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

2. 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.

3. 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.

4. 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

5. (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.

6. Time Less complicated Depends on the species Genus Magicicada

7. Space
more complicated
local population (Deme)

8. Space
more complicated
local population (Deme)

9. Distribution Patterns
Dispersal
Dispersion

10. Dispersion
Clumped

11. Dispersion
Random

12. Dispersion
Uniform

13. Dispersion

14. Distribution Pattern Depends on Scale

15. Distribution of Individuals on Small Scales

16. Distribution Patterns

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

18. 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.

19. 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

20. 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

21. Chi Square Table
[(n-1)s2]/x = [(25-1)2.68]/ = 43.5

22. 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?

23. 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 = ( )/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

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

25. Distribution Limits
Physical environment limits geographic distribution of a species.
Organisms can only compensate so much for environmental variation.

26. 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.

27. Kangaroo Distributions and Climate

28. 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.

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