Get access

Matrix dimensionality in demographic analyses of plants: when to use smaller matrices?


  • Satu Ramula,

  • Kari Lehtilä

S. Ramula and K. Lehtilä, Dept of Natural Sciences, Södertörn Univ. College, SE-14189 Huddinge, Sweden (


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 (λ) and the elasticity of λ in herbaceous and woody species. We found that when matrix dimensionality was reduced, changes in λ were significantly larger for herbaceous than for woody species. In many cases, λ 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 λ 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 λ 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.

Get access to the full text of this article