The objective of this seminar series is to introduce new topics, discuss current methodologies and explore different theories within mathematical and statistical ecology. Our seminar series will run from October to May each year. Each seminar will be cc. 40 minutes and will take place on every second Wednesday of the month with possible exceptions. There may be more than one talk per month, if time permits. You can also watch each talk on our YouTube Channel. You can join the talk each month here: Teams Link. You can also subscribe to receive a monthly email with the abstract and link for each talk here: Mailing List.
Here is a time zone conversion website to see when our talks are on in your locality: Time Zone Converter.
10 May 2023 – Wesley Godoy (University of São Paulo) [4pm Irish Standard Time/BST]
Analysing forest insect outbreaks via wavelet analysis
Oncideres impulviata is a pervasive forest pest of black wattle trees in Brazil. Available damage records indicate that this beetle can cause significant harm to tree plantations, with both environmental and economic losses. Females are known to ring (girdle) the trunks of black wattle and subsequently lay their eggs. This girdling behaviour can reduce the productivity of such trees, especially in the early stages of establishment, disrupting sap flow and therefore severely impairing tree growth. In this talk I will apply wavelet analysis to time series of damaged trees in order to deduce when there is an outbreak of O. impulviata induced tree damage, across three Brazilian municipalities over 13 years.
12 April 2023 – Laura Byrne (Trinity College Dublin)
Multivariate Statistical Models for Biodiversity Experiments
Diversity-Interactions (DI) modelling is a regression-based approach used for assessing the biodiversity and ecosystem function (BEF) relationship. It assumes that the initial proportional abundance of the species in an ecosystem is the primary driver behind the changes in its functioning, expanding on the popular use of richness. The linear predictor in a DI model includes the identity effect of each species, along with the interaction effects that may occur between species (which can take many forms) and can also include any treatment or block structures in the design. Following the introduction of the DImodels R package in 2020, we are developing an add-on package DImodelsMulti. The original package enables the automatic fitting of a range of DI models for a single ecosystem function studied at a single point in time. The new package can additionally model multiple responses and account for repeated measurements on a single experimental unit by incorporating a variety of correlation structures. Further work in the multivariate space will also be added to the package in future updates, such as the prediction of the proportional breakdown of species in biomass over time using the DI modelling framework. The new DImodelsMulti package provides considerable flexibility in model selection and estimation of DI models and will be a useful tool in the study of multifunctional BEF relationships studied over time.
8 March 2023 – Rachel McCrea (Lancaster University)
Statistical models for conservation translocations
Conservation translocations are being increasingly used in the conservation of threatened species and as part of ecological restoration programmes (Bickerton et al, 2022). Robust estimates of abundance are essential for meaningful conservation decision-making and the impact of translocations on source populations needs to be understood. Within this talk I will present a new capture-recapture model for translocated populations and will then present a modelling framework where capture-recapture is combined with removal/depletion methodology (Zhou et al, 2019). I will demonstrate that an exact likelihood is possible when individual level information is available, and I will show how a standard integrated population modelling approach (Frost, et al, 2022), which assumes independence between component data sets, can be adapted to provide an approximate likelihood when individual level data is not available. This approach, as well as providing a valuable tool for estimating the abundance of source populations post translocation, also motivates a new direction of research for overcoming issues of dependence of data within a standard integrated population modelling framework.
8 February 2023 – Anuraag Bukkuri (Moffitt Cancer Centre)
Models of Resistance in Structured Populations
Neuroblastoma is a paediatric cancer of variable clinical presentation, from spontaneous regression to metastatic therapy-resistance. Although the cause of neuroblastoma remains elusive, it is well recognized that two distinct cellular phenotypes underpin its development and progression: adrenergic (ADRN) and mesenchymal (MES). However, how these phenotypes impact the eco-evolutionary dynamics of neuroblastoma cancer cell populations, particularly under therapy, is not well understood. This is partly a result of the confusion surrounding whether the ADRN and MES phenotypes represent different cell types (species) or cell states (stages in the life cycle of a single species). This distinction has profound consequences on the way we understand neuroblastoma and its response to therapy. In this talk, we will introduce theoretical models sensu the G function framework to model the eco-evo dynamics in structured neuroblastoma populations and use these models to tease apart cell type vs. cell state hypotheses. We will then expand and generalize this framework to continuous-structured models and discuss implications for cancer and bacterial resistance more generally.
11 January 2023 – Gabriel Palma (Maynooth University)
Pattern-Based Prediction of Population Outbreaks Insect outbreaks are biotic disturbances in forests and agroecosystems that cause economic and ecological damage. This phenomenon depends on a variety of biological and physical factors. The complexity and practical importance of the issue have made the problem of predicting outbreaks a focus of recent research. In this talk I will speak on the Pattern-Based Prediction (PBP) method for predicting population outbreaks, based on the Alert Zone Procedure, combined with elements from Machine Learning. It uses information on previous time series values that precede an outbreak event as predictors of future outbreaks, which can be useful when monitoring pest species. I will illustrate the methodology using simulated datasets and real time series data obtained by monitoring aphids in wheat crops in Southern Brazil. I hope this methodology to be useful to non-specialists, such as ecologists aiming to use a quantitative approach for pest monitoring.
14 December 2022 – Rebecca Tyson (University of British Columbia Okanagan)
Generous mutualists can outcompete more selfish ones
Biodiversity is an important component of healthy ecosystems, and thus under-standing the mechanisms behind species coexistence is critical in ecology and conservation biology. We are interested in understanding mutualisms where there are multiple species sharing a resource supplied by the same partner. If, as commonly assumed, there is competition between the species, then, in general, only the superior competitor should persist. Nevertheless, close coexistence of multiple species sharing the same mutualistic partner is a widespread phenomenon. Modelling work has demonstrated that coexistence of mutualists can be made possible by invoking mechanisms such as niche differences, colonization-competition trade-offs, spatial structure, or physio-evolutionary feedbacks. None of these mechanisms, however, can explain the coexistence of species with a high degree of niche overlap in the absence of spatial structure. In this talk, I will present a series of differential equation mathematical models for mutualistic communities, using the plant-fungal relationship as our motivating example. The baseline model demonstrates that asymmetric resource exchange between the plant and its fungal guild can lead to indirect parasitic interactions between guild members, and coexistence of multiple mutualistic fungi. With a subsequent extension of this baseline model, I will present the dynamics of mutualistic communities that also compete among and between each other and show that coexistence and competitive exclusion are both possible outcomes, depending on the competition strength and on strength of the mutualistic interactions. Finally, we extend the model to the spatial context, and observe how the introduction of a commercial fungus will affect the resident fungal communities through the invasion processes that follow inoculation.
9 November 2022 – Patrick De Leenheer (Oregon State University)
The basic reproduction number for linear semigroups in \(R^n\) with an invariant cone
We consider linear ODEs \(\dot{x} = Ax\) on \(R^n\), and first characterize the class of operators \(A\) that have the property that \(e^{tA}(K)\) is contained in the cone \(K\) for all non-negative \(t\). These turn out to be the so-called cross-positive operators on \(K\), or equivalently, the class of resolvent-positive operators (with respect to \(K\)). We then introduce the notion of a basic reproduction number \(R_0\) and discuss the trichotomy which says that \(R_0 – 1\) and the spectral abscissa \(s(A)\) of \(A\) always have the same sign (positive, negative or zero). Basic reproduction numbers are often easier to calculate than the spectral abscissa, which is why they are so popular in epidemiology and ecology. We shall illustrate these concepts and results on a simple model of an infectious disease, and if time permits, show that controlling \(R_0\) one way may have an opposite effect on the spectral abscissa. This suggests that one should be (more) careful when lowering \(R_0\) in order to control an infectious disease.
5 October 2022 – André Felipe Berdusco Menezes (Maynooth University)
Detection of Structural Changes in Dynamic Linear Models: A Python Package
Bayesian dynamic models naturally allow for subjective interventions
describing probabilistic expert knowledge. Monitoring forecast errors
based on local Bayes factor is used to find structural changes and take
immediate action. In this talk we will introduce an open source Python
package called pybats-detection, proposed for Bayesian
monitoring and intervention in univariate time series data. The
implementation of these methods through the pybats-detection package,
which in the past was provided by the software BATS, is what we are most
concerned about. This methodology is scalable because, at least in the
Gaussian case, its algorithm has closed form. In order to demonstrate
the usability of the pybats-detection package, we apply it
to a simulated ecological time series dataset composed of species
density or biomass observations and discuss possible avenues for future
work.
11 May 2022 – Shandelle Henson (Andrews University)
Periodic matrix models for the seasonal dynamics of seabirds
Changes in sea surface temperatures in the Pacific Northwest are associated with changes in reproductive and feeding tactics in colonial seabirds. For example, warm years in the El Niño–Southern Oscillation are associated with tactics such as egg cannibalism and egg-laying synchrony in gulls. How do these changes in behavioral dynamics affect population dynamics, especially tipping points? In general, for structured matrix models of populations that are periodically forced by an annual breeding season, life-stage interactions and behavioral tactics may occur on a faster time scale than that of population dynamics. We use bifurcation theoretic techniques to study a class of such models, focusing on the nature of non-extinction, seasonal cycles as a function of environmental resource availability. Backward bifurcations can create tipping points as well as strong Allee effects which lead to the benefit of possible (initial condition dependent) survival in adverse environments. In the application, we find that positive density effects (component Allee effects) due to increased adult survival from cannibalism and the propensity of females to synchronize daily egg laying can produce tipping points and a strong Allee effect due to a backward bifurcation.
6 April 2022 – Ruth King (University of Edinburgh) Large data and (even not that very) complex ecological models: When worlds collide
As long-term studies of ecological systems continue to collect data, the size of such datasets continue to expand in size. This talk focuses on challenges that arise when fitting (not even very) complex ecological models to “large” data sets, motivated by a long-term study of a population of guillemots involving approximately 30,000 individuals. In particular focus lies on fitting a random effect (or hierarchical) capture-recapture model. The associated likelihood of the given model that is expressible only as an analytically intractable integral. Common techniques for fitting such models include, for example, the use of direct numerical approximations for the integral, or a Bayesian data augmentation approach. However, as the size of the data set increases (i.e. the number of individuals increases), these computational tools may become computationally infeasible, as for the motivating guillemot example. I will describe an efficient Bayesian model-fitting approach, which involves initially sampling from the posterior distribution of a smaller subsample of the data, before correcting this sample to obtain estimates of the posterior distribution of the full dataset, using an importance sampling approach. I will demonstrate how this approach leads to substantial improvements in computational time for simulated data before applying to the guillemot example and discuss some additional practical implementational aspects.
9 March 2022 – Jean-Francois Arnoldi (CNRS)
Invasions of ecological communities : hints of impact in the invader’s growth rate
Theory in ecology and evolution often relies on the analysis of invasion processes, and general approaches exist to understand the early stages of an invasion. However, predicting the long‐term transformations of communities following an invasion remains challenging. I will describe some theoretical work that uses the density dependence of an invading population’s growth rate to predict if the invasion will cause large long‐term impacts on the invaded community. This approach clarifies how the density dependence of the invasion growth rate is as much a property of the invading population as it is one of the invaded community. This theory applies to any stable community model, and directs us towards new questions that may enrich the toolset of invasion analysis, and suggests that indirect interactions and dynamical stability are key determinants of invasion outcomes.
9 February 2022 – Gates Dupont (Princeton University)
Statistical improvements for ecological learning about spatial processes
Ecological inquiry is rooted fundamentally in understanding population abundance, both to develop theory and improve conservation outcomes. Despite this importance, estimating abundance is difficult due to the imperfect detection of individuals in a sample population. Further, accounting for space can provide more biologically realistic inference, shifting the focus from abundance to density and encouraging the exploration of spatial processes. Spatial Capture-Recapture (“SCR”) has emerged as the most prominent method for estimating density reliably. SCR presents particularly interesting problems of data quality because of the requirement for spatial replication of observations of individuals. I describe two approaches for improving inference in this regard. First, I develop model-based criteria in an algorithmic framework to optimize spatial sampling. Second, I integrate finer-scale movement data to describe detailed spatial processes. These novel approaches represent essential steps in advancing SCR and offer intuitive opportunities to advance ecological learning about spatial processes.
19 January 2022 – Frederic Barraquand (CNRS and University of Bordeaux)
Inferring species interactions using Granger causality and convergent cross mapping
How to reliably infer interactions between species from time series of their population densities is a long-standing goal of statistical ecology. Usually this inference is done using multivariate (linear) autoregressive models, defining interactions through Granger causality: \(x\) causes \(y\) whenever \(x\) helps predicting future \(y\) values. However, the entangled nature of nonlinear ecological systems has suggested an alternative causal inference method based on attractor reconstruction, convergent cross mapping, which is increasingly popular in ecology. Here, we compare the two methods. They uncover interactions with surprisingly similar performance for predator-prey cycles, 2-species chaotic or stochastic competition, as well as 10- and 20-species networks. Thus, contrary to intuition, linear Granger causality remains useful to infer interactions in highly nonlinear ecological networks. We conclude on inevitable similarities between Granger-causal methods and convergent cross mapping due to interaction definitions, and provide suggestions to improve many-species interaction inference.
8 December 2021 – Chris Guiver (Edinburgh Napier University)
A switching feedback control approach for persistence of managed resources
A brief overview of research by the presenter and their collaborators on the use of tools from mathematical control theory in theoretical ecology shall be given. Control theory broadly seeks to both understand, and subsequently shape, the behaviour of interconnected dynamical systems by using measurements of the systems, and control actions to affect changes. Although feedback control is nowadays typically viewed as an engineering discipline, which traces its roots to the industrial revolution, as long ago as 1858 Alfred Russel Wallace drew parallels between feedback control and evolution by natural selection. Indeed, feedback is an inherent component of numerous biological systems, and the concepts of model uncertainty, forced nonlinear dynamics, interconnected systems and feedbacks, and control or management strategies/actions are ubiquitous in both control theory and aspects of theoretical ecology related to population conservation or control. As well as giving an overview of relevant recent work, the presentation shall focus on the results of the 2021 paper: “A switching feedback control approach for persistence of managed resources”, where a so-called adaptive switching feedback control scheme is proposed for classes of discrete-time, positive difference equations, or systems of equations, which naturally model managed quantities of interest, such as populations. The work relies on the combination of ideas from adaptive control theory and the theory of positive dynamical systems.
10 November 2021 – Niamh Mimnagh (Maynooth University)
Estimating abundance in animal communities: A multi-species N-Mixture model
Accurate estimation of animal abundance is of great importance in areas such as conservation and wildlife management. The univariate N-Mixture model (Royle, 2004) was developed with the aim of estimating animal abundance from simple count data, which is inexpensive to collect, but prone to imperfect detection. In this presentation, I will examine this existing methodology, and how the univariate N-mixture model can be extended in order to model populations of multiple species simultaneously. This permits us to estimate both species’ abundances and inter-species correlations, which allows us to begin to make inferences as to the relationships that these species have with one another. I will then examine further extensions to this model, which allow us to examine data collected over several years, and data in which a large proportion of the counts are zero. I’ll finish by looking at simulation studies, which were run to examine the accuracy of model estimates, and an application of the model to the North American Breeding Bird Survey data.
13 October 2021 – John Donohue (Kings College London)
The dynamics of disturbed scavenging communities
Anthropogenic disturbances, particularly mass poisonings, have caused crashes in vulture populations in Africa and Asia. Vultures play a crucial role in scavenging communities as apex scavengers. Scavenging communities in turn are a key component of terrestrial ecosystems, ensuring that dead biomass is removed quickly and efficiently. Here, using an empirically parameterised mathematical model, we analyse the short and long-term behaviour of such communities. In particular, we examine the dynamics of a depleted vulture population and how these dynamics influence the abundances of rival scavengers as well as the overall biomass removal rate of the ecosystem. Finally, using a combination of numerical and analytical techniques, we undertake a sensitivity analysis with a view to understanding how our findings can be transferred from our study system to other ecosystems.