Exploratory analysis of spatial-temporal patterns in length-frequency data: An example of distributional regression trees

Understanding the spatial-temporal distributions of fish populations is important for their assessment and management. Given the complex structure often present in fisheries length-frequency samples, there is a need for flexible statistical techniques to explore patterns with these types of data. We present a multivariate regression tree method for binned frequencies that uses the Kullback-Leibler divergence to measure node heterogeneity. To illustrate this approach, we apply the method to length-frequency data for yellowfin tuna caught in the purse-seine fishery of the eastern Pacific Ocean.