Biol 201-review exam 2

Biol 201-review exam 2 - Biol 201- 2nd Summer Session-...

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Biol 201- 2 nd Summer Session- Review for 2 nd Exam Population Growth Exponential growth equation: N t = N 0 e rt calculates population size Or as a differential equation dn/dt = rN (expresses the rate of population change as the product of r and N) N 0 = number of individuals at time 0 N t = number of individuals at time > 0 r = intrinsic rate of natural increase (per capita rate of increase) e = base of natural logs (2.7183) t = number of time intervals in hours, days, years, etc. Populations grow slower than the exponential model predicts but WHY? All populations live in the real world The environment is not infinite Resources are FINITE! Basically, there are constraints from the environment!! Logistic Equation of population growth (Sigmoidal Growth ) gives the rate of population change as a function of r m , n and k dn/dt = rN (1- (N/K)) as the ration of N/K increases, population growth slows!! r = per capita rate of increase N = population size K = carrying capacity of the environment for that species (i.e. the maximum # that can be supported) The maximum rate of increase, r, occurs at a very low population size r decreases as N increases if N < K , r is positive and the population grows if N = K , r = 0 and population growth stops if N > K , r is negative and the population declines Liebig’s Law of the Minimum: the resource in shortest supply relative to demand is the limiting one!!
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Assumptions of the Logistic Model K is a constant r is a constant all individuals are identical there are no time lags K is a constant? is the environment truly constant? (day night, seasonality, disturbances) its NEVER constant r is a constant? well r is a function K, and since K changes so must r all individuals identical? NO!! newborns are not identical to adolescents and adolescents aren’t equal to adults, etc. no time lags? maturation and reproduction take time BUT, we still use the logistic model b/c it works!! (populations increase rapidly when they are small and grow slowly when they’re crowded Rate of Increase (r) vs. Size from viruses to large animals, intrinsic rate of increase, r, declines predictably with increasing size Two populations are still growing exponentially!! humans and the AIDS virus (HIV) Metapopulations: the idea that populations of a species in an area are actually subdivided- due in part because separate patches of the preferred habitat are separated by less suitable habitat- the populations have some degree of gene flow (migration) between them (they are connected but not strongly) Spreading of Risk (Den Boer): metapopulations are more stable than populations which are not subdivided- each subpopulation is both a source and sink for the other subpopulations- so risks are spread across the subpopulations they’re connected but the loss of one doesn’t endanger the others Exponential growth
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Biol 201-review exam 2 - Biol 201- 2nd Summer Session-...

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