Mathematics Colloquia and Seminars
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Management-based models in ecologyMathematical Biology
|Speaker: ||Julie Blackwood, UC Davis|
|Location: ||2112 MSB|
|Start time: ||Thu, May 6 2010, 2:10PM|
Ecological management important for the persistence and biodiversity of
ecosystems is considered in two general contexts. First, optimal management
of invasive species is considered by adapting a linear-quadratic control
model which is a dynamic optimization method that accounts for spatially
explicit dynamics. Second, methods for ecosystem-based management of
Caribbean coral reefs are developed by accounting for various aspects of an
analytic model describing the dynamics of coral-algal interactions. The
model in its simplest form exhibits hysteresis between two alternative
stable states, one with high levels of coral cover and the other a degraded
coral-depleted state with corresponding high levels of macroalgae.
Extensions are made to explicitly consider exploitation of herbivorous reef
fish which are important in supressing macroalgal overgrowth of coral.
Importantly, this formulation provides a concrete example of ecosystem-based
management by determining how fisheries management fits into the wider
ecosystem impact. Other aspects of this system are considered, including the
role of time delays in grazer response to changes in habitat as well as the
long term effects of multiple interacting coral stressors, namely fishing
effort and hurricane impacts.