Exact asymptotic analysis for metapopulation dynamics on correlated dynamic landscapes

We compute the mean patch occupancy for a stochastic, spatially explicit patch-occupancy metapopulation model on a dynamic, correlated landscape, using a mathematically exact perturbation expansion about a mean-field limit that applies when dispersal range is large. Stochasticity in the metapopulation and landscape dynamics gives negative contributions to patch occupancy, the former being more important at high occupancy and the latter at low occupancy. Positive landscape correlations always benefit the metapopulation, but are only significant when the correlation length is comparable to, or smaller than, the dispersal range. Our analytical results allow us to consider the importance of spatial kernels in all generality. We find that the shape of the landscape correlation function is typically unimportant, and that the variance is overwhelmingly the most important property of the colonisation kernel. However, short-range singularities in either the colonisation kernel or landscape correlations can give rise to qualitatively different behaviour

Evaluating undercounts in epidemics: response to Maruotti et al. 2022

Maruotti et al. 2022 used a mark-recapture approach to estimate bounds on the true number of monkeypox infections in various countries. These approaches are fundamentally flawed; it is impossible to estimate undercounting based solely on a single stream of reported cases. Simulations based on a Richards curve for cumulative incidence show that, for reasonable epidemic parameters, the proposed methods estimate bounds on the ascertainment ratio of $\approx 0.2-0.5$ roughly independently of the true ascertainment ratio. These methods should not be used

Simple guide to starting a research group

Conducting cutting-edge research and scholarship becomes more complicated with each passing year; forming a collaborative research group offers a way to navigate this increasing complexity. Yet many individuals whose work might benefit from the formation of a collaborative team may feel overwhelmed by the prospect of attempting to build and maintain a research group. We propose this simple guide for starting and maintaining such an enterprise

Modelling long-distance seed dispersal in heterogeneous landscapes.

1. Long-distance seed dispersal is difficult to measure, yet key to understanding plant population dynamics and community composition. 2. We used a spatially explicit model to predict the distribution of seeds dispersed long distances by birds into habitat patches of different shapes. All patches were the same type of habitat and size, but varied in shape. They occurred in eight experimental landscapes, each with five patches of four different shapes, 150 m apart in a matrix of mature forest. The model was parameterized with smallscale movement data collected from field observations of birds. In a previous study we validated the model by testing its predictions against observed patterns of seed dispersal in real landscapes with the same types and spatial configuration of patches as in the model. 3. Here we apply the model more broadly, examining how patch shape influences the probability of seed deposition by birds into patches, how dispersal kernels (distributions of dispersal distances) vary with patch shape and starting location, and how movement of seeds between patches is affected by patch shape. 4. The model predicts that patches with corridors or other narrow extensions receive higher numbers of seeds than patches without corridors or extensions. This pattern is explained by edgefollowing behaviour of birds. Dispersal distances are generally shorter in heterogeneous landscapes (containing patchy habitat) than in homogeneous landscapes, suggesting that patches divert the movement of seed dispersers, ‘holding’ them long enough to increase the probability of seed defecation in the patches. Dispersal kernels for seeds in homogeneous landscapes were smooth, whereas those in heterogenous landscapes were irregular. In both cases, long-distance (> 150 m) dispersal was surprisingly common, usually comprising approximately 50% of all dispersal events. 5. Synthesis . Landscape heterogeneity has a large influence on patterns of long-distance seed dispersal. Our results suggest that long-distance dispersal events can be predicted using spatially explicit modelling to scale-up local movements, placing them in a landscape context. Similar techniques are commonly used by landscape ecologists to model other types of movement; they offer much promise to the study of seed dispersal

Toward a comprehensive system for constructing compartmental epidemic models

Compartmental models are valuable tools for investigating infectious diseases. Researchers building such models typically begin with a simple structure where compartments correspond to individuals with different epidemiological statuses, e.g., the classic SIR model which splits the population into susceptible, infected, and recovered compartments. However, as more information about a specific pathogen is discovered, or as a means to investigate the effects of heterogeneities, it becomes useful to stratify models further -- for example by age, geographic location, or pathogen strain. The operation of constructing stratified compartmental models from a pair of simpler models resembles the Cartesian product used in graph theory, but several key differences complicate matters. In this article we give explicit mathematical definitions for several so-called ``model products'' and provide examples where each is suitable. We also provide examples of model stratification where no existing model product will generate the desired result

Modelling collective cell behaviour

The classical mean-field approach to modelling biological systems makes a number of simplifying assumptions which typically lead to coupled systems of reaction-diffusion partial differential equations. While these models have been very useful in allowing us to gain important insights into the behaviour of many biological systems, recent experimental advances in our ability to track and quantify cell behaviour now allow us to build more realistic models which relax some of the assumptions previously made. This brief review aims to illustrate the type of models obtained using this approach

Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page