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p. 221 MollesInvestigating Distributions
PopulationsI. Demography
Defining populationsDistributionCounting populations (size/density)Age structureSex ratio
II. Population growthExponential growthLogistic growth
Population• What is a population?
– A group of organisms of the same species occupying a particular space at a particular time.
• Problems– How big is a particular
space?– When is the particular
time?– A group of organisms, of a
single species, with equal probability of breeding with any other individual.
Species
• What is a species?
Males sterile, females fertileSpecies?
TigonLiger
Population Characteristics
• Species
Equus caballus Equus asinus
Population Characteristics
• Species– A group of
organisms capable of interbreeding
A cross between a male donkey (jack) and a female horse (mare) produces a mule. A cross between a female donkey (jennet or jenny) and a male horse (stallion) produces a hinny.
Population Characteristics
• Species– A group of
organisms capable of interbreeding and producing fertile offspring.
– Isolated gene pools
• Isolation– Temporal– Spatial– Mechanical– Behavioral
Genes go in but they don’tCome out!
• Species– A group of organisms
capable of interbreeding and producing fertile offspring.
– Isolated gene pools• Temporal• Spatial• Mechanical• Behavioral
• Population– A group of organisms, of a
single species, with equal probability of breeding with any other individual.
• Distribution– Clumped– Random– Uniform
• Species– A group of organisms
capable of interbreeding and producing fertile offspring.
– Isolated gene pools• Temporal• Spatial• Mechanical• Behavioral
• Population– A group of organisms, of a
single species, with equal probability of breeding with any other individual.
• Distribution– Clumped– Random– Uniform
• Species– A group of organisms
capable of interbreeding and producing fertile offspring.
– Isolated gene pools• Temporal• Spatial• Mechanical• Behavioral
• Population– A group of organisms, of a
single species, with equal probability of breeding with any other individual.
• Distribution– Clumped– Random– Uniform
• Species– A group of organisms
capable of interbreeding and producing fertile offspring.
– Isolated gene pools• Temporal• Spatial• Mechanical• Behavioral
• Population– A group of organisms, of a
single species, with equal probability of breeding with any other individual.
• Distribution– Clumped– Random– Uniform
• Species– A group of organisms
capable of interbreeding and producing fertile offspring.
– Isolated gene pools• Temporal• Spatial• Mechanical• Behavioral
• Population– A group of organisms, of a
single species, with equal probability of breeding with any other individual.
• Distribution– Clumped– Random– Uniform
LIMITATIONS TO DISTRIBUTIONLIMITATIONS TO DISTRIBUTION LIMITATIONS TO DISTRIBUTIONLIMITATIONS TO DISTRIBUTION
DISPERSAL
BEHAVIOR
OTHER SPECIES
CHEMICAL FACTORS
WATER, OXYGEN, SALINITY, pH, NUTRIENTS
PHYSICAL FACTORSTEMP, LIGHT, SOIL, FIRE
AREA INACCESSIBLE
SPECIES ABSENT BECAUSE OF:
YESYES
NONONONO
HABITAT SELECTIONYESYESYESYES
PREDATIONPREDATIONPARASITISMPARASITISMCOMPETITIONCOMPETITIONDISEASEDISEASE
YESYES
NONONONO
(A) Original distribution of the Gypsy moth in Eurasia.
(B) Spread of the Gypsymoth in the northeasternUnited States after accidental introduction atthe end of the 19th cent.
Time• Less
complicated
• Depends on the species
http://insects.ummz.lsa.umich.edu/fauna/Michigan_Cicadas/Michigan/Index.html
Genus Magicicada
Space
• more complicated
• local population (Deme)
Space• more complicated• local population
(Deme)
Distribution Patterns• Dispersal
• Dispersion
Dispersion
• Clumped
Dispersion
• Random
• Uniform
Dispersion
Dispersion
Dispersion
Distribution Pattern Depends on Scale
Distribution of Individuals on Small Scales
Distribution Patterns
Dispersion
• How does one test for type of dispersion?
• Poisson Distribution - a mathematical description of infrequent, random events– sample mean (x) = sample
variance (s2)• Mean = average• Variance =
• Populations with a random distribution will follow a Poisson distribution– i.e., x/s2 = 1
Dispersion• If x/s2 < 1 then distribution is
clumped• If x/s2 > 1 then distribution is
Uniform• We can test this using the
following equation:– Critical value =
[(n-1)s2]/x– Where: n = number of
samples (plots)• This function has a Chi
square distribution i.e., use a Chi square table with n-1 degrees of freedom
Chi Square Table
[(n-1)s2]/x = [(25-1)2.68]/1.48 = 43.5
Distribution Limits
• Physical environment limits geographic distribution of a species.– Organisms can only compensate so much for
environmental variation.
Kangaroo Distributions and Climate
• Caughley found a close relationship between climate and distribution of the three largest kangaroos in Australia.– Macropus giganteus - Eastern Grey
• Eastern 1/3 of continent.
– Macropus fuliginosus - Western Grey• Southern and western regions.
– Macropus rufus - Red• Arid / semiarid interior.
Kangaroo Distributions and Climate
Kangaroo Distributions and Climate
• Limited distributions may not be directly determined by climate.– Climate often influences species distributions
via: • Food production • Water supply • Habitat• Incidence of parasites, pathogens and competitors.
Distributions of Plants along a Moisture-Temperature Gradient• Encelia species distributions correspond to
variations in temperature and precipitation.
Distribution of Individuals on Small Scales
• Random: Equal chance of being anywhere.– Uniform distribution of resources.
• Regular: Uniformly spaced.– Exclusive use of areas.– Individuals avoid one another.
• Clumped: Unequal chance of being anywhere.– Mutual attraction between individuals.– Patchy resource distribution.
Distributions of Individuals on Large Scales
• Bird Populations Across North America– Root found at continental scale, bird
populations showed clumped distributions in Christmas Bird Counts.
– Clumped patterns occur in species with widespread distributions.
– Brown found a relatively small proportion of study sites yielded most of records for each bird species in Breeding Bird Survey.
27 November 2001 by NASA satellites
What is the dispersion pattern?
• 5 sample plots = nPlot # # of
tiger beetles
1 2
2 5
3 3
4 1
5 3
What is the dispersion pattern?• 5 sample plots = n• df = n-1 = 4• Mean = (2+5+3+1+3)/5 = 2.8• Mean = (2+5+3+1+3)/5 = 2.8• Var = sum of the squared
differences / n-1– Sum of squares = 8.8– Var = 8.8/4 = 2.2
Ratio = 2.8/2.2 = 1.27
χ2critical = (4*2.2)/2.8
= 3.14
Plot #
# of tiger
beetles
SS
1 2 (2-2.8)2 = 0.64
2 5 (5-2.8)2 = 4.84
3 3 (3-2.8)2 = 0.04
4 1 (1-2.8)2 = 3.24
5 3 (3-2.8)2 = 0.04
Chi Square Table
Rejection region
Chi-Square value from Table