Continuous size structured lottery model for studying coexistence of forest trees in a variable environment

Background/Question/Methods

A fundamental question in community ecology is how species diversity is maintained. Species differ from one another in so many physiological and demographic attributes that intuitively we expect there to be niche partitioning between species. However, without theoretical support, it is difficult to understand the significance of such differences between species. However, simple models such as the lottery model have become powerful tools for general understanding of coexistence mechanisms in systems with recruitment variation. Yet the abstraction of these simple models creates a gap between theory and empirical systems. A recent development of a matrix model form of the lottery model made it a better theoretical tool for communities in which the species have complicated life histories, but the matrix model has various limitations due to arbitrary classification of stage classes. One fundamental issue is that in the matrix model individual growth is specified by a probability of moving to the next size class, which is hard to link with continuous growth of an individual. We overcome this problem by developing new models that significantly improve our ability to bridge the gap between theory and empirical studies. 

Results/Conclusions

We develop a continuous size structure lottery model where individuals can be sensitive to both environment and competition over the whole range of life cycle. In this new model, size of an individual is related to demographic performance in a smooth way and we can easily study a variety of life history trade-offs in fecundity, mortality, and competitive ability. The most important improvement is that different life history traits can responses to environmental fluctuation differently, as in nature they are limited by different environmental factors. Particularly, we model reproduction and growth as separate environmental responses. Growth is modeled as a continuous change in size, which allows for potential large variation.  As in the non-structured lottery model, environment and competition interact nonadditively to promote species coexistence. However, the nonadditivities arise from both variation in reproduction and variation in growth. As a result, we have two distinct storage effects in this model promoting species coexistence. It turns out that recruitment variation at different stage of life cycles could be equally important for coexistence. Individual level variation in reproduction and growth can be easily incorporated into this model to disentangle the role of individual-level variation from species-level variation in species coexistence.