TY  - JOUR
A1  - Caswell, Hal
T1  - Perturbation analysis of nonlinear matrix population models
Y1  - 2008/03/12
JF  - Demographic Research
JO  - Demographic Research
SN  - 1435-9871
SP  - 59
EP  - 116
DO  - 10.4054/DemRes.2008.18.3
VL  - 18
IS  - 3
UR  - https://www.demographic-research.org/volumes/vol18/3/
L1  - https://www.demographic-research.org/volumes/vol18/3/18-3.pdf
L2  - https://www.demographic-research.org/volumes/vol18/3/18-3.pdf
N2  - Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models), feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios), age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

ER  -