Exponential Growth, Logistic Growth – Fish Population Management | WATS 3700, Study notes of Environmental Science

Download Exponential Growth, Logistic Growth – Fish Population Management | WATS 3700 and more Study notes Environmental Science in PDF only on Docsity! 1 Fish Population Management • Exponential Growth • Logistic Growth Exponential Growth • Difference Equation – Nt+1 = Nt + r(Nt) – r = Birth rate – Death rate – Equation can be generalized – Nt = N0 erT • Differential Equation – dN/dt = rN 2 Example of Exponential Growth y = 90.9e0.095x 0 50 100 150 200 250 0 2 4 6 8 10 12 Time A bu nd an ce Logistic Growth • Difference Equation – Nt+1 = Nt + r ((K-Nt)/K) Nt – When does N increase? – When does N Decrease? – How to determine K? Generalizes to Differential Equation dN/dt = r ((K-N/K)) N 5 Arctic Char Growth 0 0.1 0.2 0.3 0.4 0.5 2002 2003 2004 2005 Year In st an eo us G ro w th (y ea r - 1 ) E-5 Fog-2 Char Density 0 20 40 60 80 100 1999 2000 2001 2002 2003 2004 2005 Year D en si ty (# /H a) E-5 Fog-2 Growth rate Is density- dependent Fecundity • Usually depends on growth and size 6 Survival of eggs • Usually small Survival of age class Depends on Habitat Predators Fishing Pressure Often size dependent Number of adults determine eggs 2007— a * Stock-Recruitment Effects Recruits o a 0 100 Spawners. Figure 7.8. Stock-recruitment relationships for a stock that consists of spatially separated sub- stocks when all substocks are present (a) and when less productive substocks have been eliminated by overexploitation (b and 9. a Seema Ree Figure 6.6: Ricker Stock-recruitment Curve Fitted to Data from the R Areto-Norwegian Cod Stock by Least Squares. 3 2 3 20 Speman Poston Se a teen eg b xs @ 3 § i 2 : a ee 3 oy = 5 ° $ cS cs 25 3 MATURE STOCK (EGGS x 10-4)