Living in groups: spatial-moment dynamics with neighbour-biased movements

Herd formation in animal populations, for example to escape a predator or coordinate feeding, is a widespread phenomenon. Understanding which interactions between individual animals are important for generating such emergent self-organisation has been a key focus of ecological and mathematical research. Here we show the relationship between the algorithmic rules of herd-forming agents, and the mathematical structure of the corresponding spatial-moment dynamics. This entails scaling up from the rules of individual, herd generating behaviour to the macroscopic dynamics of herd structure. The model employs a mechanism for neighbour-dependent, directionally-biased movement to explore how individual interactions generate aggregation and repulsion in groups of animals. Our results show that a combination of mutually attractive and repulsive interactions with different spatial scales is sufficient to lead to the stable formation of groups with a characteristic size

The necessity of tailored control of irrupting pest populations driven by pulsed resources

Resource pulses are widespread phenomena in diverse ecosystems. Irruptions of generalist consumers and corresponding generalist predators often follow such resource pulses. This can have severe implications on the ecosystem and also on the spread of diseases or on regional famines. Suitable management strategies are necessary to deal with these systems. In this study, we develop a general model to investigate optimal control for such a system and apply this to a case study from New Zealand. In particular, we consider the dynamics of beech masting (episodic synchronous seed production) leading to rodent outbreaks and subsequent stoat (Mustela erminea) irruptions. Here, stoat control happens via secondary poisoning. The results show that the main driver of the optimal control timing (June) is the population density of the control vector. Intermediate control levels are superior to higher levels if the generalist consumer is necessary as a control vector. Finally, we extend the model to a two-patch metapopulation model, which indicates that, as a consequence of the strong vector dependence, a strategy of alternating control patches yields better results than static control. This highlights that besides control level, also the design impacts the control success. The results presented in this study reveal important insights for proper pest management in the New Zealand case study. However, they also generally indicate the necessity of tailored control in such systems

Optimal control of irrupting pest populations in a climate-driven ecosystem

Irruptions of small consumer populations, driven by pulsed resources, can lead to adverse effects including the decline of indigenous species or increased disease spread. Broad-scale pest management to combat such effects benefits from forecasting of irruptions and an assessment of the optimal control conditions for minimising consumer abundance. We use a climate-based consumer-resource model to predict irruptions of a pest species (Mus musculus) population in response to masting (episodic synchronous seed production) and extend this model to account for broad-scale pest control of mice using toxic bait. The extended model is used to forecast the magnitude and frequency of pest irruptions under low, moderate and high control levels, and for different timings of control operations. In particular, we assess the optimal control timing required to minimise the frequency with which pests reach ‘plague’ levels, whilst avoiding excessive toxin use. Model predictions suggest the optimal timing for mouse control in beech forest, with respect to minimising plague time, is mid-September. Of the control regimes considered, a seedfall driven biannual-biennial regime gave the greatest reduction in plague time and plague years for low and moderate control levels. Although inspired by a model validated using house mouse populations in New Zealand forests, our modelling approach is easily adapted for application to other climate-driven systems where broad-scale control is conducted on irrupting pest populations

Optimal control of irrupting pest populations in a climate‐driven ecosystem

Irruptions of small consumer populations, driven by pulsed resources, can lead to adverse effects including the decline of indigenous species or increased disease spread. Broadscale pest management to combat such effects benefits from forecasting of irruptions and an assessment of the optimal control conditions for minimising consumer abundance. We use a climate-based consumer-resource model to predict irruptions of a pest species (Mus musculus) population in response to masting (episodic synchronous seed production) and extend this model to account for broad-scale pest control of mice using toxic bait. The extended model is used to forecast the magnitude and frequency of pest irruptions under low, moderate and high control levels, and for different timings of control operations. In particular, we assess the optimal control timing required to minimise the frequency with which pests reach ‘plague’ levels, whilst avoiding excessive toxin use. Model predictions suggest the optimal timing for mouse control in beech forest, with respect to minimising plague time, is mid-September. Of the control regimes considered, a seedfall driven biannual-biennial regime gave the greatest reduction in plague time and plague years for low and moderate control levels. Although inspired by a model validated using house mouse populations in New Zealand forests, our modelling approach is easily adapted for application to other climate-driven systems where broad-scale control is conducted on irrupting pest populations

Small-scale spatial structure influences large-scale invasion rates

Local interactions among individual members of a population can generate intricate small-scale spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines density-independent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, the invasion speed is significantly lower than standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front.</p

Model-free estimation of COVID-19 transmission dynamics from a complete outbreak.

New Zealand had 1499 cases of COVID-19 before eliminating transmission of the virus. Extensive contract tracing during the outbreak has resulted in a dataset of epidemiologically linked cases. This data contains useful information about the transmission dynamics of the virus, its dependence on factors such as age, and its response to different control measures. We use Monte-Carlo network construction techniques to provide an estimate of the number of secondary cases for every individual infected during the outbreak. We then apply standard statistical techniques to quantify differences between groups of individuals. Children under 10 years old are significantly under-represented in the case data. Children infected fewer people on average and had a lower probability of transmitting the disease in comparison to adults and the elderly. Imported cases infected fewer people on average and also had a lower probability of transmitting than domestically acquired cases. Superspreading is a significant contributor to the epidemic dynamics, with 20% of cases among adults responsible for 65-85% of transmission. Subclinical cases infected fewer individuals than clinical cases. After controlling for outliers serial intervals were approximated with a normal distribution (μ = 4.4 days, σ = 4.7 days). Border controls and strong social distancing measures, particularly when targeted at superspreading, play a significant role in reducing the spread of COVID-19

Predicting water levels in ephemeral wetlands under climate change scenarios

Ephemeral wetlands or kettle holes contain an often unique biodiversity of flora and fauna. In New Zealand they can be an important breeding ground for iconic taonga species such as kakī/black stilt. Understanding the possible effects of climate change on the holes is a challenge as there is often limited information on the local hydrology, restricting the applicability of established hydrological models. We present a mathematical model that is parameterized using only recent rainfall data and water level. We assess the efficacy of our model to predict water levels under current climatic conditions and then explore the effects of a range of simple climate change scenarios. Our simple but effective modelling approach could be easily used in other situations where complex data and modelling expertise are unavailable

Using mechanistic model-based inference to understand and project epidemic dynamics with time-varying contact and vaccination rates

Abstract Epidemiological models range in complexity from relatively simple statistical models that make minimal assumptions about the variables driving epidemic dynamics to more mechanistic models that include effects such as vaccine-derived and infection-derived immunity, population structure and heterogeneity. The former are often fitted to data in real-time and used for short-term forecasting, while the latter are more suitable for comparing longer-term scenarios under differing assumptions about control measures or other factors. Here, we present a mechanistic model of intermediate complexity that can be fitted to data in real-time but is also suitable for investigating longer-term dynamics. Our approach provides a bridge between primarily empirical approaches to forecasting and assumption-driven scenario models. The model was developed as a policy advice tool for New Zealand’s 2021 outbreak of the Delta variant of SARS-CoV-2 and includes the effects of age structure, non-pharmaceutical interventions, and the ongoing vaccine rollout occurring during the time period studied. We use an approximate Bayesian computation approach to infer the time-varying transmission coefficient from real-time data on reported cases. We then compare projections of the model with future, out-of-sample data. We find that this approach produces a good fit with in-sample data and reasonable forward projections given the inherent limitations of predicting epidemic dynamics during periods of rapidly changing policy and behaviour. Results from the model helped inform the New Zealand Government’s policy response throughout the outbreak