Stagestructured

Stage-structured, often written stage-structured or stagestructured, refers to models and analyses that categorize individuals by developmental or physiological stage rather than by age. In population ecology, stage-structured approaches divide a population into discrete stages (for example, egg, larva, juvenile, adult; seed, seedling, vegetative, reproductive) and describe how individuals transition among stages over time, as well as how many survive within each stage and how many contribute offspring.

The mathematical core is a projection matrix framework. A typical stage-structured model uses a matrix A to project a stage-based population vector n_t to n_{t+1} via n_{t+1} = A n_t. Elements a_{ij} represent the probability that an individual in stage j at time t will be in stage i at time t+1, often incorporating survival in the column j and fecundity contributions in the top row for reproductive stages. Lefkovitch matrices are a common form for stage-structured models, while Leslie matrices are more commonly used for age-structured cases, with stage-structured variants allowing transitions that depend on development or size rather than strictly time.

Stage-structured models are widely used for plants, insects, fish, and mammals where development or size governs transitions more than chronological age. They require stage-specific data on survival, transition probabilities, and fecundity, and can accommodate different time steps and, with extensions, density dependence or environmental variability.

Limitations include the need for meaningful and stable stage definitions, potential oversimplification of continuous variation within stages, and assumptions of constant transition probabilities unless explicitly modeled as time- or state-dependent. Despite these caveats, stage-structured approaches provide a flexible framework for understanding growth, persistence, and management of biological populations.