Continuous-time Markov chains as models for animal behaviour

Metz, H; Dienske, Herman; Jonge, Gerrit De; Putters, F.A.

doi:10.1007/bf02459596

Cited by 46 publications

(6 citation statements)

References 10 publications

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“…Founding articles of three important variants of these methods, continuous-time Markov (CTM) chains, correlated random walks and stochastic processes, date from the 1950s and their applications to animal behavioural studies from the 1980s. The main publication on continuous-time Markov (CTM) models applied to behavioural studies was written by Metz et al (1983), with few appearing since then. On the other hand, E. Renshaw and other authors have written many articles about correlated random walk and stochastic processes since 1981 (see Gurarie et al , 2015 for a methodological review), giving a significant advantage for the development of these methods to specific questions.…”

Section: Discussionmentioning

confidence: 99%

An inference procedure for behavioural studies combining numerical simulations, statistics and experimental results

Guarini

Coston‐Guarini

Deprez³

et al. 2017

J. Mar. Biol. Ass.

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The technical difficulties of performing underwater observation mean that marine ecologists have long relied on behavioural experiments to study reactions of marine organisms. In this article, we examine the underlying complexity of assumptions made in raceway experiments and we propose a statistical inference procedure tailored to this type of experimental protocol. As an example, experiments were performed to test if light of two different intensities affects the proximal behaviour (i.e. direct, local and immediate) of two species of crustaceans, the hermit crab (Pagurus bernhardus), and the green crab (Carcinus maenas). Individuals were collected in the vicinity of the Sven Loven Marine Center in Tjarnö (Sweden). Their movements in raceways were recorded and the statistical distance between the resulting experimental distribution and a simulated null distribution was used to compare their behaviour in two situations: dim (when they were expected to feed) and bright light (when they were expected to shelter). Initial tests indicated no differences of behaviour between dim and bright light for the two species. However, when compared with the reference state (here, a null distribution) the behaviour in dim light deviates significantly from the null distribution suggesting non-random behaviour. Our results suggest that efforts should be made to understand the behaviours of the individuals of these two species to establish a comprehensive reference state as a basis for comparison. This fundamental information should be a prerequisite before implementing experiments testing how potential disturbances affect individual organisms in behavioural ecology.

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Section: Discussionmentioning

confidence: 99%

An inference procedure for behavioural studies combining numerical simulations, statistics and experimental results

Guarini

Coston‐Guarini

Deprez³

et al. 2017

J. Mar. Biol. Ass.

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show abstract

“…For instance, the probability that a sleeping animal will start to drink after waking up most likely depends on the thirst of the animal, that is whether the animal drank before sleeping. Moreover, the duration in a given state may be an important aspect in addition to the type itself (Metz et al, 1983).…”

Section: Me Thodolog Ic Al Approache Smentioning

confidence: 99%

Fully flexible analysis of behavioural sequences based on parametric survival models with frailties—A tutorial

2021

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Recent automated systems allow collecting continuous data on individual animals with high accuracy over a long time. During this time, animals can be traced across different (discrete) types of behavioural states, with the duration in each state being known. Nevertheless, analyses of such sequences of states or behaviours may prove difficult. Classic Markov-chain methods have limitations in respect to incorporating "memory" (effects of past states), the duration in the states and accounting for dependencies. Dependencies occur in many data sets, where, for example a variety of individuals from different groups are observed and/or when an experiment is divided in different crossover treatment phases. So-called parametric survival analysis with frailties can incorporate aforementioned aspects in one coherent model. The time spent in a specific state (performing a specific behaviour) can be modelled in dependence of the subsequent state (transition probabilities) while incorporating how these transitions are influenced by experimental treatments. In addition, prior states can be used as predictor variables (accounting for past behaviour). Finally, random effects can be included to account for dependencies according to, for example individual identity, group/farm/laboratory or experimental period. Using interactions between random and fixed effects, the within-and between-subject variability of the transition probabilities can be estimated to indicate variation between and consistency within individual subjects (individuality and personality). Moreover, relative hazards describing transitions from one state to several potential follow-up states can be estimated. Behavioural sequences and their modulation by experimental situations can be studied accordingly. Using two exemplary data sets, the data type and structure adequate for parametric survival analysis are introduced and advice is given on how to specify and run such models. Overall, parametric survival analysis with frailties presents a modern and versatile approach that can revive sequential analysis. This will facilitate more detailed use of behavioural data and accordingly detect more subtle aspects of behaviour.

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“…Maximum likelihood estimates of the transition rates can then be obtained from the number of transitions between the states of the Markov chain and the duration that the foraging process is in each state from which the foraging parameters can be calculated (Billingsley 1961;Metz et al 1983;Haccou et al 1983; Van der Meer and Smallegange 2009). However, as outlined before, in this study the behavioural observations only encompass the foraging behaviour of one focal individual, and exclude that of the competitors in the arena.…”

Section: Behavioural Observationsmentioning

confidence: 99%

Testing a stochastic version of the Beddington–DeAngelis functional response in foraging shore crabs

Smallegange

Meer

2010

Mar Biol

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Current behaviour-based interference models assume that the predator population is infinitely large and that interference is weak. While the realism of the first assumption is questionable, the second assumption conflicts with the purpose of interference models. Here, we tested a recently developed stochastic version of the BeddingtonDeAngelis functional response-which applies to a finite predator population without assuming weak interferenceagainst experimental data of shore crabs (Carcinus maenas) foraging on mussels (Mytilus edulis). We present an approximate maximum likelihood procedure for parameter estimation when only one focal individual is observed, and introduce 'correction factors' that capture the average behaviour of the competing but unobserved individuals. We used the method to estimate shore crab handling time, interaction time, and searching rates for prey and competitor. Especially the searching rates were sensitive to variation in prey and competitor density. Incorporating constant parameter values in the model and comparing observed and predicted feeding rates revealed that the predictive power of the model is high. Our stochastic version of the Beddington-DeAngelis model better reflects reality than current interference models and is also amenable for modelling effects of interference on predator distributions.

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Continuous-time Markov chains as models for animal behaviour

Cited by 46 publications

References 10 publications

An inference procedure for behavioural studies combining numerical simulations, statistics and experimental results

An inference procedure for behavioural studies combining numerical simulations, statistics and experimental results

Fully flexible analysis of behavioural sequences based on parametric survival models with frailties—A tutorial

Testing a stochastic version of the Beddington–DeAngelis functional response in foraging shore crabs

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