Modeling the effects of size-dependent harvesting strategies on the population dynamics of tropical trees

Several forest plant species are harvested both lethally for their timber and non-lethally for their non-timber forest products by the local people for cultural and economic reasons. To maximize yield, harvesters target various life stages of these species including both adults and juveniles particularly when the number of harvestable adults decline. The demographic consequences of harvesting various plant sizes differ based on what life stage is targeted. In this paper, we develop a size-structured, seasonal system of difference equations and corresponding matrix model with time-varying harvest to model the effects of size-dependent harvesting strategies on the population dynamics of tropical trees. We illustrate numerically our work specifically on African mahogany, Khaya senegalensis, a tropical tree in Benin. Novel applications and combinations of previously established matrix compression algorithms are presented to determine certain rates in our model, with other rates coming from the use of generalized linear modeling and ordinary least squares estimation incorporating observed population data. Harvesting rates for two types of populations are estimated, one with simulated harvest and the other experiencing natural harvest. Eigenvalue analysis suggests that for the populations in our study, harvesting may not have a drastic effect on the long-term persistence of the population. However, this should be taken with caution given that our model does not account for stochastic environmental variations that can interactively reduce population growth rates.