# Mathematics Colloquia and Seminars

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### Saving Species and Combating Invasions with Integral Operators

**Mathematical Biology**

Speaker: | Sebastian Schreiber, UC Davis Ecology |

Location: | 2112 MSB |

Start time: | Mon, Feb 27 2017, 3:10PM |

When studying populations, ecologists often measure the sizes of individuals e.g. body mass, maximal leaf length, shell diameter. These sizes often influence whether individuals survive, grow, or reproduce. To model this continuous size structure, ecologists use integral operators known as Integral Projection Models (IPMs). These IPMs and their stochastic extensions can be used to study the viability of endangered species, the probability that a population establishes in a new habitat, the rate of spatial spread of an invasive species, and the covariance structure of populations experiencing stochastic recruitment. I will discuss how the theories of random products of operators and continuous state branching processes can be used to analyze these models. The theory will be illustrated with data from Menzies' wallflower (an endangered species), perennial pepperweed (a local pest), and the maxima clam of the Indo-Pacific.