Population Measurement

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Population Measurement

• Chapter 18, Pages 389 - 410 5th Ed.
• Chapter 11, Pages 181-193 6th Ed.

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Why do we want to know the size of a population?

• Management
• Conservation
• Ecological studies

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How can we determine population size?

• I. Can measure/count them all (direct)a true
  census.
• Practical? maybe if you are working with
  condors
• How do you do it? (aerial surveys?)
• II. Can use indirect methods.
• - For example
• 1. Subsample of density and extrapolation
• 2. Mark recapture
• 3. Population models

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Subsamples extrapolation.
Can sample the available habitat, estimate
density, and extrapolate to the total habitat
(density area) to arrive at total abundance.
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1
2
Assumptions sample units are homogenous units
or are representative of available habitat.
have identified and quantified all
available/relevant habitat. Density estimates
are not biased, or bias is known and corrected
for.
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Subsamples extrapolation.
Examples - removal sampling with expansion
(such as stream 3-pass with expansion to whole
stream abundance). - small scale animal trapping
with expansion to whole region. - herd counts
with expansion to entire regions.
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Mark Recapture. Mark recapture or
capture-recapture sampling involves trapping,
marking or tagging, and releasing a known number
of marked individuals into the
population. Later we return to recapture from
the same population while recording the number of
marked and unmarked individuals. The population
estimate is derived from the ratio of marked to
unmarked individuals in the recapture. There
are many forms of this model, but the simple,
single re-capture model is what we will utilize.
When only 1 recapture period is used the method
is called the Peterson Index or the Lincoln Index.
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The Basic Model NM nR
or N n M / R where N the population
size M number originally caught and
marked n total number of animals trapped in
the 2nd capture efforts. R the number of
recaptured animals from the 2nd capture.
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Assumptions of Mark-Recapture Models 1.
All individuals in the population have an equal
chance of capture (p). Due to p R / n, every
animal is assumed to have the same capture
probability. However, p can be influenced by
time, season, trap happy/shy. 2. Marked
unmarked ratio remains the same from release to
recapture (no greater mortality of marked
individuals???). 3. Marked ones re-distribute
homogenously in the population. 4. The mark is
not lost, or is identifiable. 5. The population
is closed (no emigration or immigration).
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An Example of the Peterson Index In
Blacklick Metropark in Ohio, Fall trapping
yielded 25 whitetail deer between 10-31 October.
All deer were marked with a plastic numbered ear
tag and released. Nightime spotlight surveys
began on 5 November. That night, 32 deer were
observed. Of these 32 deer, 12 were observed
with the plastic ear tags.
What is the population estimate for deer in this
park? N 25 3212 OR N /25
32/12 N 25 (32/12) N 66.7 deer
What would be an advantage/disadvantage of using
spotlighting and visual estimation for recapture
information?
could miss tag loss from distance
observations does avoid trap happy or shy
problems could repeat spotlighting observations
over time for estimates of n, r, and to get
replicate measures for estimating N.
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If we had originally marked 35 deer, then
spotlighted 47 with 8 observations of marked
deer, what would be the population estimate for
deer in this park? Remember, N / M as n/R..
N 35 478 OR N /35 47/8 N
35 (47/8) N 205.6 deer
Another example, we marked 2000, later censused
25,000 with 100 recaptures. What is N?
N 10025,000 / 2000 N 6.25 million
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Can we put Confidence Intervals on M-R Estimates?
Can be done using a formula for the Standard
Error (S.E.) S.E. N ?(N - M) (N -n) M n (N
- 1) The 95 CI is given by the Mean 2 SEs.
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Can we put Confidence Intervals on M-R Estimates?
Using the initial deer numbers data S.E.
66.7 (66.7 - 25) (66.7 - 12) (25 12) (66.7
-1) S.E. 66.7 2281/19710 S.E. 22.69 2S.E.
45.4 95 CI is 21.3 lt N lt 112.1
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Population Models
If we know something about the relative
abundances and mortalities of populations we can
begin to estimate population size indirectly,
mathematically from commonly collected
data First, mortality is made up of two
components M or Z N H M or Z mortality N
natural component (disease, parasites,
predation starvation) H harvest (usually
referred to as F in fisheries applications. If
we know 2 of the 3 values we can estimate the 3rd!
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How do we find out 2 of the 3 parameters?
1) Usually we assume N 0.2 or 0.4 for fish. 2)
We can get M from the Leslie Matrix or
capture/survey data. 3) With a guess or measure
of N and M we can solve for H. The Leslie
Matrix tracks the abundance or relative
abundance of an age-structured population through
time. An assumption of this is that C/f _at_ N.
C/f
Population size (N)
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For Example Following the 1990 year class of
walleye in survey gear. C/f in 1994 100
age-4 C/f in 1995 40 age-5 100 - 40 0.60
M 100 If N 0.2 then, by M N H 0.60
0.2 H 0.6 - 0.2 H 0.4 H
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Developing a Virtual Population Model 1.
Conduct continual surveys of C/f by age class. 2.
Initial estimate (maybe a guess) of natural
mortality. 3. Track age-group through time to
estimate H harvest mortality. 4. With catch
or harvest or landings data we know what the
actual harvest in numbers was. 5. Thus, we can
estimate N from actual harvest, and H from the
VPA.
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If we have standardized the CPUE (C/f) data, we
can determine the mortality rate (M) from a C/f
table, that is, in effect, a Life-Table of
Survival...
For example.the C/f number of age-2s in 1994
represent the survivors of the C/f numbers of
age-1s in 1993. From above, S 276/325
0.849, thus M 1 - S 1 - 0.849 0.151
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By tracking an age-class through the years you
can track changes in the total mortality rate
through changes in survival and representation in
the populations.
If harvest begins at age 2, then survival from
age-2 to age-3 is influenced by H, thus M N
H. If N 0.151 (assuming N is constant after
age-1) we can estimate H by difference from Z
above.
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So, from age-2 (93) to age-3 (94) the mortality
rate is M 1- S S 136 / 276 0.493 Thus,
M 1- 0.493 0.507 If H M - N (rearranged)
then, H 0.507 - 0.151 (from prev. pg.) H
0.356
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If H 0.356 that means that 35.6 of the
population starting the year as age-2 were
harvested, likewise 15.1 died of natural
causes. NOW, if we know what the harvest of
individuals of that age-class was (e.g. from
hunter check-ins etc.) we can put this into
numbers of animals, algebraically. If we know we
harvested 35.6 of the available animals, and we
know that this number (h) is, say 23,000 animals
we can estimate total numbers by h / H N
OR 23,000 / 0.356 64,607 Now we know how
many animals 1 C/f which lets us estimate
numbers of the other age classes and years..
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Now we know how many animals 1 C/f which lets
us estimate numbers of the other age classes and
years.. If 64,607 276 C/f So, 1 C/f
64,607/276 234.08 animals per C/f .now we can
convert the C/f into N by multiplying 234.08
C/f for each bin. Original C/F Data Converted
to N
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Survivorship Mortality Curves

• S M curves show age-specific mortality by
  looking at survivorship vs. time.

Type I. Survival of young is high, M
concentrated in old individuals (e.g. annual
grasses). Type II. Rate of M is fairly constant
over life (see cactus ground finch in text fig.
10.16). Type III. M is concentrated in the very
young/juveniles (e.g most fishes).
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Some other houscleaning items associated with
populations Natality is measured as birth
rates. Often times in animals we have
age-specific schedules of births of
offspring produced / time BY Age. WHY? Often
times natality changes with age. For e.g.
whitetailed deer produce 2 young per doe as
age-1, while in WV most 1 does produce 1 young.
Old does may see a reduction back to 1 fawn at
older ages.