1. In order to understand how changes in individual performance (growth, survival or reproduction) influence population dynamics and evolution, ecologists are increasingly using parameterised mathematical models. 2. For continuously structured populations, where some continuous measure of individual state influences growth, survival or reproduction, integral projection models (IPMs) are commonly used. 3. We provide a detailed description of the steps involved in constructing an IPM, explaining how to: 1) translate your study system into an IPM; 2) implement your IPM; and 3) diagnose potential problems with your IPM. We emphasize how the study organism's life cycle, and the timing of censuses, together determine the structure of the IPM kernel and important aspects of the statistical analysis used to parameterise an IPM using data on marked individuals. 4. An IPM based on population studies of Soay sheep is used to illustrate the complete process of constructing, implementing, and evaluating an IPM fitted to sample data. 5. We then look at very general approaches to parameterising an IPM, using a wide range of statistical techniques (e.g. maximum likelihood methods, generalized additive models, nonparametric kernel density estimators). Methods for selecting models for parameterising IPMs are briefly discussed. 6. We conclude with key recommendations and a brief overview of applications that extend the basic model. This article is protected by copyright. All rights reserved.
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