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.