Large data requirements may restrict the use of matrix population models for analysis of population dynamics. Less data are required for a small population matrix than for a large matrix because the smaller matrix contains fewer vital rates that need to be estimated. Smaller matrices, however, tend to have a lower precision. Based on 37 plant species, we studied the effects of matrix dimensionality on the long-term population growth rate (lambda) and the elasticity of lambda in herbaceous and woody species. We found that when matrix dimensionality was reduced, changes in lambda were significantly larger for herbaceous than for woody species. In many cases, lambda of woody species remained virtually the same after a substantial decrease in matrix dimensionality, suggesting that woody species are less susceptible to matrix dimensionality. We demonstrated that when adjacent stages of a transition matrix are combined, the magnitude of a change in lambda depends on the distance of the population structure from a stable stage distribution, and the difference in the combined vital rates weighted by their reproductive values. Elasticity of lambda to survival and fecundity usually increased, whereas elasticity to growth decreased both in herbaceous and in woody species with reduced matrix dimensionality. Changes in elasticity values tended to be larger for herbaceous than for woody species. Our results show that by reducing matrix dimensionality, the amount of demographic data can be decreased to save time, money, and field effort. We recommend the use of a small matrix dimensionality especially when a limited amount of data is available, and for slow-growing species having a simple matrix structure that mainly consists of stasis and growth to the next stage.

Stochastic matrix models are used to predict population viability and the risk of extinction. Different stochastic methods require different amounts of estimation effort and may lead to divergent estimates. We used 16 transition matrices collected from ten populations of the perennial herb Primula veris to compare population estimates produced by different stochastic methods, such as selection of matrices, selection of vital rates, selection of matrix elements, and Tuljapurkar's approximation. Specifically, we tested the reliability of the methods using different numbers of transition matrices, and examined the importance of correlations among matrix entries. When correlations among matrix entries were included in the models, selection of vital rates produced the lowest and Tuljapurkar's approximation produced the highest estimates of mean population growth rates. Selection of matrices and matrix elements often produced nearly similar population estimates. Simulations based on incompletely estimated correlations among matrix entries considerably differed from those based on all correlations estimated, particularly when correlations were strong. The magnitude of correlations among matrix entries depended on the number of matrices, which made it difficult to generalize correlations within a species. Given that selection of vital rates or matrix elements is used, correlations among matrix entries should usually be included in the model, and they should preferably be estimated from the present data rather than according to other information of the species.

In a gynodioecious plant population, where female and hermaphroditic plants co- occur, females must produce more seeds or better- quality offspring than hermaphrodites to be maintained. Further, differences in the magnitude of pollen limitation and inbreeding depression between females and hermaphrodites may affect the relative fitness of the gender morphs and consequently population dynamics. We integrated demographic data into data on pollen limitation and inbreeding depression in a gynodioecious herb. Using a matrix model approach, we then examined the effects of pollen limitation and inbreeding depression on population growth rate and sex ratio. Hermaphrodites tended to contribute more to population growth rates than females. Because of the insensitivity of population growth rates to variation in annual fecundity, pollen limitation of either females or hermaphrodites had a negligible effect on population sex ratio. Inbreeding depression expressed simultaneously in three fitness components of the offspring produced by hermaphrodites reduced stochastic population growth rate and increased female frequency. Given that population growth rates are insensitive to fecundity transitions and that hermaphrodites have moderate selfing rates, our results suggest that inbreeding depression plays a larger role in the maintenance of females in gynodioecious populations than pollen limitation.