Objectives:
 To be introduced to random sampling
 To understand the importance of sample size and how it can affect results
 To understand the concept of replication and how it can affect results
Introduction
The abundance of organisms and how this abundance changes in time and space are important concerns in ecology (Molles 1999). However, knowing the abundance of organisms is not an end in itself but rather is information used to help understand the characteristics and ecology of a population. For example, in the study and conservation of rare species, population sizes are needed to complete population viability analyses, determine potential genetic composition of a population and establish management and protection guidelines.
Estimating the size of a population for many species is difficult. Very small organisms (e.g., springtails) may be either rare or very common but still difficult to count. Aquatic (e.g. whales) and arboreal (e.g. songbirds) organisms live in environments that we find difficult to cohabitate, while the nocturnal behavior of other organisms (e.g. scorpions) make them less visible to us for measuring their abundance. In addition to temporal behavior, many organisms exhibit a spatial behavior by distributing themselves in a random, even, or clumped pattern in the environment. All of these factors make estimating population sizes difficult. Four basic strategies are used to acquire this information:
Census. In very few cases, the population boundary is strictly defined, and the organisms are sufficiently large and few that a complete count of the number of individuals can give you the population size.
Mark-Recapture. This technique is commonly used for elusive, moving organisms from insects to birds and whales. Essentially, a known number of individuals are captured, marked , and released back into the habitat. After some period of time, during which the marked individuals will have thoroughly intermixed with the rest of its population, another sample of individuals is captured, and the number of marked and unmarked individuals are noted. The presumption of the Lincoln-Peterson index described below is that the ratio of the number of marked and released organisms to the true population size is the same as the ratio of the number of recaptured individuals to the total number of individuals captured in the second sample.
The basic assumptions of the mark-recapture technique are:
All individuals in the population have an equal and independent chance of being captured.

The ratio of marked to unmarked individuals does not change between the
first and second samples. If individuals immigrate into or emigrate from a population between your sampling periods, or if individuals are born or die, then the proportion of marked animals to the true population size will vary for the two sampling periods and hence your estimate will not be accurate.
Marked individuals distribute themselves homogeneously with respect to
unmarked individuals. If capturing and marking makes individuals less likely to be captured in the future, this too will violate the assumption that the proportion of marked individuals to the true population size does not vary between sampling periods.
Many populations violate one or more of the above assumptions, so researchers have developed more complex approaches to using the mark-recapture technique. Usually, more episodes of marking and/or recapturing occurs, resulting in a closer estimate of the population size; refer to Cox (1990) for additional information on these techniques.
Catch per Unit Effort. In this technique, the principle of diminishing returns is used to give an estimate of the population size for a relatively small population (Cox 1990). As successive equal-effort samples are obtained and not returned to the habitat, the number of individuals caught decreases with continued sampling.
Sampling. If the organisms are stationary, you may consider sampling the population by using quadrats or plotless distance methods to obtain the density or cover (e.g. algae) of all individual of the species. For example, consider the problem of estimating the number of stems (genets + ramets), or density, of hay-scented fern along a forest edge. Hay-scented fern is often distributed in irregular or clumped patterns. Two basic techniques are used to gain density data in this situation (Barbour et al. 1999): Quadrats and Distance measures.
Quadrats. The number and species of individuals are recorded within randomly located plots within a particular area. The plot shape may be rectangular to take in more of the variable landscape or circular to minimize edge effect, while the plot size is determined by the type of individuals measured; if trees are the subject, then the plot size must be larger than for counting ants. The standard deviation and mean number of individuals per quadrat can be calculated and converted to a larger unit of area (e.g., number per hectare).
Distance Methods. A number of variants from the nearest individual method have been developed to estimate the density of a population (e.g., point-centered quarter, nearest neighbor, random pairs), but Engeman et al. (1994) showed that a slightly modified nearest individual method using up to three individuals is most accurate, efficient, and computationally straightforward. The base nearest individual method uses the distance from randomly selected points to the nearest individual to estimate population density. For example, points could be randomly selected from transects or coordinates laid over a map of the area, then the distance from each point to the nearest hay-scented fern is measured.
Take only one distance measurement per point. After many points have been used, you can calculate density per hectare (10,000m 2 ).

Literature Cited:
Bailey, N.T.J. 1951. On estimating the size of mobile populations for recapture data.
Biometrika 38: 293-306.
Bailey, N.T. J. 1952. Improvements in the interpretation of recapture data. Journal of Animal
Ecology 21 : 120-127.
Barbour, M.G., J.H. Burk, W.D. Pitts, F.S. Gilliam, and M.W. Schwartz. 1999. Terrestrial Plant
Ecology, 3 rd Edition. Benjamin/Cummings, Menlo Park, California, USA.
Cox, G.W. 1990. Laboratory Manual for Ecology, 6 th Edition. McGraw-Hill, New York, NY,
USA.
Engeman, R.M., R.T. Sugihara, L.F. Pank, and W.E. Dusenberry. 1994. A Comparison of plotless density estimators using Monte Carlo Simulations. Ecology 75: 1769-1779.
Molles, M. C. Jr. 1999. Ecology: Concepts and Applications. WCB/McGraw-Hill, Boston,
Massachusetts, USA.
ACTIVITY
Today, you will estimate the population size or density of a local species in the woods behind the Science Building. You will be given a compass, a 30m tape, and flagging for you to use in this exercise. You will collect your data using two different sampling methods to estimate the population of stationary organisms.
First, use the random number table below to determine your first sample location, randomly pick a series of number from the table, which will consist of your north, west, south and east coordinates by grouping them in twos. For example, if the series of number you randomly selected is 7639122, then 76 would be your north coordinate, 39, would be the west, 12 the south and 2 the east. These numbers correspond to the number of steps you need to take in each direction; use your compass to help you determine each direction.
Once you have reached your plot, set up a 10m x 10m quadrat using the tape measure and flagging. Count and record all of your species that are in your quadrat. Use your random number table again to find the location of your next sample plot. Set up a 20m x 2m quadrat in the new location. Count and record all of your species in the new quadrat.
After collecting your data, spend 10-15 minutes analyzing your data. Take your data from each quadrat and scale your values up to the number of individuals in 1 hectare (1 hectare=10,000m 2 ). In order to do this, determine how many individuals are in 1m2 of each quadrat and multiply each value by 10,000. Now you should have two estimates of the number of individuals in 1 hectare. Compare the two estimates found by your group and then share your data with the other groups. Calculate the mean, variance, standard deviation and standard error for each quadrat type using the data from all groups.
Next, think of the following questions. What are your estimates of population size or density? Why might the two estimates be similar or different? How do your estimates compare to the class average? Other than time, which is a restriction in all ecological studies, in what ways could you have improved your study? Turn in your calculations (1 copy per group) at the end of the lab.

Data Sheet: Names: