Search

This work was supported by Engineering and Physical Sciences Research Council (EPSRC) grant no. EP/R014604/1. M.C. was funded by the Engineering and Physical Sciences Research Council (EPSRC) grant no. EP/V054236/1. G.M. is supported by the Scottish Government’s Rural and Environment Science and Analytical Services Division (RESAS). J.P-G’s work is supported by funding from the UK Health Security Agency and the UK Department of Health and Social Care. L.P. is funded by the Wellcome Trust, UK and the Royal Society, UK (grant no. 202562/Z/16/Z). L.P. is supported by the UK Research and Innovation (UKRI) through the JUNIPER modelling consortium (grant no. MR/V038613/1). L.P. is also supported by The Alan Turing Institute for Data Science and Artificial Intelligence, UK. R.R was supported by the Natural Environment Research Council (NERC) grant no. NE/T004193/1 and NE/T010355/1, the Engineering and Physical Sciences Research Council (EPSRC) grant no. EP/V054236/1 and the Science and Technology Facilities Council (STFC) grant no. ST/V006126/1. The use of data has been essential throughout the unfolding COVID-19 pandemic. We have needed it to populate our models, inform our understanding, and shape our responses to the disease. However, data has not always been easy to find and access, it has varied in quality and coverage, been difficult to reuse or repurpose. This paper reviews these and other challenges and recommends steps to develop a data ecosystem better able to deal with future pandemics by better supporting preparedness, prevention, detection and response. Publisher PDF

Natural control of invertebrate crop pests has the potential to complement or replace conventional insecticide-based practices, but its mainstream application is hampered by predictive unreliability across agroecosystems. Inconsistent responses of natural pest control to changes in landscape characteristics have been attributed to ecological complexity and system-specific conditions. Here, we review agroecological models and their potential to provide predictions of natural pest control across agricultural landscapes. Existing models have used a multitude of techniques to represent specific crop-pest-enemy systems at various spatiotemporal scales, but less wealthy regions of the world are underrepresented. A realistic representation of natural pest control across systems appears to be hindered by a practical trade-off between generality and realism. Nonetheless, observations of context-sensitive, trait-mediated responses of natural pest control to land-use gradients indicate the potential of ecological models that explicitly represent the underlying mechanisms. We conclude that modelling natural pest control across agroecosystems should exploit existing mechanistic techniques towards a framework of contextually bound generalizations. Observed similarities in causal relationships can inform the functional grouping of diverse agroecosystems worldwide and the development of the respective models based on general, but context-sensitive, ecological mechanisms. The combined use of qualitative and quantitative techniques should allow the flexible integration of empirical evidence and ecological theory for robust predictions of natural pest control across a wide range of agroecological contexts and levels of knowledge availability. We highlight challenges and promising directions towards developing such a general modelling framework. (Less)

Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain changes in fine-scale community dynamics, their effect is sometimes fairly minimal, and demographic scenarios in which this difference is important have not been systematically investigated. We take a simple mean-field model which simulates birth, growth and death processes, and rewrite it with spatially distributed discrete individuals. Each individual's growth and mortality is determined by a competition measure which captures the effects of neighbours in a way which retains the conceptual simplicity of a generic, analytically-solvable model. Although the model is generic, we here parameterise it using data from Caledonian Scots Pine stands. The dynamics of simulated populations, starting from a plantation lattice configuration, mirror those of well-established qualitative descriptions of natural forest stand behaviour; an analogy which assists in understanding the transition from artificial to old-growth structure. When parameterised for Scots Pine populations, the signature of spatial processes is evident, but their effect on first-order statistics, such as density and biomass, is fairly limited. The sensitivity of this result to variation in each individual rate parameter is investigated; distinct differences between spatial and mean-field models are seen only upon alteration of the interaction strength parameters, and in low density populations. Under the Scots pine parameterisation, dispersal also has an effect on spatial structure, but not density and biomass. Only in more intense competitive scenarios does altering the relative scales of dispersal and interaction lead to a clear signal in first order behaviour. The study acts as an important reminder that, even in scenarios where individual processes are localised in space, simple models are often sufficient to capture many population scale aspects of observed ecological dynamics.

Plantation transformation is a goal of increasing interest to silviculturalists. The target forest state is characterised by high variance in age and size, and an irregular spatial structure, which leads to inhomogeneous interactions between, and consequent development of, trees in the stand. This presents a difficulty for traditional methods such as yield tables, and demands a more careful consideration of stand dynamics. On the other hand, while forestry has a great heritage of simulation, the level of complexity implemented at an individual level generally precludes direct understanding of stand scale behaviours, and leads to difficulties in verification with appropriate data. A promising approach is the application of relatively simple models developed by ecologists. These can be adapted to yield accurate representations of forest stands, while being highly amenable to analysis. Motivated by data from Scots pine (Pinus sylvestris L.) stands, we here apply a simple spatial birth-death-growth model to the comparison and analysis of transformation strategies for plantation stands. The model captures the effects of neighbours in a way which retains the conceptual simplicity of a generic, analytically solvable model, while allowing insights into the driving factors of population dynamics. Timing and intensity of management interventions, as opposed to their specific criteria, are of primary importance: thinnings of a moderate intensity performed over a long period produced the best results. Variation in the strategy applied leads to more subtle effects which transformation strategies must also take into account, such as the development of variation in size of the remaining trees (increased using spatially correlated thinnings), the survival chances of regeneration and “underplanted” trees, and the overall productivity of the stand (increased using spatially homogeneous crown thinning). Finally, we demonstrate the robustness of model predictions to fundamental choices of model formulation.

Animal behaviour is often a function of the animal’s physiological state. Groups of animals will often contain individuals with a range of physiological states and the grazing behaviour of herbivores is affected by their physiological state. This study compared the grazing decisions of animals in groups of single and mixed physiological states. Using a grazing model that simulated individual herbivore behaviour in relation to environmental distributions of forage resource (grass) and parasites (faeces), we tested the hypothesis that an animal’s level of parasite exposure via the faecal–oral route is affected by the composition of physiological states in the group. Four physiological states were considered: parasite-naive, parasitized, lactating and parasite-immune animals. Baseline parasite exposure levels for each state were generated by simulating single-state groups and were compared to simulations of each of the six two-state combinations. In single-state groups parasitized animals had the least and lactating animals had the greatest levels of parasite exposure. When co-grazing with lactating animals, parasitized, immune and naive animals increased their parasite exposure, relative to single-state groups. When co-grazing with parasitized animals, lactating, immune and naive animals reduced their parasite exposure, relative to single-state groups. There was no difference in parasite exposure of the immune or naive animals co-grazing together when compared to the single-state groups. These results highlight the need to recognize the impact of the individual when studying group-living animals.

In grazing systems, heterogeneous distributions of forage resources and faeces result in localised accumulations of nutrients and parasites (both macroparasites and microparasites), creating trade-offs between the costs of exposure to infestation or infection and the benefits of nutrient intake. Each contact between livestock and faeces in the environment is a potential parasite/pathogen transmission event. Thus, herbivores must make foraging decisions in complex environments which will affect their intake of both nutrients and parasites. However, the pattern of forage and faecal resources in agricultural environments will also be affected by the grazing management system in place. The aim of this study was to investigate the effect of grazing management on the risk of infection/infestation to livestock. We used a spatially explicit individual based stochastic foraging model to simulate livestock contact (both grazing and investigative) with faeces in the environment. The model was parameterised to simulate cattle grazing under three types of grazing management: set stock (i.e. where sward growth and cattle intake are in equilibrium in a single field); a two pasture rotation grazing system with increasing number of rotations; and a rotational grazing system with two rotations and increasing subdivisions of the pasture. Overall the amount of cattle contact with faecal-contaminated patches was similar in both set stocking and rotational grazing scenarios, suggesting no difference in the risk of infection or infestation between the different systems. However, the timing and absolute amounts of peak contact varied greatly indicating that different grazing management systems expose livestock to risks of different types of parasites at different times of the grazing season. Intensive rotational systems with small pasture blocks (especially the first grazing period) maximised livestock contact with fresh faeces, and thus exposure to microparasites (e.g. bacterial pathogens). Livestock re-entering pasture blocks in rotational systems and set stocked livestock had the highest contact with old faeces and thus have a greater risk of macroparasite transmission (gastrointestinal nematodes). This study highlights how livestock management affects the highly dynamic interaction between livestock and distributions of parasites in the environment and thus the levels of livestock exposure to parasites and pathogens via the faecal-oral route.

Bovine tuberculosis (bTB; Mycobacterium bovis) is a bacterial infection of cattle that also affects certain wildlife species. Culling badgers (Meles meles), the principal wildlife host, results in perturbation of the badger population and an increased level of disease in cattle. Therefore, the priority for future management must be to minimize the risk of disease transmission by finding new ways to reduce the contact rate among the host community. At the farm level, targeting those individuals that represent an elevated risk of transmission might prove to be effective. At the landscape level, risk mapping can provide the basis for targeted surveillance of the host community. Here, we review the current evidence for bTB persistence in Britain and make recommendations for future management and research.

Nonlinear stochastic models are typically intractable to analytic solutions and hence, moment-closure schemes are used to provide approximations to these models. Existing closure approximations are often unable to describe transient aspects caused by extinction behaviour in a stochastic process. Recent work has tackled this problem in the univariate case. In this study, we address this problem by introducing novel bivariate moment-closure methods based on mixture distributions. Novel closure approximations are developed, based on the beta-binomial, zero-modified distributions and the log-Normal, designed to capture the behaviour of the stochastic SIS model with varying population size, around the threshold between persistence and extinction of disease. The idea of conditional dependence between variables of interest underlies these mixture approximations. In the first approximation, we assume that the distribution of infectives (I) conditional on population size (N) is governed by the beta-binomial and for the second form, we assume that I is governed by zero-modified beta-binomial distribution where in either case N follows a log-Normal distribution. We analyse the impact of coupling and inter-dependency between population variables on the behaviour of the approximations developed. Thus, the approximations are applied in two situations in the case of the SIS model where: (1) the death rate is independent of disease status; and (2) the death rate is disease-dependent. Comparison with simulation shows that these mixture approximations are able to predict disease extinction behaviour and describe transient aspects of the process.

The importance of animal selection behaviour in determining spatial structure of grazing systems has implications for sustainable grazing management. Although changes in stocking density provide a mechanism for direct control of animal impact, grazing behaviour is also responsible for influencing vegetation dynamics. A spatially explicit grazing model was used to explore the impact of movement in search of higher intake (search rate) and search distance on spatial sward structure, specifically the distribution of sward surface height. The model simulated a two-stage grazing process in heterogeneous environments i.e. searching then biting. As search rate and search distance increased so the spatial variance of sward structure decreased. Changes in herbivore search rate have a greater impact on spatial variance of pastoral grazing systems than search distance. Herbivores foraging in heterogeneous environments with greater search rates may better utilise the available forage resources. Higher search rates in natural and agricultural systems may determine herbivore fitness and survival or production, respectively.

We examined how decision-making processes at small spatial scales can account for individual movements and food intake at larger scales. Our experiment used two currencies that might affect animal decisions: food reward at the patch scale and spatial distribution of the patches. We used Soay sheep, Ovis aries, as the model species in conjunction with an artificial arena that allowed us to modify food-handling conditions and the distribution of the food patches to record variation in food intake of both sexes. The main variable that affected food intake was how efficient the animals were at avoiding patches that were depleted in previous visits. Intake was also affected by mouth size and the spatial distribution of the feeding stations. Sheep were more efficient at exploiting clustered patches with a high energy reward than a matrix of homogeneously distributed patches of lower energy reward. Females' intake was higher than males'; we discuss this in relation to different foraging strategies related to sexual differences in fibre digestibility and the distribution of food resources of different quality that both sexes might use in field conditions. The results indicated that variation in food-handling conditions at the patch level affects food intake at larger scales, providing support for the hypothesis that animal movement related to grazing activity is a hierarchical process, scaling up from bite size to large spatial scales. However, spatial memory is important for maximizing the use of patchily distributed food.

Stochastic process models are useful in describing a broad range of individual-based phenomena and are increasingly being applied in ecology. However, the estimation of parameters in such models is an important issue which has typically received much less attention than the exploration of model behaviour. The difficulties of parameter estimation are compounded by the fact that in most situations the available data are incomplete in some sense. Here, we demonstrate how methods of Markov chain Monte Carlo (McMC) Gibbs sampling can be combined within reversible-jump Metropolis–Hastings McMC frameworks to produce a hybrid sampler which can be used to obtain estimates of parameters and missing data for a broad class of stochastic process rate models. We apply these methods to two stochastic models arising from the ecology of grazed ecosystems in order to display the benefits of the hybrid sampler and the usefulness of a stochastic modelling approach to experiments where limited data exist.

We demonstrate how unknown process rates within a stochastic modelling framework based on Markov processes can be approximated from time series data using polynomial basis functions. The problem of model selection is considered by adapting basis function selection methods and the minimum description length information criteria which have previously been developed for nonlinear autoregressive models of time series under Gaussian noise assumptions. We investigate the effectiveness of the methods with application to stochastic biological population models.

Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic system x (t)=f(x(t)) into the Ito form d x(t)=f(x(t)) d t+g(x(t)) d w(t) , and show that although the solution to the original ordinary differential equation may explode to infinity in a finite time, with probability one that of the associated stochastic differential equation does not.