From Wikipedia,
the free encyclopedia.
Mark and recapture is a
method commonly used in ecology to
estimate population size and
population vital rates (i.e.,
survival, movement, and growth).
This method is most valuable when
a researcher fails to detect all
individuals present within a
population of interest every time
that researcher visits the study
area. Other names for this method,
or closely-related methods,
include: capture-recapture,
capture-mark-recapture, sight-resight,
and band recovery.
Field Work Related to
Mark-Recapture
Typically a researcher visits a
study area and uses traps to
capture a group of individuals
alive. Each of these individuals
is marked with a unique identifier
(e.g., a numbered tag or band),
and then is released unharmed back
into the environment.
Sufficient time is allowed to pass
for the marked individuals to
redistribute themselves among the
unmarked population.
Then the researcher returns and
captures another sample of
individuals. Some of the
individuals in this second sample
will have been marked during the
initial visit and are now known as
recaptures. Other animals captured
during the second visit will not
have been captured during the
first visit to the study area.
These unmarked animals usually are
given a tag or band during the
second visit and then are
released.
Population size can be estimated
from as few as two visits to the
study area. Although, commonly
more than two visits are made,
particularly if estimates of
survival or movement are desired.
Regardless of the total number of
visits, the researcher simply
records the date of each capture
of each individual.
An example of a partial
hypothetical data set appears
below.
A 01
B 11
C 10
D 10
E 11
In the above example, a "0"
means an individual was not
captured on a particular visit and
a "1" means an individual was
captured on a particular visit.
So, Animal B and Animal E were
captured on each of two visits.
Animal C and Animal D were
captured on the first visit, but
were not captured on the second
visit. Animal A was not captured
on the first visit, but was
captured on the second visit.
Such "capture histories" are
analyzed with a mathematical
formula to estimate population
size, survival, or movement.
Calculations for the
Lincoln-Petersen Method
The Lincoln-Petersen Method can be
used to estimate population size
if only two visits are made to the
study area. This method assumes
that the study population is
"closed". In other words, the two
visits to the study area are close
enough in time so that no
individuals die, are born, move
into the study area (immigrate) or
move out of the study area
(emigrate) between visits. The
model also assumes that no marks
fall off of animals between visits
to the field site by the
researcher, and that the
researcher correctly records all
marks.
Given those conditions, estimated
population size is:
Where:
- N = Estimate of total
population size
- n1 = Total number of animals
captured on the first visit
- n2 = Total number of animals
captured on the second visit
- m = Number of animals
captured on the first visit that
were then recaptured on the
second visit
The above equation is easily
derived from first principles as
follows. The researcher defines
the sample on the first visit, n1,
to be a population. The researcher
can then estimate the proportion
of this newly-defined population
that is captured on the second
visit: m / n1. This ratio provides
the probability of capturing an
previously-marked individual
during the second visit.
For example, suppose 50
individuals are marked on the
first visit and 25 of those
individuals are recaptured on the
second visit. The researcher
concludes that the probability of
capturing a previously-marked
individual on the second visit is:
m / n1 = 25 / 50 = 0.50
The researcher then assumes on the
second day that all individuals in
the actual population, N, have the
same capture probability as did
the recaptured individuals.
Imagine the researcher thinking on
the second visit, "I know that
today I recaptured 50% of the
animals I marked during my first
visit, so today I probably also
captured 50% of the individuals
that I did not mark on my first
visit. Indeed, today I probably
captured 50% of all the
individuals present in the study
site regardless of whether or not
those individuals were marked on
my first visit." This is expressed
as:
The first equation is simply a
re-expression of the equation
immediately above after solving
for N on the left-hand side.
Turtle Example
Suppose that you are a biologist
and you need to estimate the size
of a population of turtles in Lake
Turtelinia. You captured 10
turtles on your first visit to the
lake, and you colored their back
with red paint. A week later you
return to the lake and capture 15
turtles. Five of these 15 turtles
already had red paint on their
back, meaning they are recaptured
animals marked the previous week.
This means there are at least 20
turtles in the lake. However, to
estimate the population size in
Lake Turtelinia multiply 10 by 15,
and divide that product by 5. In
this example, the Lincoln-Petersen
Method estimates that there are 30
turtles in Lake Turtelinia.
A Refined Form of the
Lincoln-Petersen Method
A slightly better estimate of
population size can be obtained
with a modified version of the
first formula above. This modified
formula reduces bias in the
population estimate:
Where, as before:
- N = Estimate of total
population size
- n1 = Total number of animals
captured on the first visit
- n2 = Total number of animals
captured on the second visit
- m = Number of animals
captured on the first visit that
were then recaptured on the
second visit
Note that N + 1 in the above
equation is not a mistake: N is
obtained by subtracting 1 from
both sides of the above equation.
I simply did not write N isolated
by itself on the left hand side of
the equation due to my
unfamiliarity with the
mathematical syntax of equation
generation in Wikipedia.
An approximately unbiased variance
of N, or var(N), can be estimated
as:
Summary
The above is an outline for the
Lincoln-Petersen Method, the most
basic capture-recapture model.
However, there are a large number
of more sophisticated
mark-recapture models: the
Schnabel Census, the Jolly-Seber
Method and numerous variations
thereof, Change in Ratio Methods,
Multiple Observer Methods, Removal
Methods, Band Recovery Methods,
various Sight-Resight Methods, and
Radio Telemetry, as well as
Distance Sampling.
References
- Phillips, C. A., M. J.
Dreslik, J. R. Johnson, and J.
E. Petzing. 2001. Application of
population estimation to pond
breeding salamanders.
Transactions of the Illinois
Academy of Science
94(2):111-118.
- Seber, G. A. F. 1982. The
Estimation of Animal Abundance
and Related Parameters, 2nd
Edition. Blackburn Press,
Caldwell, New Jersey. ISBN:
1-930665-55-5.
