Mathematical models for invasive species management: Grey squirrel control on Anglesey

Immune interactions and heterogeneity in transmission drives the pathogen-mediated invasion of grey squirrels in the UK

Mathematical models highlighted the importance of pathogen-mediated invasion, with the replacement of red squirrels by squirrelpox virus (SQPV) carrying grey squirrels in the UK, a well-known example. In this study, we combine new epidemiological models, with a range of infection characteristics, with recent longitudinal field and experimental studies on the SQPV dynamics in red and grey squirrel populations to better infer the mechanistic basis of the disease interaction. A key finding is that a model with either partial immunity or waning immunity and reinfection, where individuals become seropositive on the second exposure to infection, that up to now has been shown in experimental data only, can capture the key aspects of the field study observations. By fitting to SQPV epidemic observations in isolated red squirrel populations, we can infer that SQPV transmission between red squirrels is significantly (4×) higher than the transmission between grey squirrels and as a result our model shows that disease-mediated replacement of red squirrels by greys is considerably more rapid than replacement in the absence of SQPV. Our findings recover the key results of the previous model studies, which highlights the value of simple strategic models that are appropriate when there are limited data, but also emphasise the likely complexity of immune interactions in wildlife disease and how models can help infer disease processes from field data.

Partial differential equation models for invasive species spread in the presence of spatial heterogeneity

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread which appear qualitatively similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasions and must be considered when designing models of invasive species spread.

Exploring the effects of competition and predation on the success of biological invasion through mathematical modeling

Biological invasions are a major cause of species extinction and biodiversity loss. Exotic predators are the type of introduced species that have the greatest negative impact, causing the extinction of hundreds of native species. Despite this, they continue to be intentionally introduced by humans. Understanding the causes that determine the success of these invasions is a challenge within the field of invasion biology. Mathematical models play a crucial role in understanding and predicting the behavior of exotic species in different ecosystems. This study examines the effect of predation and competition on the invasion success of an exotic generalist predator in a native predator-prey system. Considering that the exotic predator both consumes the native prey and competes with the native predator, it is necessary to study the interplay between predation and competition, as one of these interspecific interactions may either counteract or contribute to the impact of the other on the success of a biological invasion. Through a mathematical model, represented by a system of ordinary differential equations, it is possible to describe four different scenarios upon the arrival of the exotic predator in a native predator-prey system. The conditions for each of these scenarios are described analytically and numerically. The numerical simulations are performed considering the American mink (Mustela vison), an invasive generalist predator. The results highlight the importance of considering the interplay between interspecific interactions for understanding biological invasion success.

Brood size in an uncertain world

Reproduction in an uncertain world is fraught. The consequences of investing in too many offspring in a resource poor season can be disastrous but so too is missing the opportunity of a resource rich year. We consider a simple population and individual growth model and use Lyapunov exponents to find analytical results for the optimum brood size under stochastic environmental conditions. We show that if the environment shows dramatic changes between breeding seasons choosing a smaller brood size is more likely to be successful but the best strategy is to synchronize your reproduction to the food availability. Finally, we show that if the cost of having offspring is high it can be better to live in a highly varying world with a plastic strategy that synchronizes to the environment than to live in a deterministic world with a constant strategy, a finding with implications for invasive species and climate change.

Interactions between native and invasive species: A systematic review of the red squirrel-gray squirrel paradigm

The eastern gray squirrel (Sciurus carolinensis) has been labeled as one of the 100 worst invasive alien species by the IUCN. In Europe, the species has been introduced to Britain, Ireland and Italy, and its subsequent spread has resulted in wide-scale extinction of native Eurasian red squirrels (Sciurus vulgaris) from the areas colonized by the gray squirrel. This replacement of a native by an alien competitor is one of the best documented cases of the devastating effects of biological invasions on native fauna. To understand how this replacement occurs, we present a systematic review of the literature on competition and interactions between red and gray squirrels. We describe the patterns of red and gray squirrel distribution in those parts of Europe where gray squirrels occur and summarize the evidence on the different processes and mechanisms determining the outcome of competition between the native and alien species including the influence of predators and pathogens. Some of the drivers behind the demise of the red squirrel have been intensively studied and documented in the past 30 years, but recent field studies and mathematical models revealed that the mechanisms underlying the red-gray paradigm are more complex than previously thought and affected by landscape-level processes. Therefore, we consider habitat type and multi-species interactions, including host-parasite and predator-prey relationships, to determine the outcome of the interaction between the two species and to better address gray squirrel control efforts.

An Opportunistic Assessment of the Impact of Squirrelpox Disease Outbreaks upon a Red Squirrel Population Sympatric with Grey Squirrels in Wales

Simple Summary

In Europe, squirrelpox virus is carried by non-native grey squirrels and spread into native red squirrel populations. The virus causes a large proportion of infected red squirrels to die and contributes to local declines and the replacement by grey squirrels. There are relatively few published studies quantifying the impact of disease amongst red squirrels. We present findings from a short-term study in north Wales, United Kingdom.

Abstract

Native red squirrels (Sciurus vulgaris) persisted in the coastal mainland woodlands of northern Gwynedd whilst sympatric with an invasive grey squirrel (Sciurus carolinensis) population suppressed by culling. Squirrelpox disease in the red squirrel population was recorded in 2017 and 2020/21. An autumn 2020 outbreak was associated with only 17.4% of animals caught and marked in the preceding June known to be present in March 2021. Despite an opportunistic data collection lacking the rigour of empirical experimental design, we observed low local survival rates similar to previously published accounts reported during major squirrelpox outbreaks. The use of a conservation dog to detect red squirrel carcasses resulted in positive detection and confirmation of a temporal and spatial expansion of one disease outbreak. The study is the first in Wales to use conservation dogs and the findings reinforce the vital strategic importance of geographical isolation reducing sympatry of red with grey squirrels in European regions where the introduced congener is a source of the squirrelpox infection.

Infection dynamics in ecosystems: on the interaction between red and grey squirrels, pox virus, pine martens and trees

Ecological and epidemiological processes and interactions influence each other, positively and negatively, directly and indirectly. The invasion potential of pathogens is influenced by the ecosystem context of their host species' populations. This extends to the capacity of (multiple) host species to maintain their (common) pathogen and the way pathogen dynamics are influenced by changes in ecosystem composition. This paper exemplifies these interactions and consequences in a study of red and grey squirrel dynamics in the UK. Differences and changes in background habitat and trophic levels above and below the squirrel species lead to different dynamic behaviour in many subtle ways. The range of outcomes of the different interactions shows that one has to be careful when drawing conclusions about the mechanisms and processes involved in explaining observed phenomena concerning pathogens in their natural environment. The dynamic behaviour also shows that planning interventions, for example for conservation purposes, benefits from understanding the complexity of interactions beyond the particular pathogen and its threatened host species.

Natural strongholds for red squirrel conservation in Scotland

The Eurasian Red Squirrel (Sciurus vulgaris) is under threat from the invasive North American eastern Grey Squirrel (Sciurus carolinensis) with 80% of the remaining red squirrel populations in the British Isles found in Scotland. In this study we develop a spatially explicit mathematical model of the red and grey squirrel system and use it to assess the population viability of red squirrels across Scotland. In particular, we aim to identify existing forests – natural strongholds for red squirrels – that can successfully support red squirrels under UK Forestry Standard management and protect them from potential disease-mediated competition from grey squirrels. Our model results indicate that if current levels of grey squirrel control, which restrict or reduce the distribution of grey squirrels, are continued then there will be large expanses of forests in northern Scotland that support viable red squirrel populations. Model results that represent (hypothetical) scenarios where grey squirrel control no longer occurred indicated that grey squirrel range expansion and the process of red squirrel replacement would be slow. Model results for an assumed worst-case scenario where grey squirrels have expanded to all regions in Scotland identified forest regions – denoted natural strongholds – that could currently support red squirrels under UK Forestry Standard management practice. The results will be used to inform forest management policy and support a strategic review of red squirrel management by land management agencies and other stakeholders.

Meta-modeling on detailed geography for accurate prediction of invasive alien species dispersal

Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematical approaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on the assumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can be considered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in different situations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC) to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suited to handle important landscape heterogeneities as elevation and the complex geometries associated with the boundaries of an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing the uncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain.