An approximate Bayesian computation approach for estimating parameters of complex environmental processes in a cellular automata

Modelling an environmental process involves creating a model structure and parameterising the model with appropriate values to accurately represent the process. Determining accurate parameter values for environmental systems can be challenging. Existing methods for parameter estimation typically make assumptions regarding the form of the Likelihood, and will often ignore any uncertainty around estimated values. This can be problematic, however, particularly in complex problems where Likelihoods may be intractable. In this paper we demonstrate an Approximate Bayesian Computational method for the estimation of parameters of a stochastic CA. We use as an example a CA constructed to simulate a range expansion such as might occur after a biological invasion, making parameter estimates using only count data such as could be gathered from field observations. We demonstrate ABC is a highly useful method for parameter estimation, with accurate estimates of parameters that are important for the management of invasive species such as the intrinsic rate of increase and the point in a landscape where a species has invaded. We also show that the method is capable of estimating the probability of long distance dispersal, a characteristic of biological invasions that is very influential in determining spread rates but has until now proved difficult to estimate accurately.

Are alien fish a reliable indicator of river health?

1. The ability of many introduced fish species to thrive in degraded aquatic habitats and their potential to impact on aquatic ecosystem structure and function suggest that introduced fish may represent both a symptom and a cause of decline in river health and the integrity of native aquatic communities. 2. The varying sensitivities of many commonly introduced fish species to degraded stream conditions, the mechanism and reason for their introduction and the differential susceptibility of local stream habitats to invasion because of the environmental and biological characteristics of the receiving water body, are all confounding factors that may obscure the interpretation of patterns of introduced fish species distribution and abundance and therefore their reliability as indicators of river health. 3. In the present study, we address the question of whether alien fish (i.e. those species introduced from other countries) are a reliable indicator of the health of streams and rivers in south-eastern Queensland, Australia. We examine the relationships of alien fish species distributions and indices of abundance and biomass with the natural environmental features, the biotic characteristics of the local native fish assemblages and indicators of anthropogenic disturbance at a large number of sites subject to varying sources and intensities of human impact. 4. Alien fish species were found to be widespread and often abundant in south-eastern Queensland rivers and streams, and the five species collected were considered to be relatively tolerant to river degradation, making them good candidate indicators of river health. Variation in alien species indices was unrelated to the size of the study sites, the sampling effort expended or natural environmental gradients. The biological resistance of the native fish fauna was not concluded to be an important factor mediating invasion success by alien species. Variation in alien fish indices was, however, strongly related to indicators of disturbance intensity describing local in-stream habitat and riparian degradation, water quality and surrounding land use, particularly the amount of urban development in the catchment. 5. Potential confounding factors that may influence the likelihood of introduction and successful establishment of an alien species and the implications of these factors for river bioassessment are discussed. We conclude that the potentially strong impact that many alien fish species can have on the biological integrity of natural aquatic ecosystems, together with their potential to be used as an initial basis to find out other forms of human disturbance impacts, suggest that some alien species (particularly species from the family Poeciliidae) can represent a reliable 'first cut' indicator of river health.

Cell invasion with proliferation mechanisms motivated by time-lapse data

Cell invasion involves a population of cells which are motile and proliferative. Traditional discrete models of proliferation involve agents depositing daughter agents on nearest- neighbor lattice sites. Motivated by time-lapse images of cell invasion, we propose and analyze two new discrete proliferation models in the context of an exclusion process with an undirected motility mechanism. These discrete models are related to a family of reaction- diffusion equations and can be used to make predictions over a range of scales appropriate for interpreting experimental data. The new proliferation mechanisms are biologically relevant and mathematically convenient as the continuum-discrete relationship is more robust for the new proliferation mechanisms relative to traditional approaches.

Understanding the mechanism behind invasion of African lovegrass

African lovegrass (Eragrostis curvula) is a C4 perennial grass, native to southern Africa, that was accidentally introduced into Australia in the late 1900s as a contaminant of pasture seed. Its utility for pasture improvement and soil conservation was explored because of its recognised ability to grow in areas of low rainfall and on nutrient-poor sandy loams. Several different agronomic types have now been intentionally introduced across Australia. African lovegrass is now found in all Australian states and territories. It is a declared weed in 33 council areas of New South Wales, a declared pest plant in the ACT and Tasmania and a Regionally Prohibited Weed in 5 out of 11 regions in Victoria. Victoria has also placed it in the very serious threat category (Carr et al. 1992). In Queensland, it has yet to be declared except under local law in the Eidsvold shire (Leigh and Walton, in press).

Unravelling the mechanisms behind the invasion of an introduced and now undesirable grass species

The introduction of Eragrostis curvula (African Lovegrass, herafter Lovegrass) for pasture improvement across Australia has not been successful. Instead Lovegrass, a C4 perennial grass originating from Southern African, has proven unpalatable to stock and to have low nutritional value if stocks do eat it. It has spread prolifically along roadsides, stream banks, conservation areas and pastures. Because control efforts have not been effective, our aim was to determine the putative mechanisms responsible for the dominance of Lovegrass, specifically disturbance (selective grazing) and competition.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Predicting invasion in grassland ecosystems: is exotic dominance the real embarrassment of richness?

Invasions have increased the size of regional species pools, but are typically assumed to reduce native diversity. However, global-scale tests of this assumption have been elusive because of the focus on exotic species richness, rather than relative abundance. This is problematic because low invader richness can indicate invasion resistance by the native community or, alternatively, dominance by a single exotic species. Here, we used a globally replicated study to quantify relationships between exotic richness and abundance in grass-dominated ecosystems in 13 countries on six continents, ranging from salt marshes to alpine tundra. We tested effects of human land use, native community diversity, herbivore pressure, and nutrient limitation on exotic plant dominance. Despite its widespread use, exotic richness was a poor proxy for exotic dominance at low exotic richness, because sites that contained few exotic species ranged from relatively pristine (low exotic richness and cover) to almost completely exotic-dominated ones (low exotic richness but high exotic cover). Both exotic cover and richness were predicted by native plant diversity (native grass richness) and land use (distance to cultivation). Although climate was important for predicting both exotic cover and richness, climatic factors predicting cover (precipitation variability) differed from those predicting richness (maximum temperature and mean temperature in the wettest quarter). Herbivory and nutrient limitation did not predict exotic richness or cover. Exotic dominance was greatest in areas with low native grass richness at the site- or regional-scale. Although this could reflect native grass displacement, a lack of biotic resistance is a more likely explanation, given that grasses comprise the most aggressive invaders. These findings underscore the need to move beyond richness as a surrogate for the extent of invasion, because this metric confounds monodominance with invasion resistance. Monitoring species' relative abundance will more rapidly advance our understanding of invasions.

Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

A multi-genome analysis approach enables tracking of the invasion of a single Russian wheat aphid (Diuraphis noxia) clone throughout the New World

This study investigated the population genetics, demographic history and pathway of invasion of the Russian wheat aphid (RWA) from its native range in Central Asia, the Middle East and Europe to South Africa and the Americas. We screened microsatellite markers, mitochondrial DNA and endosymbiont genes in 504 RWA clones from nineteen populations worldwide. Following pathway analyses of microsatellite and endosymbiont data, we postulate that Turkey and Syria were the most likely sources of invasion to Kenya and South Africa, respectively. Furthermore, we found that one clone transferred between South Africa and the Americas was most likely responsible for the New World invasion. Finally, endosymbiont DNA was found to be a high resolution population genetic marker, extremely useful for studies of invasion over a relatively short evolutionary history time frame. This study has provided valuable insights into the factors that may have facilitated the recent global invasion by this damaging pest.