W09_L7_Population+Growth_II_final

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

This preview shows pages 1–2. Sign up to view the full content.

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?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/08/2009 for the course BIS 2 taught by Professor Schwartzandkeen during the Spring '09 term at UC Davis.

### Page1 / 6

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online