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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 KN =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 KN =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, DD with long time lags
Population density E E Time Time Metapopulations
Population is divided into discrete subpopulations 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  19751977 (drought) 3 subpopulations became extinct  Morgan Hill (largest subpopulation) 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.
 Winter '07
 Evan

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