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Ecology 3

# Ecology 3 - S mormonia male population size 6000 Males 6.3...

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1 S. mormonia male population size Year 85 86 87 88 89 90 # Males / 6.3 ha 0 1000 2000 3000 4000 5000 6000 Population growth: violating the assumptions ? How did we get that curve? From the finite growth equation: N t+1 = λ N t solve for λ : λ = N t+1 /N t in the limit as approach infinitesimally small time unit: λ Æ e r take the ln of both sides: r = ln ( λ ) substitute for λ : r = ln {(N t+1 )/(N t )} How did we get that curve? r = ln {(N t+1 )/(N t )} Calculate r from data: mean r = 0.65 Start with N 0 = 202 (from data) Then: r = ln {(N t+1 )/(N t )} e r = (N t+1 )/(N t ) N t+1 = N t e r N 1 = N 0 e r N 1 = (202)e 0.65 = 387

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2 For 1990: N 1990 = (N 1989 )e 0.65 = (2860)e 0.65 = 5478 butterflies S. mormonia male population size Year 85 86 87 88 89 90 91 # Males / 6.3 ha 0 1000 2000 3000 4000 5000 6000 Reality check! Assumptions of exponential growth: 1) r is constant for a given population 2) No limit to population growth….
3 Logistic Growth Equation dN/dt = rN (1-N/K) where K = carrying capacity exponential growth Factor describing closeness to carrying capacity K Time N Logistic Population Growth dN/dt = rN(1-N/K) Note: dN/dt = rN(1-N/K) r = constant

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