Splitting Behaviour Into Bouts; a Maximum Likelihood Approach

Non-song social call bouts of migrating humpback whales

“…A number of statistical methods have been developed for splitting behaviors into bouts, which define a BEC based on the distribution of behaviors within behavioral states [i.e., log survivorship analysis, Slater and Lester, 1982; logfrequency analysis, Sibly et al, 1990; maximum likelihood estimation method (MLM), Langton et al, 1995;Luque and Guinet, 2007]. In all methods, the distributions of intervals between behaviors are considered to be a mixture of two or more Poisson processes, which at the smallest scale separate behaviors within bouts (fast processes) and, at the larger scale, separate different groups of behaviors or bouts (slow processes).…”

“…A MLM was used to calculate the BEC, as this method accounts for a number of causes of subjectivity that affect the methods described above (see Langton et al, 1995;Luque and Guinet, 2007). Four starting parameters were initially calculated from the call interval data by fitting a "broken stick" model to the data as described in the paragraph above (Sibly et al, 1990).…”

“…Four starting parameters were initially calculated from the call interval data by fitting a "broken stick" model to the data as described in the paragraph above (Sibly et al, 1990). However, a maximum likelihood estimation of all the observed data was used to generate the model parameters, rather than fitting a curve to a histogram of observed data (as in Sibly et al, 1990), which removed any subjectivity involved in the choice of histogram bin widths (Langton et al, 1995). These four parameters were then used to calculate a single mixing parameter, calculated from the proportions of fast and slow processes, which reduced the four model parameters to three (the number of inter-call intervals occurring in both the fast and slow processes and the mixing parameter, Langton et al, 1995).…”

“…However, a maximum likelihood estimation of all the observed data was used to generate the model parameters, rather than fitting a curve to a histogram of observed data (as in Sibly et al, 1990), which removed any subjectivity involved in the choice of histogram bin widths (Langton et al, 1995). These four parameters were then used to calculate a single mixing parameter, calculated from the proportions of fast and slow processes, which reduced the four model parameters to three (the number of inter-call intervals occurring in both the fast and slow processes and the mixing parameter, Langton et al, 1995). The final maximum likelihood estimates for the model parameters were obtained from these parameter estimates and used to calculate the BEC.…”

“…The final maximum likelihood estimates for the model parameters were obtained from these parameter estimates and used to calculate the BEC. How well the model fit the observed data was assessed by plotting the observed cumulative frequency distribution of intervals to those of the fitted model (Langton et al, 1995;Fig. 2).…”