Lec4EEMB2W08

# Lec4EEMB2W08 - Logistic Growth Model Logistic Growth: No...

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Unformatted text preview: Logistic Growth Model Logistic Growth: No natural populations can maintain exponential growth indefinitely Population density fluctuates around a constant number of individuals As population size increases resources become limiting for growth and reproduction Logistic Growth Model Logistic Growth: Carrying Capacity (K) = The maximum population size that an environment can support - (K) varies over space and time - Crowding and resource limitation effects the population growth rate (r) - Population growth slows as its density approaches (K) Logistic Growth Model Logistic Growth Model: Modify the exponential growth model to incorporate changes in (r) as the population size grows toward (K) dN K-N =rN dt K Dynamics: Logistic Growth Model Logistic Growth Model: Modify the exponential growth model to incorporate changes in (r) as the population size grows toward (K) N dN K-N =rN dt K Time Dynamics: N K = Maximum sustainable population K - N = How many individuals environment can support K - N = Fraction of (K) available for population growth K Multiply (r) by K - N reduces (r) as N increases K Time - When population size is below (K) pop growth increases - When population size is near (K) pop growth decreases 1 Logistic Growth Model Natural populations; How well does the logistic model fit the growth of natural populations? - Populations of very small organisms fit fairly well - Many populations do not stabilize at (K) and deviate from sigmoid curves Logistic Growth Model Natural populations: So why does the logistic curve not fit well for most natural population growth patterns? Assumptions: 1) Each individual added to population has same negative effect on population growth Examples of exceptions: isolated plants and flamingos, chance events Predictions are correct only when: (rare) - environment is constant, no predators, no competition from other species Logistic Growth Model Natural populations: So why does the logistic curve not fit well for most natural population growth patterns? Assumptions: 1) Each individual added to population has same negative effect on population growth 2) Population approaches (K) smoothly - Time lag between the negative effect of population size increase and when they are realized - Time lags cause population size to overshoot and undershoot (K) - Populations may oscillate about (K) Logistic Growth Model Natural populations: Assumptions: 1) Each individual added to population has same negative effect on population growth 2) Population approaches (K) smoothly 3) Populations are large and density is important in regulation Examples: Insects, Microorganisms - sensitive to environmental fluctuations 2 Limiting Factors Any essential resource that is in short supply can limit population growth Density - Dependent Control: - Factors that alter per capita birth or death rates in a population are dependent on population density Limiting Factors Density - Dependent Control: Example: Bubonic Plague (Yersinia pestis) - Blood pathogen, existing in rats, rabbits and other small mammals. Transmitted by flea bites. - 14th century European cities, 25 million deaths - 1994 Indian Bubonic plague outbreak # killed Prey Density % killed Prey Density Limiting Factors Density - Independent Control: Factors that alter per capita birth or death rates in a population are independent of population density - Most common factors are climate and weather Limiting Factors Density - Independent Control Example: Monarch Butterfly - Migrate from Canada to Mexico - Logging removed temperature buffer -1995 freeze killed millions of Monarchs Natural populations % killed # killed A mix of density - dependent and density - independent factors Over long time scales many populations remain stable and close to (K) (Density - Dependent Control) Prey Density Prey Density Short term fluctuations in populations due to density independent factors 3 Population Regulation Stable and Unstable Populations: (At equilibrium the population does not change unless disturbed) Stable Equilibrium (birth = death) - If perturbed population will return to initial density - Stabilizing forces dampen population fluctuations - Density dependent control Population density Population Regulation Stable and Unstable Populations: Unstable Equilibrium - If perturbed, population may not return to initial density - Destabilizing forces enhance population fluctuations - Inverse density dependence, D-D with long time lags Population density E E Time Time Metapopulations Population is divided into discrete sub-populations which are connected by immigration and emigration Dynamics - Growth and reproduction within patches - migration between patches or colonization of empty patches Metapopulations Example - Bay checker spot butterfly (Euphydryas editha bayensis) Larvae (caterpillar) feeds on specialized plants which grow on serpentine soils Drought years most of the host plants die killing larvae - 1975-1977 (drought) 3 sub-populations became extinct - Morgan Hill (largest sub-population) serves as source of new colonists - Butterfly has recolonized formerly extinct patches of habitat Migration 1) Increase - local fluctuations are dampened 2) Decrease - local fluctuations are enhanced - increase probability of extinction 3) Intermediate - shifting mosaic of occupied and unoccupied patches 4 ...
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## This note was uploaded on 04/07/2008 for the course EEMB 2 taught by Professor Evan during the Winter '07 term at UCSB.

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