Lefkovitch

Lefkovitch is a surname and, in population biology, the name of a stage-structured population projection model known as the Lefkovitch matrix. The model, named after Leon Lefkovitch, extends the idea of the Leslie matrix to life stages rather than strict age classes. It is used to describe how individuals progress through discrete stages (for example, larva, juvenile, adult) with probabilities of surviving, remaining in the same stage, or advancing to the next stage, as well as stage-specific reproductive output.

Mathematically, the population at time t is a vector x_t whose components are abundances in each stage, and x_{t+1} = A x_t, where A is a square projection matrix. In a typical Lefkovitch matrix, the first row contains fecundities, the subdiagonal contains transition probabilities to the next stage, and diagonal elements reflect the probability of remaining in the same stage; other entries can represent backward transitions or skip-step progressions depending on the biology. The dominant eigenvalue of A gives the asymptotic growth rate, while the corresponding eigenvectors describe the stable stage distribution and reproductive value.

Applications include wildlife management, fisheries, plants, and any species with clearly defined life stages. The Lefkovitch model is often preferred when age cannot be easily tracked or when stage transitions are more informative than exact ages.

See also Leslie matrix.