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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 – 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 HABITAT SELECTION YES DISPERSAL YES PREDATION PARASITISM COMPETITION DISEASE PHYSICAL FACTORS TEMP, LIGHT, SOIL, FIRE YES NO BEHAVIOR OTHER SPECIES NO 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 • 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 = sum of the squared differences / n-1 • 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 What is the dispersion pattern? • 5 sample plots = n • What is the mean # tiger beetles? • What is the variance (s2) in # of tiger beetles? Plot # 1 # of tiger beetles 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 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 # 1 # of SS tiger beetles 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 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.

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