Using piecewise regression to identify biological phenomena in biotelemetry datasets

Abstract

Technological advances in the field of animal tracking have greatly expanded the potential to remotely monitor animals, opening the door to exploring how animals shift their behaviour over time or respond to external stimuli. A wide variety of animal-borne sensors can provide information on an animal's location, movement characteristics, external environmental conditions and internal physiological status. Here, we demonstrate how piecewise regression can be used to identify the presence and timing of potential shifts in a variety of biological responses using multiple biotelemetry data streams. Different biological latent states can be inferred by partitioning a time-series into multiple segments based on changes in modelled responses (e.g. their mean, variance, trend, degree of autocorrelation) and specifying a unique model structure for each interval. We provide six example applications highlighting a variety of taxonomic species, data streams, timescales and biological phenomena. These examples include a short-term behavioural response (flee and return) by a trumpeter swan Cygnus buccinator following a GPS collar deployment; remote identification of parturition based on movements by a pregnant moose Alces alces; a physiological response (spike in heart-rate) in a black bear Ursus americanus to a stressful stimulus (presence of a drone); a mortality event of a trumpeter swan signalled by changes in collar temperature and overall dynamic body acceleration; an unsupervised method for identifying the onset, return, duration and staging use of sandhill crane Antigone canadensis migration; and estimation of the transition between incubation and brood-rearing (i.e. hatching) for a breeding trumpeter swan. We implement analyses using the mcp package in R, which provides functionality for specifying and fitting a wide variety of user-defined model structures in a Bayesian framework and methods for assessing and comparing models using information criteria and cross-validation measures. These simple modelling approaches are accessible to a wide audience and offer a straightforward means of assessing a variety of biologically relevant changes in animal behaviour.

FIGURE 1

Hourly net‐squared displacement measured from the point of release of a trumpeter swan Cygnus buccinator after collar deployment. Grey lines show 25 draws from the posterior distribution, with 95% credible intervals for the mean response shown as red dotted lines. The posterior distribution for the change point is shown in blue on the x‐axis.

FIGURE 2

Displacement (distance from each location to the location at the start of the observation period) for a pregnant moose Alces alces. The green area is the period identified by researchers as immediately preceding parturition. Grey lines represent 25 draws from the posterior distribution of the mean displacement. Red dotted lines depict 95% credible intervals for the mean displacement and green dotted lines depict 80% prediction intervals. The posterior distribution for the change point is shown in blue on the x‐axis.

FIGURE 3

A kernel density posterior predictive check compares the distribution of observed outcomes (displacement in kilometres by a pregnant moose Alces alces), shown in the black line, against 50 distributions of replicated datasets produced by the fitted model, each shown as a light blue line.

FIGURE 4

Heart rate of a black bear Ursus americanus in relation to a drone flight. The green box indicates the duration of a drone flight. Grey lines represent 25 draws from the posterior distribution of the mean response. Red dotted lines depict the 95% credible intervals for the mean response. The posterior distribution for the change point is shown in blue on the x‐axis.

FIGURE 5

The x‐axis is an index of time since the start of the time series for overall dynamic body acceleration on the top figure and temperature on the bottom figure for a trumpeter swan Cygnus buccinator. Grey lines show 25 draws from the posterior distribution, with 95% credible intervals for the mean response shown as red dotted lines. The posterior distribution for the change point is shown in blue on the x‐axis.

FIGURE 6

An annual migration cycle of a sandhill crane Antigone canadensis. Average daily displacement from the breeding territory (in kilometres) on the y‐axis, and an index of time since the start of the time series on the x‐axis. Grey lines show 25 draws from the posterior distribution, with 95% credible intervals for the mean response shown as red dotted lines and 80% prediction intervals in green dotted lines. The posterior distributions for the change points are shown in blue on the x‐axis.

FIGURE 7

The top plot shows the accelerometer sensor dataset for a nesting trumpeter swan Cygnus buccinator, with time on the x‐axis expressed in hourly time intervals and averaged ODBA values on the y‐axis. The bottom plot shows the 19 data points from the visual observation dataset with the estimated hatch date (the midpoint between the last incubation observation and the first cygnet observation; purple dotted line).

FIGURE 8

Date is on the x‐axis and average hourly overall dynamic body acceleration for a trumpeter swan Cygnus buccinator is on the y‐axis. The coloured markers just above the x‐axis correspond to visual observations of the swan's nesting status. The dashed vertical line in purple is the observed transition from incubation to cygnets, and the solid brown line is the estimated change point from the piecewise regression model. Grey lines show 25 draws from the posterior distribution, with 95% credible intervals for the mean response shown as red lines.