Using Zipf–Mandelbrot law and graph theory to evaluate animal welfare

This work deals with the construction and testing of metrics of welfare based on behavioral complexity, using assumptions derived from Zipf–Mandelbrot law and graph theory. To test these metrics we compared yellow-breasted capuchins (Sapajus xanthosternos) (Wied-Neuwied, 1826) (PRIMATES CEBIDAE) found in two institutions, subjected to different captive conditions: a Zoobotanical Garden (hereafter, ZOO; n=14), in good welfare condition, and a Wildlife Rescue Center (hereafter, WRC; n=8), in poor welfare condition. In the Zipf–Mandelbrot-based analysis, the power law exponent was calculated using behavior frequency values versus behavior rank value. These values allow us to evaluate variations in individual behavioral complexity. For each individual we also constructed a graph using the sequence of behavioral units displayed in each recording (average recording time per individual: 4 h 26 min in the ZOO, 4 h 30 min in the WRC). Then, we calculated the values of the main graph attributes, which allowed us to analyze the complexity of the connectivity of the behaviors displayed in the individuals’ behavioral sequences. We found significant differences between the two groups for the slope values in the Zipf–Mandelbrot analysis. The slope values for the ZOO individuals approached −1, with graphs representing a power law, while the values for the WRC individuals diverged from −1, differing from a power law pattern. Likewise, we found significant differences for the graph attributes average degree, weighted average degree, and clustering coefficient when comparing the ZOO and WRC individual graphs. However, no significant difference was found for the attributes modularity and average path length. Both analyses were effective in detecting differences between the patterns of behavioral complexity in the two groups. The slope values for the ZOO individuals indicated a higher behavioral complexity when compared to the WRC individuals. Similarly, graph construction and the calculation of its attributes values allowed us to show that the complexity of the connectivity among the behaviors was higher in the ZOO than in the WRC individual graphs. These results show that the two measuring approaches introduced and tested in this paper were capable of capturing the differences in welfare levels between the two conditions, as shown by differences in behavioral complexity.