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Lecture 5

Lecture 5 & 6

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University of Toronto St. George
Ingrid L.Stefanovic

Lecture 4 & 5 22:09 Models of Population Ecology Population ecology was developed by zoologists More ambiguity about plant individuals Plants: Aspen: one seed produces many identical, connected stems Larkspur: many unique seeds; produce many unique plants Dandelion: no sex; many identical seeds produce many identical, unconnected plants. Hemi-epiphyte: plants that start life as an epiphyte, seed grows but as it gets bigger the roots descend to the ground. Strangler Fig: multiple different seedlings fuse together to make on tree with several genotypes Mathematical Models: Continuous versus discrete generations (= differential equations vs. difference equations) Density-dependent vs. density independent models Models with or without age-structure The goal of most population models: Project the trajectory of population growth through time; i.e., N as a function of t How many individuals are in the population now? N sub t Time advances one step t t + 1 When using differential equations, time steps are infinitesimally small: use concept of limits and calculus; growth is smooth; best suited for species with continuous reproduction. When using difference equations, time steps are discrete units (days, years, etc): use iterated recursion equations; growth is stepwise. Assume no immigration or emigration Treat birth and death as per-capita rates that are fixed constants Then, population changes by a constant factor each time step: N sub t+1=N sub t
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