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Lecture 12: Population Analysis
Reading: Economy of Nature, pp. 331-340.
Populations and Demography
Population: group of individuals
of the same species in a given place at a given time.
Population Statistics
Census = number or density measures (number/unit area
or volume)
Primary Statistics
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natality
= births |
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mortality
= deaths |
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immigration
= migration in |
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emigration
= migration out |
Secondary Statistics
age distribution,
genetic composition, spatial distribution pattern
Collection of census
and primary population statistics makes it possible to construct a life
table analysis. A life table is a tabulation of mortality and/or fecundity
patterns (schedules) at
each age or stage in the life of individuals in a population. A life table
of mortality data permits
the construction of a survivorship curve for a given population.
An absolute census,
a direct count of each individual in a population can be very difficult,
in organisms other than birds and mammals, and even among birds and mammals
a complete
census may be impossible.
Population Estimation
Single Census, Mark-Recapture
Assumptions:
Closed population
Random captures
Random mortality with
respect to marks
Marks (tags) not lost
Methods:
1. Capture, mark, and release back to
the source population a sample of individuals
(time  ).
2. After an interval of time (at time
 ), capture a new sample from
the same population, the recapture sample, and determine the number
of marked individuals from
recaptured and the number of new unmarked captures.
Logic behind population estimation:
Calculations:
Population Estimate = Total number
marked in population and released at
/PPM
Multiple Census, Mark-Recapture
Sequential population estimation
Assumption of a closed population
no longer necessary
Total population at time +n
= Total population at + dilution
(gain) - loss
Sequential sampling of a given population
permits an estimate of survival rates:
Loss Rate = Death + Emigration
(per unit time)
= 1.0 - Survival Rate
Gain Rate = Births + Immigration (per unit
time)
Methods:
1. Capture, mark, and release back to
the source population a sample of individuals
(time ).
2. After an interval of time (at time
), capture a new sample from
the same population, the recapture sample, and determine the number
of marked individuals from recaptured
and the number of new unmarked captures.
3. Resample the same population at a
later time (at time ) and
determine the number of marked individuals from recaptured
and the number of unmarked captures.
Multiple Census Example:
Mark 500 field mice at and
release them at the site of capture.
At time (one
day later), capture a total of sixty (60) field mice at the same site.
Among these 60 mice are 20 marked individuals. Release all animals
back to population.
Estimate field mouse population:
Proportion marked = 20/60
= 1/3 = 0.33
Population estimate = 500/0.33
= 1500 field mice
At time  (one-hundred
days after the first recapture), another sample of 60 field mice
are captured. Among
these 60 mice are 16 marked individuals (originally marked and
released at )
Estimate field mouse survival rate and
population size:
Survival rate = 16/20 = 0.8
loss rate = 0.2 per 100 days
Proportion marked = 16/60
= 0.267
Number of mice from original population
expected in population at =
number marked and released at x
survival rate = 500 (0.8) = 400
At population
estimate = 400/0.267 = 1498
The number of unmarked mice in the population
at time was:
1500 - 500 = 1000
and the number of these unmarked mice expected to have survived to is:
1000 (0.8) = 800
so the total mouse population at should
be 400 + 800 = 1200
The extra 298 animals are new individuals,
representing gain to the population from either births and/or immigration.
Relative Density Estimates
Not a numerical estimate but
a means of making comparisons between sites or time intervals. Counting
burrows, scat, or individuals attracted to a bait.
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