By Lee-Ann C. Hayek & Ron Heyer, Smithsonian Institution
Although amphibian fieldwork sampling needs to be done according to what we know of statistical principles, we often wish our random selection had been in a better, more productive area. Field samples are often pitiably small in number or non-informative, yet we know the amphibians are out there, somewhere beyond the boundaries of our samples. Use of the techniques of Adaptive Cluster Sampling (ACS) is one way to enhance our catch or observations for certain types of sampling techniques. Below we describe the basics of this approach and give a reference for further information.
DEFINITION Adaptive Cluster Sampling (ACS) designs are statistical strategies for the selection of initial random (unrestricted or restricted) samples of plots, areas, transects, or traps that allow for inclusion of all relevant observations (animals, calls, signs) in the vicinity of the initial sample.
PURPOSE ACS increases sampling effectiveness by taking advantage of amphibian population characteristics, which you observe in your field sampling effort. ACS allows for a more accurate statistical estimate of the population parameters for animals that are patchily distributed in the habitat being sampled.
ADVANTAGES
1. In conventional amphibian field sampling, once the random selection has been made, the amphibian fieldworker is not allowed to look beyond the pre-determined boundaries of the samples or final population estimates will be biased (see Heyer et al., 1994, especially Chapters 2 and 6).
2. In cases where the amphibians are clearly more abundant outside of the sample area boundaries, any final estimate will be an underestimate. ACS allows boundaries to be extended when high density patches are discovered during the fieldwork. ACS thus provides for better estimates of population numbers.
3. ACS provides for more efficient, smaller variance, unbiased statistical estimates of population richness or mean density.
DISADVANTAGE
Because additional samples are added next to sampling units that have the target organisms, this technique will be reliable only for non-invasive techniques where organisms are not disturbed by the sampling procedure involved. Thus, large ground litter quadrat sampling would not be appropriate, as the clearing of leaf litter outside the randomly located quadrat perimeter would disturb the amphibians in that area. The technique could be adapted for large ground litter quadrat sampling by determining what the disturbance zone would be between two quadrats and then using that distance to separate “adjacent” quadrats. In such cases, it is absolutely critical to associate these modifications with the data so that other workers can replicate studies or compare results accordingly. The technique should work best for methods such as the small quadrat sampling technique for such species as terrestrial salamanders.
GENERAL DESIGN In the field, whenever an inventory object, or an unusually large number of such objects, is located within a sample plot, areas adjacent to the plot are searched. These new areas define neighborhoods, which may contain the target objects that can then be added to the initial sample and increase the accuracy (and decrease the variance) of population estimates.
METHOD
1. A statistical sample size and method is determined, which uses unrestricted or restricted (cluster, stratification, systematic) sampling. For example, determining transects, placing box plots etc. For convenience, let us discuss the placing of box plots along a gradient (looking for specimens in leaf litter).
2. A predefined condition is defined, for example (a) in any given sample, if one salamander is observed or found; or (b) in a given sample, if three or more amphibians and reptiles are seen.
3. When this predefined condition is not met we continue to our next sample.
4. If this condition obtains, say we found a number of salamanders in our plot, we lay the box as close as possible to or original placement spot, in four adjacent areas - above, below, and each of the sides in some ordered manner.
5. We continue laying the plots about the four sides of each and every sample plot that meets our condition (say that we find at least 1 salamander), until we find each of the four adjacent plots to be without any salamanders. We then continue with our original sampling plan, stopping to take additional samples whenever our condition is met.
6. In this way we have not only located a patch of observation but we have included them into the sample and made an attempt to avoid a severe underestimate.
7. The added plots are included in an ordered manner and thus become part of the statistical sample.
8. The final parameter estimates are unbiased and more accurate with lower variance than if the observed patchiness had been ignored.
EXAMPLE For illustrative purposes, we set up a 20 x 30 grid in which numbers representing individuals were distributed in three clusters. We summarize the results of this example here and explain the example in detail, including all steps in sampling and analysis of the data, on the DAPTF web site (http://www.open.ac.uk/daptf/index.htm).
Our example data set contained a total of 126 specimens. We first randomly sampled 10 quadrats (= grid cells). Only one of our quadrats had two individuals. The estimate under simple random sampling for these data gives an estimated total of six specimens.
We next used the adaptive cluster sampling technique for these same ten quadrats. One of the quadrats was in one of the three clusters of specimens. The adaptive cluster sampling estimate for these data gives an estimated total of 27 specimens.
We then increased our sample size to 20 random quadrats. The 20 random quadrats found one of the other clusters. Only two quadrats had a total of six6 specimens from the 20 random quadrats. The estimate under simple random sampling for these data gives an estimated total of 15 specimens.
The adaptive cluster sampling data yield data yield an estimatean of a total of 40 specimens.
If neighborhood overlaps are taken into statistical consideration, the adjusted adaptive cluster sampling estimate is 176 specimens.
RECOMMENDATIONS As can be seen from the above example, for patchily distributed amphibians, the adaptive cluster sampling technique performs better than the simple random sampling method, but only the neighborhood overlap adjustment of the adaptive cluster sampling method comes close to estimating the true number of individuals in the area of interest.
If the patches can be recognized before sampling takes place, then the best technique to use is the patch sampling technique (Heyer et al. 1994: 107-109).
If the patches cannot be recognized before sampling takes place, then the adaptive cluster sampling technique will do a better job than simple random sampling. However, the user must bear in mind that even the adaptive cluster sampling technique will seriously underestimate the population size of very patchily distributed organisms unless neighborhood overlap is taken into statistical consideration.
Standard random quadrat sampling is appropriate when the distribution of amphibians is not highly clumped in the area of interest.
References
Heyer, W.R., Donnelly, M.A., McDiarmid, R.W., Hayek, L.C. & Foster, M.S. (eds). (1994) Measuring and Monitoring Biological Diversity: Standard Methods for Amphibians. Smithsonian Institution Press: Washington, DC.
Thompson, S.K. (1991) Adaptive Cluster Sampling: Designs with Primary and Secondary Units. Biometrics 47(1103-1115).