Estimating the Size of a Population of Birds
Population estimation is an important tool to a wildlife biologist or ecologist because before proper management techniques can be applied, the population of a species in an area must be known. There are many methods of trapping used to gather data. For this exercise we will use a method of mark-recapture. Animals will be caught, marked and then recaptured to collect data.
We will estimate the size of a population of birds. The birds will be caught around a feeder. Individuals will be marked (banded) so that we will be able to identify those individuals that we have captured previously. On several later dates we will again capture birds at the feeder and count the number of marked and unmarked birds.
There are several methods of estimating the population size, but we will use only the Lincoln-Petersen technique. All mark-recapture techniques involve a number of assumptions:
a) all individuals in the population have an equal chance of being captured and recaptured;
b) the ratio of marked to unmarked individuals remains the same from the time of capture to the time of recapture;
c) marked individuals distribute themselves randomly throughout the population;
d) marked individuals do not lose their marks;
e) the population is closed: no immigration or emigration occurs during the sampling period.
You will answer the following questions in writing:
1) Exactly what population is being sampled and estimated by birdbanding?
2) Calculate your estimate of the size of the population, N, for each species for which we caught a workable number of individuals, using the Petersen estimate.
The basic model is that the ratio of marked and unmarked individuals in a sampling is the same as the ratio in the total population. That is,
N : M :: n : R
This can be rearranged to
N = (nM)
R
where
M = number marked in the initial collection
R = number of marked animals recaptured on the subsequent capture day
N = the population estimate
n = total number of animals captured on the subsequent capture day
However, experience has shown that this formula overestimates the population size. Hence, a correction factor has been added:
N = (n)(M + 1)
(R + 1)
3) Calculate the 95% confidence interval for each of these. To determine the limits within which the population lies, add and subtract two standard errors from the estimate.
(N-M)(N-n)
Standard Error (SE)= N Mn(N-1)
95% Confidence Interval = N + 2 SE
A large confidence standard error and confidence interval are the result of a small number of recaptures and a small sample size.
4) The Petersen estimate is based on several assumptions. If these are not met (and they usually are not fully considered), the estimate will be biased. For each one of the following Petersen estimates, assume the following violations of your assumptions has occurred and explain the effects on the estimate. No calculations are necessary—just explain the effects on the estimate. Will it produce an overestimate, an underestimate, or have no effect?
a) 5 marked (and released) birds die due to stress caused by handling during capture.
b) About half of the marked birds remain near the release site after the initial marking
c) About 100 birds immigrated into the area after the initial marking period.
d) There were 50 birds caught by neighborhood cats during the experiment
e) About 35 birds died during an especially cold night.
f) Previously caught birds can spot the net and avoid it as they fly to the feeder.
g) About 20% of the marked birds have lost their bands due to sloppy technique of tagging by a bleary-eyed biologist who partied too much the night before.
5) Which assumptions seem to be met by our banding exercise? Which do you feel were violated or are still unproven? Why? What could we do to justify these assumptions?
Sample Banding Data
(to be used only if we don’t catch enough real birds)
Black-capped ChickadeeInitial Collection / New / 52
Sample Day 1 / New / 30
Recapture / 12