Capture

ESTIMATING NUMBERS Basic to the study of animal populations is the estimation of their numbers, no small task in wild populations. During the past several decades, much work has gone into the development of techniques and statistical methods to arrive at some estimates of animal populations. Basically the methods of estimating the numbers of animals can be put into three categories: true census, a count of all individuals on a given area; sampling estimate, derived from counts on sample plots; and indices, the use of different types of counts, such as roadside counts, animal signs, and call counts, to determine trends of populations from year to year or from area to area.

True Census. A true census is a direct count of all individuals in a given area. It is difficult to do for most wild populations, but there are situations where a total count can be made. Many territorial species are easily seen and heard and can be located in their specific area. Such a census is regularly used for birds. The spot-map method is probably the best approach. A sample plot of at least 10 hectares is marked out in a grid with numbered stakes or tree tags placed at intervals of 50 m.

1

Five or more daily counts are made throughout the breeding season. Each time a bird is observed, it is marked on a map of the plot. At the end of the census period all the spots at which a species is observed are placed on one map. The spots should fall into groups, with each group indicating the presence of a breeding pair.

The groups for each species can then be counted in order to arrive at the total population for the given area. Results are usually expressed as animals per hectare. Direct counts can be made in areas of concentration. Deer in open country, herds of elk and caribou, waterfowl on wintering grounds, rookeries, roosts, breeding colonies of birds and mammals permit direct counting usually either from the air or from aerial photographs.

Sampling Estimates. The sample estimate of population size involves two basic assumptions: (1)

the mortality and recruitment during the period the data are being taken are negligible or can be accounted for; and

2

(2)

(2) all members have an equal probability of being counted—they are not trap-shy or trap-addicted, they are distributed randomly through the population if marked and released, and they do not group by age, sex, or some other characteristic.

Sampling also involves one major general consideration. The method employed must be adapted to the particular species, time, place, and purpose. Relatively immobile forms, such as barnacles, mollusks, and cicada emergence holes, can be estimated by the quadrat method, similar to that employed for plants. The data can be analyzed for presence, frequency, and so on, or the results can be converted to a density per hectare. The size and shape of the quadrat will depend upon the density of the population, the diversity of the habitat, and the nature of the organism. A few preliminary surveys are made before settling on a quadrat size. Foliage arthropods may be sampled by a number of strokes with a standard sweep net over a 10-in2 area. The number of strokes needed to secure the sample must be predetermined. It will vary with the type of vegetation.

3

Estimates of zooplankton, obtained by pulling a plankton net through a given distance of water at several depths, can be made by filtering a known volume of sample through a funnel using a filter pump. The filter paper should be marked off in equal squares. With the aid of a hand lens or a binocular microscope, the organisms in each square can be counted. The numbers then can be related back to the total volume of water sampled.

CAPTURE-RECAPTURE METHODS

Introduction None of the numerous techniques available for estimating the size of animal populations is foolproof, and none can apply equally well to all populations. This section presents a popular method useful for estimating the population size of a single species of highly mobile animal, such as most small, medium and large vertebrates.

It

is

called

technique.

In

the

capture-recapture,

honor

of

some

early

or

mark-recapture,

contributors

to

its

4

development, fishery biologists refer to the basic procedure as Petersen’s method. ornithologists and mammalogists call it Lincoln’s method, and diplomatic ecologists refer to it as the Lincoln-Petersen method. Historical Background

One way to estimate the size of a population is to capture and mark individuals from the population, release them, and then resample to see what fraction of individuals carry marks. John Graunt first used this simple principle to estimate the human population of London in 1662. The first ecological use of mark-and-recapture was carried out by Danish fisheries biologist C. G. J. Petersen in 1896 (Ricker, 1975).

Tagging of fish was first used to study movements and migration of individuals, but Petersen realized that tagging could also be used to estimate population size and to measure mortality rates. Fisheries biologists were well advanced over others in applying these methods.

5

Lincoln (1930) used mark-recapture to estimate the abundance of ducks from band returns, and Jackson (1933) was the first entomologist

to

apply

mark-recapture

methods

to

insect

populations. The strength of mark-and-recapture techniques is that they can be used to provide information on birth, death, and movement rates in addition to information on absolute abundance.

The weakness of these techniques is that they require considerable time and effort to get the required data and, to be accurate, they require a set of very restrictive assumptions about the properties of the population being studied. Mark and recapture techniques may be used for open or closed populations. A closed population is one that does not change in size during the study period, that is, one which the effects of births, deaths, and movements are negligible.

An open population is the more usual case, a population that changes in size and composition from births, deaths, and movements. Different methods

must be applied to open and

closed populations. 6

1. Closed populations, single marking – Petersen method 2. Closed populations, multiple marking – Schnabel method 3. Open populations, multiple census – Jolly-Seber method

PETERSEN METHOD The Petersen method is the simplest mark and recapture method because it is based on a single episode of marking animals and a second episode or recapturing individuals. The basic procedure is to mark a number of individuals over a short time, release them, and then recapture individuals to check for marks. The second sample must be a random sample for this method to be valid; that is, marked and unmarked individuals must have the same chance of being captured in the second sample. The data obtained are M = Number of individuals marked in the first sample C = Total number of individuals captured in the second sample R = Number of individuals in second sample that are marked From these variables, we need to obtain an estimate of N = Size of population at time of marking

7

By a proportionality argument, we obtain N=C M R Or transposing N = CM R Where

(1)

N = estimate of population size at time or marking M = Number of individuals marked in first sample C = Total number of individuals captured in second sample R = Number of individuals in second sample that are marked

Example; Estimation of the population size of Rattus norvegicus in 1 ha plot. M = 200 Rattus norvegicus C = 250 R = 50 From Equation 1 N = CM R = 250 x 200 50 = 1000

8

This formula is the “Petersen estimate” of population size and has been widely used because it is intuitively clear. Unfortunately, formula (1) produces a biased estimator of population size, tending to overestimate the actual population. This bias can be large for small samples, and several formulas have been suggested to reduce this bias. Chapman (1951) and Seber (1982) recommends the estimator N = (M + 1)(C + 1) - 1 R+1

(2)

Which is unbiased if (M + C) > N and nearly unbiased if there are at least seven recaptures of marked animals (R > 7). This formula assumes sampling without replacement in the second sample, so any individual can be counted only once. In some ecological situations, the second sample of a Petersen series is taken with replacement so that a given individual can be counted more than once. For example, animals may be merely observed at the second sampling and not captured. For these cases the size of the second sample (C) can be even larger than the total population size (N) because individuals might be sighted several times. In this situation we must assume that

9

the chances of sighting a marked animals are on average equal to the chances of sighting an unmarked animal. The appropriate estimator, from Bailey (1952), is

N = M(C + 1) R+1

(3)

Which differs only very slightly from equation (2) and is nearly unbiased when the number of recaptures (R) is 7 or more.

Equation (3) is appropriate if the second sample of animals is obtained by collecting the animals one at a time, returning each to the population before taking another (which is analogous to removing a ball from the pot and returning it before taking another). This means that an animal (or ball) can be counted more than once as a member of the second sample (contributing more than once to the determination of R). Equation (2) is a more typical situation is where the animals of the second sample are captured all at once, so individual can only be counted once as a member of that sample. N = (M + 1)(C + 1) - 1 R+1

(2)

10

N = (200 + 1)(250+1) - 1 = 988 50 + 1 and N = M(C + 1) R+1

(3)

N = 200 (250 +1) = 984 50 + 1 As with all population estimates made from samples, there is an uncertainty caused by the error associated with examining a sample rather than the entire population. A measure of this error that expresses the uncertainty of a capture-recapture population estimate is the standard error (SE).

For Equation (2), this computed as SE =

SE =

(M + 1) (C + 1) (M - R) (C – R) (R + 1)2 (R + 2)

(4)

(200 + 1) (250 + 1) (200 – 50) (250 – 50) (50 + 1)2 (50 + 2)

= 105.8

11

For Equation (3), this computed as SE =

M2(C + 1)(C – R) (R + 1)2 (R + 2)

(5)

And for our example above,

SE =

2002(250 + 1)(250 – 50) = 121.8 (50 + 1)2 (50 + 2)

The precision with which the capture estimates population size is inversely dependent on the number of marked animals recaptured. Thus, attempt to obtain a reasonably large R by making C large. Confidence interval for mark recapture estimates may be approximated from the standard error. A 1 – α confidence interval may be computed as

N + (t)(SE)

(6)

Where t is student’s t for DF = ∞ (i.e., a 95% confidence interval calculation would use t = 1.96, and one would use t = 2.58 for a 99% confidence interval).

12

For our above example, the 95% confidence interval for Equation (2) could be calculated as: 988 + (1.96)(105.8) = 988 + 207 and we would say, with 95% confidence, that the population size is between 781 and 1195. The 95% confidence interval for Equation (3) could be calculated as: 984 + (1.96)(121.8) = 984 + 238 and we would say, with 95% confidence, that the true population size is between 746 and 1222.

Many modifications have been proposed to correct for some of the limitations of the Lincoln-Petersen technique. Discussions of a large number of them are in Andrewartha (1971). Burnham et al. (1987), Caughley (1977), Krebs (1989), Pollack (1991), Pollack et al. (1990), Seber (1982, 1986), and Southwood (1978).

Commonly recommended alternatives are the Schnabel method and the Jolly-Seber method. Newer procedures often use theory and sampling procedures based on multiple markings and/or multiple recaptures. While such procedures may in some

13

circumstances yield more accurate estimates than the LincolnPetersen procedure, they typically require more time and effort (and they may have more restrictive assumptions). Some of these methods are applicable if death, migration, or emigration alters the ratio of marked to unmarked animals. Assumptions of the Petersen Method 1. The population is closed, so N is constant 2. All animals have the same chance of getting caught in the first sample 3. Marking individuals does not affect their catchability 4. Animals do not lose marks between the two sampling periods 5. All marks are reported on discovery in the second sample Application

Capture-recapture methods may be applied to a variety of animals. Field sampling may be done with sweep nets for larger and slower arthropods or dip nets for benthic sampling of aquatic invertebrates. Collect clams and other relatively sessile animals in a small body of water by hand, employing random plots or transects. Capture fish or crayfish with seines.

14

Small mammals such as brown rat may be live-trapped using a grid of 100 traps spaced 10 to 20 m apart. Be sure to use the same sampling effort on all sampling days. In the laboratory, populations such as tenebrionid beetles, goldfish, or other convenient animals, as well as inanimate objects, such as beans, corks, or marbles, may be used to demonstrate the principles of capture-recapture.

Inanimate objects may also be subjected to experiments to test the importance of the assumptions given above and to investigate the effect of sample size on the standard error of the population estimate. Identify, mark, record, and release animals as soon after capture as possible. Animals with an exoskeleton or shell may be marked with rapid-drying, weatherproof paint; dyes or more permanent tags or bands may be applied to vertebrates. Fish may be marked by clipping off a portion of the dorsal, caudal, or anal fin. Amphibians or mammals may be toe-clipped. Consider the permanence of the marking procedure. Markings on exoskeletons or feathers will be lost if molting occurs between sampling; also, some types of tags can wear off. The proper 15

elapsed time between samplings depends largely on how long it takes for members of the first sample to distribute themselves randomly within the entire population. A week or two should suffice for most animals, but slow-moving forms may take longer.

Data in addition to numbers (e.g., weight, length, may also be collected from these samples). To obtain an estimate of density (D), an estimate of the area (A) sampled must be had in addition to the estimate of population size (N):

D = N/A

(7)

Indices. Indices are estimates of animal populations derived from counts of animals signs, calls, roadside counts, and so on. In this type of estimating all data are relative and must be compared with data from other areas or other time periods. The results do not give estimates of absolute populations, but they do indicate trends of populations from year to year and from habitat to habitat. Often this type of information is all that is needed.

16

Call Counts

Call counts are used chiefly to obtain population trends of certain game birds, such as the mourning dove, bobwhite quail, woodcock, and pheasant. A predetermined route is established along country roads; it should be no longer than can be covered in one hour’s time. Stations are located at quarter- or half-kilometer intervals, depending upon the terrain, and the species involved. The exact time to start must be determined for each area by the investigator. The observer stops at each station, listens for a standardized period of time (a minute or two), records the calls heard, and goes on to the next station. Routes should be run several times and an average taken. The number of calls divided by the number of stops gives a call-index figure. Roadside Count

The roadside count is similar to a call count, except with the exception that the number of animals observed along the route is recorded and the results divided by number of miles or kilometers. Other variations include counting of animal tracks, browse, signs, active dens and lodges, and so on.

17