted not as population size, but rather as the probability of species occurrence. We proceed to show how landscape heterogeneity can be included in the model by utilizing the concept of statistical habitat suitability models which condense diverse ecological data into a single statistic. As ecologists often deal with species presence data rather than population size, we argue that a model for probability of occurrence allows for a realistic determination of initial conditions from data. Finally, we present numerical results of our deterministic model and compare them to simulations of the underlying stochastic process.     

Use of niche models in invasive species risk assessments

Risk maps summarizing landscape suitability of novel areas for invading species can be valuable tools for preventing species’ invasions or controlling their spread, but methods employed for development of such maps remain variable and unstandardized. We discuss several considerations in development of such models, including types of distributional information that should be used, the nature of explanatory variables that should be incorporated, and caveats regarding model testing and evaluation. We highlight that, in the case of invasive species, such distributional predictions should aim to derive the best hypothesis of the potential distribution of the species by using (1) all distributional information available, including information from both the native range and other invaded regions; (2) predictors linked as directly as is feasible to the physiological requirements of the species; and (3) modelling procedures that carefully avoid overfitting to the training data. Finally, model testing and evaluation should focus on well-predicted presences, and less on efficient prediction of absences; a k-fold regional cross-validation test is discussed.     

Optimizing the location of watercraft inspection stations to slow the spread of aquatic invasive species

The accidental spread of aquatic invasive species (AIS) by recreational boaters is a major concern of state and county environmental planners in the USA. While programs for watercraft inspection to educate boaters and slow AIS spread are common practice, large numbers of boats and waterbodies, together with limited budgets, make program design difficult. To facilitate program design, we developed an integer programming model for allocation of scarce inspection resources among lakes. Our model uses species-specific infestation status of lakes and estimates of boat movement between lakes. The objective is to select lakes for inspection stations to maximize the number of risky boats inspected, where risky boats are ones that move from infested to uninfested lakes. We apply our model in Stearns County in central Minnesota, USA, to prioritize lakes for inspection stations and evaluate alternative management objectives. With an objective of protecting uninfested lakes within and outside Stearns County, the optimal policy is to locate stations at infested lakes having the most boats departing for uninfested lakes inside and outside the county. With an objective of protecting only Stearns County lakes, the optimal policy is to locate stations at both infested and uninfested lakes having the riskiest boats arriving from within and outside the county and departing to in-county lakes. The tradeoff between these objectives is significant.

     

Community dynamic models of two dioecious tree species

The effects of dioecy on community dynamics were examined by using transition matrix models for two dioecious tree species, one a superior competitor with a narrow dispersal range and the other an inferior competitor with a wide dispersal range. The models are based on tree-by-tree replacements in each identical microsite occupied by either male or female canopy trees of the superior competitor and canopy trees of the inferior competitor. Coexistence of the two species is possible not only because of a trade-off between competitive and dispersal abilities but also because of the existence of a competitor gap, which the superior competitor cannot occupy. The competitor gap is created under the male trees of the superior competitor. The inferior competitor occupies the competitor gap because of its wide dispersal range. The relative abundance of the two species depends on the dispersal ability and sex ratios of the superior competitor. The decreasing dispersal ability and the female abundance of the superior competitor increase the competitor gap, which allows the regeneration of the inferior competitor.An erratum to this article can be found at     

Modeling the spread of Phytophthora

We consider a model for the morphology and growth of the fungus-like plant pathogen Phytophthora using the example of Phytophthora plurivora. Here, we are utilizing a correlated random walk describing the density of tips. This random walk incorporates a delay in branching behavior: newly split tips only start to grow after a short while. First, we question the effect of such a delay on the running fronts, for uniform- as well as non-uniform turning kernels. We find that this delay primarily influences the slope of the front and therewith the way of spatial appropriation, and not its velocity. Our theoretical predictions are confirmed by the growth of Phytophthora in concrete experiments performed in Petri dishes. The second question addressed in this paper, concerns the manner tips are interacting, especially the point why tips stop to grow “behind” the interface of the front, respectively in confrontation experiments at the interface between two colonies. The combination of experimental data about the spatially structured time course of the glucose concentration and simulations of a model taking into account both, tips and glucose, reveals that nutrient depletion is most likely the central mechanism of tip interaction and hyphal growth inhibition. We presume that this is the growing mechanism for our kind of Phytophthora in infected plant tissue. Thus, the pathogen will sap its hosts via energy depletion and tissue destruction in infected areas.     

The habitat and conduit functions of roads in the spread of three invasive plant species

Nonnative plant species commonly occur along roadsides, and populations are often assumed to invade by spread along the road axis. To distinguish between the function of roadsides as movement corridors and as habitat, nonnative plant species were surveyed along roads in deciduous forest sites in southeastern Ohio, USA. The importance of road proximity was tested by comparing nonnative species abundance in 100 m transects along roads with transects in undisturbed forest. Nonnative species were most abundant and most frequently observed in roadside sites in valleys. Three common species were chosen for closer scrutiny. In a seed sowing experiment roads and open sites proved to be better locations for the germination and growth of Microstegium vimineum than non-roadside and closed-canopy sites. Tussilago farfara and Rosa multiflora occurred in a small number of disjunct patches suggesting infrequent arrival in the sampled transects. Both species were strongly clustered at scales consistent with diffusive spread by vegetative growth and short-range seed dispersal. Comparisons of distributions parallel and perpendicular to roads showed no evidence for enhanced dispersal along the road axis. Microstegium distributions were correlated with local light availability implying site saturation. Microstegium micro-distributions suggested that spread along the road axis was facilitated by movement of dormant seeds in road maintenance. Thus, roadsides appear to function as both habitat and a conduit for population expansion, with the rate of spread dependent on the life history of the individual species. These results suggest a hierarchical process of regional invasion, with different dispersal mechanisms functioning at different spatial scales.     

Modeling the eradication of invasive mammals using the sterile male technique

Large vertebrates, like the domestic goat (Capra hircus), have been transported all over the world and are an ecological disaster to numerous island and mainland ecosystems. Eradication measures for such species are generally centered on lethal methods of removing individuals, an increasingly difficult process as populations become smaller and individual animals become much more difficult to detect. In addition, methods of lethal removal are becoming less desirable in the public eye, prompting the necessity to explore alternatives. Here we investigate the use of the sterile males technique as an effective strategy in the eradication of large mammals. The results of our simulations suggest that the use of sterile males as a single strategy would only be an effective measure to eradicate relatively small (no more than 100 individuals) isolated feral vertebrate populations. However, our results indicate that the technique could be employed as a successful and potentially cost-effective end-point complement to lethal control and/or as a preventative measure against re-invasion.     

Diffusion versus network models as descriptions for the spread of prion diseases in the brain

In this paper we will discuss different modeling approaches for the spread of prion diseases in the brain. Firstly, we will compare reaction-diffusion models with models of epidemic diseases on networks. The solutions of the resulting reaction-diffusion equations exhibit traveling wave behavior on a one-dimensional domain, and the wave speed can be estimated. The models can be tested for diffusion-driven (Turing) instability, which could present a possible mechanism for the formation of plaques. We also show that the reaction-diffusion systems are capable of reproducing experimental data on prion spread in the mouse visual system. Secondly, we study classical epidemic models on networks, and use these models to study the influence of the network topology on the disease progression.