Formalizing developmental phenomena as continuous-time systems: Relations between mathematics and language development

Keel bone fractures affect laying hens' mobility, but no evidence for reciprocal effects

Keel bone fractures (KBF) are prevalent in commercial laying hens and are considered one of the greatest welfare concerns in the egg-production industry. While clear associations exist between KBF and animal mobility, suggesting that KBF impair mobility, the effect of mobility on KBF remains unclear. We combined data from three studies that assessed keel bone fracture severity through radiographs and monitored hens' transitions between different zones of a multi-tier aviary system (the three tiers, a littered floor, and a winter garden) the week prior to radiograph. For each hen, we extracted two daily movement behaviours: the vertical distance travelled and the mean number of zones crossed within one transition; and two daily space-use behaviours: the time spent in the top tier and the unevenness of time spent across zones. We used hierarchical Bayesian continuous time dynamic modelling to estimate how a change in a behaviour predicted a later change in keel bone fracture severity, and vice versa. Increased fracture severity did not predict later changes in space-use behaviours, but it did predict changes in movement behaviours. Specifically, increased fracture severity led to decreased vertical travelled distance and a tendency to cross more zones within one transition, suggesting impaired mobility in hens with increased fracture severity. In contrast, we found no evidence that movement or space-use behaviours predict later change in fracture severity, challenging previous literature suggesting that vertical locomotion through jumping and flying may exacerbate keel bone fractures in complex three-dimensional systems due to increased risk of collisions. However, similar efforts accounting for the location of fractures on the keel could unveil the potential influence of movement and space-use behaviours in the formation and change (healing or worsening) of KBF and increase our ability to mitigate their effects.

Formalizing theories of child development: Introduction to the special section

Here we introduce a Special Section of Child Development entitled "Formalizing Theories of Child Development." This Special Section features five papers that use mathematical models to advance our understanding of central questions in the study of child development. This landmark collection is timely: it signifies growing awareness that rigorous empirical bricks are not enough; we need solid theory to build the house. By stating theory in mathematical terms, formal models make concepts, assumptions, and reasoning more explicit than verbal theory does. This increases falsifiability, promotes cumulative science, and enables integration with mathematical theory in allied disciplines. The Special Section contributions cover a range of topics: the developmental origins of counting, interactions between mathematics and language development, visual exploration and word learning in infancy, referent identification by toddlers, and the emergence of typical and atypical development. All are written in an accessible manner and for a broad audience.