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