Many behaviors such as birdsong or play often are described and analyzed as sequences of discrete patterns which do not overlap in time. The most commonly used technique in analyzing such sequences is the application of a Markov chain model and analysis of first (or higher order) transition rates between patterns. Using this model requires that the sequence is stationary, i.e. that the probability of a specific pattern is, if at all, influenced only by the specific quality of the immediately preceding pattern(s) and does not show a general or temporary increase or decrease due to other factors. However, often probabilities of behaviors are not stationary, i.e. they change temporarily or in longer terms within sequences. Many species of the bird family Turdidae, for instance, tend to repeat a song type within the next few songs after it occurred once [1]. If such a tendency to repeat patterns within short intervals does not lead to an increased rate of immediate repetitions or recurrence after a specific interval, it may not be detected by analyzing transition rates. Thus, as an alternative approach for analyzing sequences with regard to a possible lumped occurrence of patterns of the same type, I suggest to analyze the distribution of intervals between those patterns. When patterns of the same type occur lumped within a sequence, the distribution of intervals between them should be biased towards shorter intervals.

For this purpose I developed a procedure which estimates the distribution of intervals between patterns of the same type, as expected under the assumption that the sequence is a random sequence. This procedure is based on a randomization technique. A visual comparison of this expected distribution and the distribution obtained from the original sequence allows a first decision whether or not intervals between patterns of the same type in the original sequence are biased towards shorter intervals. To test if this bias is significant I developed a second procedure, which is again based on a randomization technique. This procedure estimates whether or not the frequency of intervals being shorter than a certain value is significantly larger than expected under the null hypothesis. I tested several different sequences using the described procedure and found that it allowed to detect a lumped occurrence of patterns of the same type also in cases where common procedures such as the runs test or tests based on chi-square failed. On the poster I will present the procedure in general, an example of its application, and discuss the number of permutations needed for a valid result.

References

1. Todt, D. (1973). Biologisch-kybernetische Analyse des Gesanges verschiedener Vögel. Nova Acta Leopoldina, 37, 311-331.