Integral Projection Models for trees: a new parameterization method and a validation of model output

1. Matrix models are popular tools for plant demographic studies, but their application to long-lived, slow-growing species is hampered by the fact that (i) model output is highly sensitive to category width and (ii) growth variation between individuals can only be partially accounted for. Integral Projection Models (IPMs) - an extension of matrix models - offer a solution to these problems. 2. Here, we introduce a new method to parameterize IPMs for trees - the 'integration method'- which allows constructing IPMs for long-lived, slow-growing species. This approach is more suitable than the 'midpoint rule', which is customarily used. 3. We built IPMs for six tree species from Vietnamese (sub)tropical forests. For four of these species, population growth rate (lambda) was highly sensitive to the number of categories in the transition matrix. Population growth stabilized for IPMs with 100-1000 categories, corresponding to categories of 0.1-1 cm in trunk diameter. This preferred width is much narrower than the 10-cm-wide categories customarily used in tree models. 4. The distribution of elasticity values over transition types (stasis, progression to next and further categories) is also highly sensitive to matrix dimension in IPMs. In addition, elasticity distribution is influenced by including or excluding growth variation. 5. Age estimates obtained from IPMs were also highly sensitive to matrix dimension: an IPM with 1000 size categories yielded 2-4 times higher age estimates for large trees than one with 10 size categories. Observed ages obtained from tree ring analyses for four of the study species allowed validating these estimates. IPMs with 10 categories strongly underestimated age, while those with 1000 categories yielded slight age overestimates. Underestimating age in small matrices is caused by the occurrence of unrealistically fast pathways through the life cycle and is probably widespread among tree models with broad categories. Overestimating ages in IPMs with narrow categories may be due to temporally autocorrelated growth or errors in fitting growth curves. 6. Synthesis. IPMs are highly suitable tools to analyse tree demography. We recommend that tree IPMs (and classical matrix models) apply narrow diameter categories (0.1-1 cm width) to obtain reliable model output.