Populations I. Demography II. Population growth Defining populations Distribution Counting populations (size/density) Age structure Sex ratio II. Population growth Exponential growth Logistic growth

Population What is a population? A group of organisms of the same species occupying a particular space at a particular time. Problems A group of organisms, of a single species, with equal probability of breeding with any other individual.

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.

LIMITATIONS TO DISTRIBUTION SPECIES ABSENT BECAUSE OF: AREA INACCESSIBLE YES DISPERSAL NO YES HABITAT SELECTION BEHAVIOR PREDATION PARASITISM COMPETITION DISEASE YES OTHER SPECIES NO PHYSICAL FACTORS TEMP, LIGHT, SOIL, FIRE CHEMICAL FACTORS WATER, OXYGEN, SALINITY, pH, NUTRIENTS

(A) Original distribution of the Gypsy moth in Eurasia. (B) Spread of the Gypsy moth in the northeastern United States after accidental introduction at the end of the 19th cent.

Time Less complicated Depends on the species Genus Magicicada http://insects.ummz.lsa.umich.edu/fauna/Michigan_Cicadas/Michigan/Index.html

Space more complicated local population (Deme)

Space more complicated local population (Deme)

Distribution Patterns Dispersal Dispersion

Dispersion Clumped

Dispersion Random

Dispersion Uniform

Dispersion

Distribution Pattern Depends on Scale

Distribution of Individuals on Small Scales

Distribution Patterns

Distribution of Individuals on Small Scales Random: Equal chance of being anywhere. Regular: Uniformly spaced. Clumped: Unequal chance of being anywhere.

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.

Dispersion i.e., x/s2 = 1 Most species exhibit a clumped distribution 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 sum of the squared differences / n-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

What is the dispersion pattern? Plot # # of tiger beetles 1 2 5 3 4 5 sample plots = n What is the mean # tiger beetles? What is the variance (s2) in # of tiger beetles?

What is the dispersion pattern? Plot # # of tiger beetles SS 1 2 (2-2.8)2 = 0.64 5 (5-2.8)2 = 4.84 3 (3-2.8)2 = 0.04 4 (1-2.8)2 = 3.24 5 sample plots = n df = n-1 = 4 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

Chi Square Table Rejection region Chi-Square value from Table

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.