Populations
Outline:
• Properties of populations
• Population growth
• Intraspecific population
• Metapopulation
Readings: Ch. 9, 10, 11, 12
Definition
• Population is a group of individuals of the
same species that inhabit a given area
Unitary organisms
Modular organisms
genet
ramet
Distribution of a population
Distribution of a population
Red maple
Distribution of a population
Moss (Tetraphis pellucida)
Abundance
versus
Population
density
Patterns of dispersion
Effect of scale on pattern of dispersion
Populations have age structure
Populations have age structure
Determining age
Determining age
wild turkey
quail
grey squirel
bat
Dispersal
•
•
•
•
Movement of individuals in space
Moving out of subpopulation = emigration
Moving into a subpopulation = immigration
Moving and returning= migration
Yellow-poplar
Gray whale
Ring-necked
duck
Gypsy-moth
POPULATION
GROWTH
Darwin’s 1st observation:
All species have such great potential fertility that
their population size would increase exponentially
if all individuals that are born reproduce
successfully.
Example of exponential growth:
the ring-necked pheasant, Phasianus colchicus
•
•
•
Native to Eurasia
1937: Eight birds introduced
to Protection Island
(Washington state)
1942: Population had
increased to 1,325 birds (a
166-fold increase!)
N/t = (b - d) Nt
Population Growth Models
• Assume no immigration or emigration
• Let N = population size
• Let N/ t = change in population size/unit time
= total # births - total # deaths
• Let mean birth rate per individual = b
= # births / individual / unit time
• Let mean death rate per individual = d
= probability of death for an individual / unit time
• N/ t = bN - dN
• Let r = b-d
Population Growth Models
• r = instantaneous rate of increase a.k.a. per
capita rate of increase
• Calculus notation is commonly used;
N/t = dN/dt
• If r > 0, population will increase exponentially at
rate, dN/dt, = rN
• For an exponentially growing population, the
number of individuals at time t, Nt = N0e(rt)
where No = initial population size and e = base
of natural logarithms
Exponential growth model: Nt = N0 e(rt)
St. Paul
reindeer
Life tables
cohort - all individuals born within a period
cohort life table – survivorship of a cohort over
time
Life tables
lx = represents the probability at birth of surviving to any given age
Life tables
dx = represents the age-specific mortality
Life tables
qx = represents the age-specific mortality rate
Mortality curves
Mortality curves
sedum
Survivorship curves
- plot of lx vs. time
Red deer
Theoretical survivorship curves
What happened to population in 1940s?
Human population growth
Darwin’s 2nd observation:
Populations tend to remain stable in
size, except for seasonal
fluctuations
Darwin’s 3rd observation:
Environmental resources are limited
• In real world, populations don’t increase
exponentially for very long
--> run out of resources
• An N increases, b decreases and/or d
increases
Population limiting factors
Density-dependent: effect intensifies as N
increases. E.g.:
1. Intraspecific competition
–
Between members of same species
2. Toxic waste accumulation
–
E.g. yeast cells: produce ethanol as byproduct of fermentation (see next slide)
3. Disease
–
Spreads more easily in crowded
environments
Effect of crowding on birth rate
Effect of crowding on survivorship
Intraspecific population regulation
Carrying capacity, K
= maximum number of individuals that a
particular environment can support
• Take into account by the Logistic Growth
Equation,
dN/dt = rN (1-N/K)
Logistic model
Logistic model
Exponential vs. logistic model
Gray squirrel
How good is the logistic
model?
• Describes growth of simple organisms well,
e.g. Paramecium in a lab
• Water fleas (Daphnia spp.): population
initially overshoots K until individuals use up
stored lipids --> crash down to K
• Song sparrows: populations crash frequently
due to harsh winter conditions
– N never have time to reach K
– Population growth not well described by the
logistic model
Life History Strategies
• When N is usually << K, natural selection
favors adaptations that increase r
--> lots of offspring
= r selection
– E.g. species that colonize short-lived environments
• When N is usually close to K, better to produce
fewer, “better quality” (i.e. more competitive)
offspring
= K selection
• E.g species that live in stable, crowded environments
Density dependence
Density dependence
with Allee effect
Density dependence
with Allee effect
American ginseng
Types of competition
• Competition: individuals use a common
resource that is in short supply relative to the
number seeking it
• Intraspecific vs. interspecific
• Scramble vs. contest
• Exploitation vs. interference
Density effect on growth
Density effect on growth
Density effect on growth
Density effect on growth
Self thinning
Horseweed
Density effect on reproduction
Territoriality
Grasshopper sparrow
Ammodramus savannarum
White-crowned sparrow, Zonotrichia leucophrys
Banding study in California: 24% of current territory holders had been floaters for 25 yrs. before acquiring a territory.
Uniform distribution of plants occurs due to the development of
resource depletion zones around each individual
Population limiting factors
Density-independent: effect does
not depend on N.
– E.g. weather / climate
– Thrips insects:
• Feed on Australian crops (pest)
• Population growth very rapid in early
summer
• Drops in late summer due to heat,
dryness
--> N never has time to get close to K
Density-independent factors
Density-independent factors
DRY
Turbid
WET
Clear
e.g. Dungeness crabs
• Density-dependent
factors:
competition;
cannibalism
• Density-independent
factors: water
temperature
Metapopulations
a population of populations
Chapter 12
Metapopulation: A group of moderately isolated
populations linked by dispersal
Criteria for a metapopulation
1. Habitat occurs in discrete patches
2. Patches are not so isolated as to prevent
dispersal
3. Individual populations have a chance of
going extinct
4. The dynamics of populations in different
patches are not synchronized
–
i.e., they do not fluctuate or cycle in synchrony
Metapopulation dynamics:
spatial scales
1. Local (within-patch)
2. Metapopulation (regional)
 Shifting mosaic of occupied
and unoccupied patches
Checkerspot butterfly
Levin’s model of metapopulation dynamics
• E - subpopulation extinction rate = eP
• e – probability of a patch going extinct/unit time
• P – proportion of occupied patches
• C – colonization rate = mP (1-P)
• m – dispersal rate
• (1-P) – unoccupied habitats
E=C
equilibrium point,
Where
0 = [mP(1-P)] - eP
If C>E, P increases; If C<E, P decreases
Pequilibrium= 1-e/m
Bush cricket
Larger patches have larger
populations (and therefore
lower risk of extinction)
Skipper
butterfly
Effect of habitat heterogeneity
Mainland-island
population
structure: one large
population (low
extinction risk)
provides colonists for
many small
populations (high risk)
Checker-spot
butterfly
Rescue effect: island recolonized from “mainland”
• High quality / permanent population = source
population
• Temporary patches = sink populations
Skipper
butterfly