Integrating an individual-based model with approximate Bayesian computation to predict the invasion of a freshwater fish provides insights into dispersal and range expansion dynamics

Short-distance dispersal enables introduced alien species to colonise and invade local habitats following their initial introduction, but is often poorly understood for many freshwater taxa. Knowledge gaps in range expansion of alien species can be overcome using predictive approaches such as individual based models (IBMs), especially if predictions can be improved through fitting to empirical data, but this can be challenging for models having multiple parameters. We therefore estimated the parameters of a model implemented in the RangeShifter IBM platform by approximate Bayesian computation (ABC) in order to predict the further invasion of a lowland river (Great Ouse, England) by a small-bodied invasive fish (bitterling Rhodeus sericeus). Prior estimates for parameters were obtained from the literature and expert opinion. Model fitting was conducted using a time-series (1983 to 2018) of sampling data at fixed locations and revealed that for 5 of 11 model parameters, the posterior distributions differed markedly from prior assumptions. In particular, sub-adult maximum emigration probability was substantially higher in the posteriors than priors. Simulations of bitterling range expansion predicted that following detection in 1984, their early expansion involved a relatively high population growth rate that stabilised after five years. The pattern of bitterling patch occupancy was sigmoidal, with 20 % of the catchment occupied after 20 years, increasing to 80 % after 30 years. Predictions were then for 95 % occupancy after 69 years. The development of this IBM thus successfully simulated the range expansion dynamics of this small-bodied invasive fish, with ABC improving the simulation precision. This combined methodology also highlighted that sub-adult dispersal was more likely to contribute to the rapid colonisation rate than expert opinion suggested. These results emphasise the importance of time-series data for refining IBM parameters generally and increasing our understanding of dispersal behaviour and range expansion dynamics specifically

Predicting the outcomes of management strategies for controlling invasive river fishes using individual-based models

1. The effects of biological invasions on native biodiversity have resulted in a range of policy and management initiatives to minimise their impacts. Although management options for invasive species include eradication and population control, empirical knowledge is limited on how different management strategies affect invasion outcomes. 2. An individual based model (IBM) was developed to predict how different removal (‘culling’) strategies affected the abundance and spatial distribution of a virtual, small-bodied, r-selected alien fish (based on bitterling, Rhodeus sericeus) across three types of virtual river catchments (low/intermediate/high branching tributary configurations). It was then applied to nine virtual species of varying life history traits (r- to K-selected) and dispersal abilities (slow/intermediate/fast) to identify trade-offs between the management effort applied in the strategies (as culling rate and the number of patches it was applied to) and their predicted effects. It was also applied to a real-world example, bitterling in the River Great Ouse, England. 3. The IBM predicted that removal efforts were more effective when applied to recently colonized patches. Increasing the cull rate (proportion of individuals removed per patch), and its spatial extent was effective at controlling the invasive population; when both were relatively high, population eradication was predicted. 4. The characteristics of the nine virtual species were the main source of variation in their predicted abundance and spatial distribution. No species were eradicated at cull rates below 70%. Eradication at higher cull rates depended on dispersal ability; slow dispersers required lower rates than fast dispersers, and the latter rapidly re-colonised at low cull rates. Optimum trade-offs between management effort and invasion outcomes were generally when intermediate effort was applied to intermediate numbers of patches. In the Great Ouse, model predictions were that management interventions could restrict bitterling distribution by 2045 to 21% of the catchment (versus 90% occupancy without management). 5. Synthesis and application: This IBM predicted how management efforts can be optimized against invasive fishes, providing a strong complement to risk assessments. We demonstrated that for a range of species’ characteristics, culling can control and even eradicate invasive fish, but only if consistent and relatively high effort is applied

Description of diffusive and propagative behavior on fractals

The known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes. After that, we propose a description developed in the context of the intrinsic metric of fractals, which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime. We show that our approach has a stronger physical justification than previous works on this field. The most important result we present is the introduction of a dependence on time and space for the conductivity in fractals, which is deduced by scaling arguments and supported by computer simulations. Finally, the diffusion equation is used to introduce the possibility of reaction-diffusion processes on fractals and analyze their properties. Specifically, an analytic expression for the speed of the corresponding travelling fronts, which can be of great interest for application purposes, is derived

Invasive species control: incorporating demographic data and seed dispersal into a management model for Rhododendron ponticum

Rhododendron ponticum is a serious invasive alien plant in the British Isles and is of significant conservation and economic concern. Here, we integrate information on both the life-history and spatial dynamics of this species within an individual-based, spatially-explicit model and investigate the effectiveness of different control strategies. Importantly, we simulate seed movement and dispersal using a mechanistic seed dispersal model. We investigate the effectiveness of initiating control at the edge versus the core of the infestation, with and without returning each year to remove seedlings. We compare these results to an age-dependent strategy whereby the oldest plants are removed each year. Age-dependent control, in which the oldest plants were removed first, was the most effective strategy investigated, both in terms of the probability of successful eradication and the number of years taken to control. We demonstrate that this is because the older (and taller) plants towards the core produce more seeds that, on average, travel further. Indeed, our results suggest that the expansion of the invading front is actually driven as much by seeds that disperse long distances from these larger plants as by the seed rain from recently matured plants located much closer to the front. Finally, we investigate the potential use of ‘quarantine lines’ - corridors of unsuitable habitat that are sufficiently wide to contain an infestation, preventing spread to vulnerable areas. This study has provided generic insights into best practice for management based on the current understanding of the biology and ecology of this pernicious, invasive plant

Prospecting and dispersal: their eco-evolutionary dynamics and implications for population patterns

Dispersal is not a blind process, and evidence is accumulating that individual dispersal strategies are informed in most, if not all, organisms. The acquisition and use of information are traits that may evolve across space and time as a function of the balance between costs and benefits of informed dispersal. If information is available, individuals can potentially use it in making better decisions, thereby increasing their fitness. However, prospecting for and using information probably entail costs that may constrain the evolution of informed dispersal, potentially with population-level consequences. By using individual-based, spatially explicit simulations, we detected clear coevolutionary dynamics between prospecting and dispersal movement strategies that differed in sign and magnitude depending on their respective costs. More specifically, we found that informed dispersal strategies evolve when the costs of information acquisition during prospecting are low but only if there are mortality costs associated with dispersal movements. That is, selection favours informed dispersal strategies when the acquisition and use processes themselves were not too expensive. When non-informed dispersal strategies evolve, they do so jointly with the evolution of long dispersal distance because this maximizes the sampling area. In some cases, selection produces dispersal rules different from those that would be ‘optimal’ (i.e. the best possible population performance—in our context quantitatively measured as population density and patch occupancy—among all possible individual movement rules) for the population. That is, on the one hand, informed dispersal strategies led to population performance below its highest possible level. On the other hand, un- and poorly informed individuals nearly optimized population performance, both in terms of density and patch occupancy.Peer reviewe

The interplay of positive and negative species interactions across an environmental gradient: insights from an individual-based simulation model

Positive interspecific interactions are commonplace, and in recent years ecologists have begun to realize how important they can be in determining community and ecosystem dynamics. It has been predicted that net positive interactions are likely to occur in environments characterized by high abiotic stress. Although empirical field studies have started to support these predictions, little theoretical work has been carried out on the dynamic nature of these effects and their consequences for community structure. We use a simple patch-occupancy model to simulate the dynamics of a pair of species living on an environmental gradient. Each of the species can exist as either a mutualist or a cheater. The results confirm the prediction: a band of mutualists tends to occur in environmental conditions beyond the limits of the cheaters. The region between mutualists and cheaters is interesting: population density here is low. Mutualists periodically occupy this area, but are displaced by cheaters, who themselves go extinct in the absence of the mutualists. Furthermore, the existence of mutualists extends the area occupied by the cheaters, essentially increasing their realized niche. Our approach has considerable potential for improving our understanding of the balance between positive and negative interspecific interactions and for predicting the probable impacts of habitat loss and climate change on communities dominated by positive interspecific interactions

Dispersal costs and kin selection have a strong effect on the evolution of migratory strategy

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