Download limitations to distribution

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.