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

2. Population What is a population?

3. Species What is a species?

4. Population Characteristics Species Equus caballus Equus asinus

5. Species Population Distribution

7. 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

8. (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.

9. Time http://insects.ummz.lsa.umich.edu/fauna/Michigan_Cicadas/Michigan/Index.html Genus Magicicada

10. Space

12. Distribution Patterns Dispersal Dispersion

13. Clumped

14. Dispersion Random

15. Uniform Dispersion

16. Distribution Pattern Depends on Scale

17. Distribution of Individuals on Small Scales

18. Distribution Patterns

19. 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

20. 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

21. Chi Square Table [(n-1)s 2 ]/x = [(25-1)2.68]/1.48 = 43.5

22. Distribution Limits Physical environment limits geographic distribution of a species.

23. 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.

24. Kangaroo Distributions and Climate

25. 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.

26. Distributions of Plants along a Moisture-Temperature Gradient Encelia species distributions correspond to variations in temperature and precipitation.

27. 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.

28. 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.

29. What is the dispersion pattern? 5 sample plots = n Plot ## of tiger beetles 12 25 33 41 53

30. 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 χ 2 critical = (4*2.2)/2.8 = 3.14 Plot # # of tiger beetles SS 12(2-2.8) 2 = 0.64 25(5-2.8) 2 = 4.84 33(3-2.8) 2 = 0.04 41(1-2.8) 2 = 3.24 53(3-2.8) 2 = 0.04

31. Chi Square Table Rejection region Chi-Square value from Table