A specific kind of dominance hierarchy in which A dominates B, B dominates C, C dominates D, and so on, in a strict line, with each individual having a defined rank relative to every other.

Linear hierarchies are rare in actual social mammals. Most observed hierarchies have circular elements (where A dominates B, B dominates C, but C dominates A), context-dependent reversals (where the dominance relationship between two individuals depends on what resource is being contested or what other individuals are present), or distributed leadership across multiple individuals (where different individuals lead in different contexts).

In horses, detailed observation of free-ranging populations consistently fails to find the simple linear hierarchies that popular horsemanship culture assumes. What exists is a complex pattern of bilateral relationships, with context-dependent outcomes, and with leadership of movement and other group activities being distributed across multiple individuals rather than concentrated in a single “alpha”. The popular framing of horse herds as linear hierarchies with an alpha at the top is not supported by detailed observation of free-ranging horses, and represents a significant gap between popular training culture and contemporary research.

In other species, similar patterns of complexity emerge when groups are studied carefully. Wolves do not form linear hierarchies in family groups; they form parent-led family structures. Free-ranging dogs do not form linear hierarchies; they form loose associations with context-dependent relationships. Even in chickens, where the original “pecking order” research was done, more detailed study has revealed substantial complexity beyond the simple linear model.

The persistence of linear hierarchy thinking in popular animal training is partly historical inertia (the model has been in widespread use for decades) and partly conceptual appeal (a linear hierarchy is simple to understand and produces clear behavioural prescriptions). The cost is that handling and training practices built on the model often misread what animals are doing and produce welfare concerns the research does not support.

Contemporary applied animal behaviour work has largely moved away from linear hierarchy thinking, in favour of frameworks that recognise context-dependence, bilateral relationships, and the central role of affiliative behaviour in stable social groups.