p. 221 Molles Investigating Distributions

Populations I. Demography 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 –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 fertile Species? Tigon Liger

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’t Come 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 DISTRIBUTION DISPERSAL BEHAVIOR OTHER SPECIES CHEMICAL FACTORS WATER, OXYGEN, SALINITY, pH, NUTRIENTS PHYSICAL FACTORS TEMP, LIGHT, SOIL, FIRE AREA INACCESSIBLE SPECIES ABSENT BECAUSE OF: YES NONO HABITAT SELECTION YESYES PREDATIONPARASITISMCOMPETITIONDISEASE YES NONO

(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

Space more complicated local population (Deme)

Space more complicated local population (Deme)

Distribution Patterns Dispersal Dispersion

Clumped

Dispersion Random

Uniform 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 (s 2 ) Mean = average Variance = Populations with a random distribution will follow a Poisson distribution – i.e., x/s 2 = 1

Dispersion If x/s 2 < 1 then distribution is clumped If x/s 2 > 1 then distribution is Uniform We can test this using the following equation: –Critical value = [(n-1)s 2 ]/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)s 2 ]/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

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 = n Plot ## of tiger beetles

What is the dispersion pattern? 5 sample plots = n df = n-1 = 4 Mean = ( )/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 χ 2 critical = (4*2.2)/2.8 = 3.14 Plot # # of tiger beetles SS 12(2-2.8) 2 = (5-2.8) 2 = (3-2.8) 2 = (1-2.8) 2 = (3-2.8) 2 = 0.04

Chi Square Table Rejection region Chi-Square value from Table