W09_L7_Population+Growth_II_final

W09_L7_Population+Growth_II_final - dN dt = rN(K-N K...

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Population Growth Continued! d N d t = r N (K-N) K Maximum sustained yield Survivorship curves Reproductive value Population viability Time lags, Self thinning, Law of Constant Final Yield and other tidbits of interest Clarification • What is a ‘closed’ population? – I said that for estimating population size with a simple Lincoln- Peterson mark-recapture method (1 recapture period); the assumption is that the population is ‘closed’ with no B,D,I or E. I also mentioned that repeated surveys could allow you to relax this assumption (Jolly-Seber mark recapture, but you don’t need to know those terms) and estimate (B+I) and (D+E). It is always tough to distinguish between processes that add individuals (B vs. I), or subtract (D vs E). – The Logistic equation was also a ‘closed’ population, but this time only to E and I. B and D are fundamental to population growth. – So, ‘closed’ means that we take some natural processes and exclude them. This is necessary when we can’t estimate them through this process. dN/dt = rN [1-(N/K)] Logistic population growth model Exponential growth Fraction of K remaining If N is very close to K, then population growth will be slow If N is very small relative to K, then growth will be nearly exponential What happens if N > K?? In words : population growth equals the amount expected under exponential growth multiplied by what percent of the carrying capacity is left [understand this!] Growth accelerates nearly exponentially as 1-(N/K) is small (density dependence weak) Maximum growth rate is reached at K/2 Growth rate decelerates to zero as N=K and 1- (N/K) approaches zero dN/dt = rN [1-(N/K)] dN/dt Graphically: APPLICATION: In managing a extracted resource (e.g., a fishery), the way to maximize sustained yield would be to maintain populations with the highest absolute growth This article from Dec. 2008 suggests that setting sustainable yield targets remains a problematic objective of fisheries management. The basis of this begins with this logistic equation and the observation that maintaining stocks at ~50% of carrying capacity will maximize the input of new fish into the system. Constraint?
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W09_L7_Population+Growth_II_final - dN dt = rN(K-N K...

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