if n is very small relative to k then growth will be

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Unformatted text preview: relative to K, then growth will be nearly exponential! ! ! What happens if N > K??! (derivation of this is in Appendix at end of lecture slides)! Graphically:! r and K from the logistic growth eqn. are borrowed to describe the ends of a continuum of life-history strategies! dN/dt = rN [1-(N/K)]! Maximum growth rate is reached at K/2! dN/dt = rN [1-(N/K)]! dN/dt! Growth accelerates nearly exponentially as 1-(N/K) is small (density dependence weak)! area under this curve Growth rate decelerates to zero as N=K and 1- (N/K) approaches zero! high r, do well in exponential growth r-selected species (high intrinsic rate of population growth) ! traits that are successful when densities are far from K and popn growth is driven by r : early reproduction, large number of offspring with little parental care, etc.! N! K-selected species (traits that are favored when population sizes are near K): large investment in few offspring; continuous reproduction, etc.! So how do we get to estimate things like r ?! Survivorship Curves! Demography: a study of the vital statistics (birth, death) of a population and how they vary with age! Life table: vital statistics of a cohort (group of individuals born about the same time)! Survivorship (lx) = proportion of individuals surviving to age or stage x! Reef coral (marine invertebrates) Type I: most individuals survive to old age (large mammals)! Type II: constant probability of dying (some birds)! Type III: most newly born individuals die, but survival of adults is high! #(most commonly observed: marine invertebrates, insects, plants)! Can also use life table approach to look at the value of each age class! Age-specific fecundity (mx) average number of offspring produced by an individual of age or stage x! Net Reproductive Rate (R0) = ave...
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