Statistical Approaches for Hidden Variables in Ecology

Nathalie Peyrard, Olivier Gimenez

• Publisher: Wiley-ISTE
• Year: 2022
• Print ISBN:
  9781789450477
• Edition: 1
• eBook ISBN:
  9781119902782
• Topic: Social Sciences
• Subtopic: Probability & Statistics
• Index: Social Sciences

The study of ecological systems is often impeded by components that escape perfect observation, such as the trajectories of moving animals or the status of plant seed banks. These hidden components can be efficiently handled with statistical modeling by using hidden variables, which are often called latent variables. Notably, the hidden variables framework enables us to model an underlying interaction structure between variables (including random effects in regression models) and perform data clustering, which are useful tools in the analysis of ecological data.

This book provides an introduction to hidden variables in ecology, through recent works on statistical modeling as well as on estimation in models with latent variables. All models are illustrated with ecological examples involving different types of latent variables at different scales of organization, from individuals to ecosystems. Readers have access to the data and R codes to facilitate understanding of the model and to adapt inference tools to their own data.

1
Trajectory Reconstruction and Behavior Identification Using Geolocation Data

Marie-Pierre ETIENNE¹ and Pierre GLOAGUEN²

¹Institut Agro, Agrocampus Ouest, CNRS, IRMAR – UMR 6625, Rennes, France

²Paris-Saclay University, AgroParisTech, INRAE, UMR MIA-Paris, France

1.1. Introduction

The study of movement in ecology has taken off in recent years, driven by questions relating to the determinisms of individual movement. Interest in the ecology of movement has been largely fueled by the emergence and development of GPS technologies over the last 20 years, helped along by the creation of numerous databases made up of individual trajectories. These observations, on fine spatial and temporal levels, can be used to study the behavior of individuals in relation to their living environment. A variety of trajectory models have been developed and applied with the aim of reconstructing these behaviors and understanding the underlying determinisms. In this chapter, we shall present two latent variable models, widely used in movement ecology for trajectory analysis. Each model corresponds to a specific objective: the reconstruction of real trajectories with the removal of any geolocation errors, and the identification of different behaviors in the course of movement.

1.1.1. Reconstructing a real trajectory from imperfect observations

Trajectory data are frequently marred by errors for a variety of reasons (satellite accessibility issues, geolocation errors, etc.). This results in noisy observations of the real position of the animal, which is itself unknown. The hidden variable is, therefore, the real position and the observed variable is the noisy version. In Figure 1.1, we can see that some recorded positions of a Cape dolphin, tracked using the Argos system, are actually on land – a situation which is evidently improbable. This observation almost certainly corresponds to noisy data concerning the actual position of the tracked individual.

Figure 1.1. The map at the top shows the tracking data for a male Cape dolphin (Cephalorhynchus heavisidii) in St. Helena Bay, South Africa. The coastline is shown in black, and we see that some recorded positions are actually on land. These positions are obtained using an Argos system. Figure taken from Elwen et al. (2006). Photo of a Cape dolphin by Jutta Luft, distributed under the GNU Free Documentation License. For a color version of this figure, see www.iste.co.uk/peyrard/ecology.zip

Observation errors are generally small (a few meters) in cases where positions are obtained using a GPS system on open ground and with good satellite coverage. Far larger errors may occur using other technologies, such as the Argos system (into the tens of kilometers). A hierarchical model for reconstructing real trajectories from observed trajectories is presented in section 1.2.1.

1.1.2. Identifying different behaviors in movement

Individuals rarely move in a homogeneous manner, and different movement patterns are often observed. In Nathan et al. (2008), the authors propose a formalization of the mechanisms responsible for individual movement. Among the different aspects mentioned, the internal state of the individual and the environment in which it exists are identified as important mechanisms of movement. It seems reasonable to believe that the internal state of an individual affects its behavior, resulting in a change of movement regime.

Any study of individual movement must permit the identification of different states or activities. In this case, the hidden variable is the activity of the individual, while the observed variable is its position, or various metrics derived from this position, as we shall see ...

Table of contents

• Cover
• Table of Contents
• Title Page
• Copyright
• Introduction
• 1 Trajectory Reconstruction and Behavior Identification Using Geolocation Data
• 2 Detection of Eco-Evolutionary Processes in the Wild: Evolutionary Trade-Offs Between Life History Traits
• 3 Studying Species Demography and Distribution in Natural Conditions: Hidden Markov Models
• 4 Inferring Mechanistic Models in Spatial Ecology Using a Mechanistic-Statistical Approach
• 5 Using Coupled Hidden Markov Chains to Estimate Colonization and Seed Bank Survival in a Metapopulation of Annual Plants
• 6 Using Latent Block Models to Detect Structure in Ecological Networks
• 7 Latent Factor Models: A Tool for Dimension Reduction in Joint Species Distribution Models
• 8 The Poisson Log-Normal Model: A Generic Framework for Analyzing Joint Abundance Distributions
• 9 Supervised Component-Based Generalized Linear Regression: Method and Extensions
• 10 Structural Equation Models for the Study of Ecosystems and Socio-Ecosystems
• List of Authors
• Index
• End User License Agreement