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A Theoretical Model of Oak Persistence Under Competition and Herbivory

M.V. Eitzel, Science & Justice Research Center, University of California, Santa Cruz


Oak tree populations in California face a number of challenges for population persistence.  Adult mortality due to diseases like Sudden Oak Death and cutting for development, seedling competition with annual grasses for scarce water resources during dry summers, and herbivory by cattle, deer, and rodents all threaten different oak life stages.  I use a differential equation-based theoretical model to represent three life stages of oaks: seedlings, juveniles, and adults.  I include the population dynamics of seedlings transitioning to juveniles, juveniles to adults, and adults producing new seedlings, as well as survival rates for each of the stages.  I also include a model of competition for light and water within seedlings and between seedlings and annual grasses.  Finally, I include a predation term to represent herbivores eating seedlings and grasses, using a Holling Type II (satiating) response with interference for predators and a death rate which depends on the resource extraction rate.  After seeking an equilibrium with non-zero amounts of seedlings, juveniles, adults, grasses, and browsers, I then conduct a sensitivity analysis to parameters representing life stage transitions and survival, parameters representing the competition with grasses, and parameters representing herbivory.  The analysis reveals that even low amounts of juveniles still result in overall persistence, and the most important parameters in determining this persistence are first the reproductive rate of adults, and second the survival rate of adults.  Oaks in this model are not strongly impacted by competition and very little by browsing. This result implies that protecting adults is a key part of conservation strategy and therefore continuing to defend and strengthen policies preventing cutting of adults could be as important as improving seedling survival and transitions to juvenile stages.