Outline of Lecture:

I. Laboratory examples of population growth

II. Studies of populations in "real" world

III. Metapopulation

1. Concepts

2. Example

I. Laboratory examples of population growth

A. Gauss, 1934

Two species of Paramecium in salt solution Initial population size=2 Results: Different carrying capacities

B. Jordan and Jacobs, 1947

Escherichia coli aerobic, constant temp, pH renewed food at 2 temps result: different growth patterns

C. Park, Leslie, Mertz, 1964

flour beetles, Tribolium castaneum Two strains grown under same conditions Results: different r's, K's declining asymptote

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II. Studies of populations in "real" world

A. Field test: reindeer in Alaska

1911: reindeer introduced into 2 islands in Berring Sea St. Paul Island (41 sq miles): 4 males, 21 females St. George Island (35 sq mi): 3 males, 12 females results: no stable K different K St. Paul population crashed

B. Human population: Pearl and Reed 1920, Proc. Natl Acad. Sciences 6:275-288

.

Based on same equation introduced by Verhulst Used US census data for 1790-1910 Fitted data to logistic growth model Results 1920-1940 accurate 1940: actual pop showed geometric increase They predicted K=197 Million in 2006 In 1968, US population size was 196 K Pop size today? 278 million 6.2 Billion!   For other estimates of human carrying capacity see: http://www.bemidjistate.edu/PeoplEnv/carrycap.html

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III. Metapopulation

A. Concept

Definition:

Population of populations in discrete patches linked by migration and extinction.

Assumptions of approach

• Metapopulations are composed of discrete subpopulations
• Some degree of migration, colonization, and extinction
• If migration is high, the set of populations will be one large population
• Physical separation of patches
• Models are based on persistence and existence of patches, not numbers of individuals within patches.
• Regional or landscape scale

Elements of model

1. Parameters:

• p = fraction of patches occupied by subpopulations
• e = probability that subpopulation will go extinct
• c = rate of colonization
• I = immigration rate = proportion of sites successfully colonized per unit time
• E = extinction rate = proportion of sites that go extinct per unit time.

2. Probabilities

• probability of local extinction, p_e , is that probability that an occupied patch goes extinct in a given year
• Probability of persistence for a given time interval, n, is:

  

• [e.g. for two years with p_e = .7: P₂= (1-.7)(1-.7)=.09]
• Probability of regional persistence, P_x , where x is the number of patches

  a) probability that at least 1 patch remains occupied for a year

  b) or, 1- probability that all patches go extinct.



 

Basic metapopulation model

1. parameters of model

f = fraction of sites occupied

I = Immigration rate = proportion of sites successfully colonized per unit time

E = extinction rate = proportion of sites that go extinct per unit time.

a. Immigration rate, I, is dependent on p_I and the availability of unoccupied sites, 1-f:

b. Extinction rate, E, depends on local extinction, p_e. and fraction of sites occupied, f.

2. Model assumptions

a. homogeneous patches

d. no spatial structure

c. no time lags

d. constant probabilities of extinction and immigration

e. regional occurrence, f, affects local colonization and extinction

f. large number of patches

 

B. Other kinds of metapopulation models

1. Mainland-island model System of habitat patches (islands) located within dispersal distance from a very large habitat patch (mainland) where the local population never goes extinct; similar to island biogeography model.

2. Source-sink metapopulation. Metapopulation in which there are patches in which the population growth rate at low density and in the absence of immigration is negative (sinks) and patches in which the growth rate at low density is positive (sources); this definition differs from that of Pulliam (1988) when he first proposed source-sink dynamics to include small patches that have a low but positive equilibrium value in absence of migration.

C. Metapopulation examples

1. Butterfly populations
2. Tropical forest gap-dependent tree species

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