  This study examines how patterns on mammal body surfaces change as they
transition from juveniles to adults and with seasonal variations. Our previous
research suggests that patterns formed in infancy may fade due to the growing
domain effects, typically linked to the body's surface expanding as it grows,
but this transition is influenced by various factors. Here, we focus on how
heat, which can change with body growth, affects this process. Generally,
smaller organisms lose heat more easily due to their higher surface
area-to-volume ratio, while larger organisms retain heat more effectively. In
fact, thermoregulation during infancy is a crucial factor directly influencing
survival. We propose a theoretical model that incorporates both growing domain
and metabolic rate effects to explain the mechanisms behind these pattern
transitions. The model suggests that Turing patterns formed during juvenile
stages disperse in adulthood due to domain growth and changes in metabolic
rates affecting reaction rates. Numerical analysis shows that when both growing
domain and metabolic rate effects are considered, patterns disperse more
rapidly than when only growing domain effects are accounted for. Furthermore,
we discuss potential correlations among pattern transitions, growth, and
thermoregulation mechanisms, emphasizing the role of metabolic rates in
maintaining body temperature. Our findings shed light on the intricate
relationship between growth, thermoregulation, and pattern transitions in
mammals, possibly useful for further research in this field.
