Chapter 10 Concepts
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Survivorship curves summarize patterns of mortality in populations
Age distributions are an indication of the dynamic of a population
Combining patterns of mortality with estimates of reproduction allow estimation
of population growth potential
Are Populations Stable?
NO!
What causes them to fluctuate?
Are there patterns?
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Basic Components
What are the basic processes
Births
that can cause a population to
increase or decrease?
Population additions:
– Births
– Immigrations
Population subtractions:
– Deaths
– Emigrations
(+)
Deaths
Population
Size
Immigrants
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(-)
Emigrants
Death = Mortality
What is the probability that any individual in a population will die?
The probability of death is expressed as a mortality rate.
Mortality rates can be calculated for:
– an entire population between two points in time, or
– single cohorts during specific life stages, or
– all age classes within a population.
Birth = Natality
How many new individuals will be introduced into the population each year?
Natality (also known as fecundity) is a measure of population additions
Two approaches:
– Semelparity
• Grow, reach sexual maturity, breed once, then die
– Iteroparity
• Grow, reach sexual maturity, breed more than once, then die
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Iteroparous Breeders
In general, fecundity is age specific in iteroparous breeders
– “Young” breeders usually have low fecundity
– “Experienced” breeders have increasing fecundity
– Fecundity declines as old age approaches
Calculation of “population fecundity rate” must take this into account.
Life Tables
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Two basic types:
– Dynamic or cohort life table
• Follows fate of a single group born at the same time
• Must be able to collect data on fates of significant portion of the
population at frequent intervals
– Static life table
• Assesses age structure of population at a single point in time
• Assumes that vital rates (birth and death) have been constant
Both mortality and fecundity can be assessed with life tables
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Basic Calculation (Mortality)
Start with a population of known individuals.
Count all individuals that die from the beginning to the end of your time period.
Divide the number dying by the number you started with.
This is the mortality rate, or probability of death.
Cohort Example
n(x) = number of living
individuals observed
during time x
d(x) = number dead in
interval = n(x) n(x+1)
m(x) = mortality rate =
d(x)/n(x)
l(x) = survivorship =
n(x)/n(0)
Age (x) n(x)
d(x)
m(x)
l(x)
e(x)
0
750
600
0.80 1.00 0.81
1
150
100
0.67 0.20 1.03
2
50
25
0.50 0.07 1.10
3
25
20
0.80 0.03 0.70
4
5
5
1.00 0.01 0.50
5
0
0
0.00
Basic Calculations (Fecundity)
• Estimate survivorship rate [l(x)]
• Survivorship = number alive at age (x) divided by number in original cohort
[n(0)]
• Estimate number of offspring produced per individual (female) in each age
class [b(x)]
• Multiply l(x) by b(x) to obtain survival weighted estimate of fecundity
• Sum l(x)b(x) column to obtain expected number of offspring per individual in
the original population
Cohort Example
• b(x) = number of offspring
produced per female
• l(x) * b(x) = number of
offspring produced by each
age class
• R(0) = the number of
offspring per cohort
A g e (x) n (x)
l(x)
b (x) l(x)b (x)
0
750
1 .0 0 0
0
0 .0 0 0
1
150
0 .2 0 0
1
0 .2 0 0
2
50
0 .0 6 7
4
0 .2 6 7
3
25
0 .0 3 3
8
0 .2 6 7
4
5
0 .0 0 7
2
0 .0 1 3
5
0
0 .0 0 0
N et R eproductive R ate = R (0 )
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0 .0 0 0
0 .7 4 7
Age Structure
The distribution of individuals among age classes defines the “age structure” of
a population.
Age structure is determined by:
– the probability of survival from one age to next
– the number of individuals entering the population in a given year
Age structure can tell us:
– whether the population is expanding
– patterns of survivorship (or mortality)
Age Determination
To determine age structure, we need two pieces of information:
– the age of individuals in the population
– the number of individuals in each age class
Methods of aging include:
– counting “annual rings”
– condition of teeth
– known age estimation
Oak Tree Age Structure (Fig. 10.19)
Population Structure of Cottonwoods (Fig. 10.20)
Finches and Variable Environments (Fig. 10.21)
Survivorship Curves (Fig. 10.18)
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Survivorship curves:
– show the average number of individuals remaining in the population as a
function of age class.
– They are based on the fate of an initial “cohort” individuals.
– A cohort is simply all individuals born during a single year or breeding
period.
Type I
Low early mortality
Once through “infancy”, high probability of survival to adulthood
Mortality primarily due to senescence
Type II
Mortality is relatively constant across ages
Sources of mortality affect age classes equally
Type III
• Very high early mortality
• Once through “infancy”, high probability of survival to adulthood
• Most individuals making it to the adult stage survive
Chapter 11 Concepts
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With unlimited resources, populations will expand rapidly
When resources are limited, populations will tend to remain at a constant level
Resource limitations affect birth and death rates and population growth
potential