For single-species, even-aged and uniform growth, we used systematic sampling. If the growth was not uniform and high variability, stratified sampling did better. In forest inventory work, the purpose of stratification is to reduce variation within forest subdivisions and increase the precision of population estimates.

If you are sampling even-aged monocultures, systematic sampling is the norm. In Swedish forestry, we often use systematic sampling of blocks sized 5-30 ha because it is efficient to implement, easy to comprehend (=easy-to-understand instructions), suitable for use with GIS/GPS tools, and minimizes the risk of bias (when e.g. recruiting 1st year forestry students to perform the sampling).

The most ‘convenient’ method of sampling is that in which the investigator selects a number of sampling units which he considers ‘representative’ of the whole population. For example, in estimating the whole volume of a forest stand, he may select a few trees which may appear to be of average dimensions and typical of the area and measure their volume. A walk over the forest area with an occasional stop and flinging a stone with the eyes closed or some other simple way that apparently avoids any deliberate choice of the sampling units is very tempting in its simplicity. However, it is clear that such methods of selection are likely to be biased by the investigator’s judgement and the results will thus be biased and unreliable. Even if the investigator can be trusted to be completely objective, considerable conscious or unconscious errors of judgement, not frequently recognized, may occur and such errors due to bias may far outweigh any supposed increase in accuracy resulting from deliberate or purposive selection of the units. Apart from the above points, subjective sampling does not permit the evaluation of the precision of the estimates calculated from samples. Subjective sampling is statistically unsound and should be discouraged.

Danung Nur Adli Thank you for the answer. Could you recommend a procedure to avoid subjective sampling? I feel conducting random sampling working through a forest area can be subjective. If we select random points before accessing the field, is it also subjective?

Joni Waldy Thank you for the answer. It is clear if we conduct stratified sampling, we have to study the forest in-depth to identify the strata. Do you recommend using google images or any remote sensing analysis? or observers should walk to the area and identify the variation?

Back Tomas Ersson Thank you for the answer. Do you recommend systematic sampling for a same-aged but unevenly grown stand? As an example, we have even-aged teak plantations, which are highly damaged by wild elephants. As well as some plantations are unevenly mixed with naturally grown other timber species.

Answer to your follow-up question: well, that depends... Now you are getting at the heart of sampling dilemma: the trade-off between precision/accuracy and invested resources.

-When there is obvious variation: stratify.

-What sort of accuracy do you really need? What is the cost of (relatively)

poorer sampling results? How will the means/range be used? Here you could estimate the cost of poorer accuracy by using sensitivity analyses (these analyses must not be complicated but can be rather coarse/quick just to get a feel for the cost of poorer sampling results)..

-How easily can you stratify?

-Whats the cost of increasing the sample size from e.g. 25 to 40 plots per block, so as to better capture the variation ?

Back Tomas Ersson I get an idea to design the sampling procedure. I should prepare a criterion (or some keys) to match the sampling requirement. Following this general criteria field managers can design their sampling case by case. Thanks a lot for the support.

Systematic sampling is your best choice to find your stand volumes. You could use stratefied sampling only if you could identify the basis for your strata (i.e. soils, aspect, silviculture treatments, etc.). If you see variation in your stand and they are all the same age then you may be seeing simply the inherent natural variability of your population, which you would want to sample to get a representative coefficient of variability. Do not try and "pick representative" example of your stand. That is called sampling bias and will give you false calculations. Random sampling in even-aged stands is inefficient since random sampling requires higher sample points to get the CV down and is unnecessary in an even-aged forest.

Lloyd Fuller Thank you for the answer.

We can observe higher variability of tree density specifically in teak plantations due to damage of wild elephants. Do you recommend Systematic sampling for such kind of plantations?

If you are sampling different species or, as mentioned, different treatments, and in your case a disturbance by elephants, then stratification certainly could reduce your variability. If you have different species that are not intermixed on the same sample area, you could just sample separately. If the elephant damage has a pattern (i.e. along trails, between water, etc.) you could stratify using that as a strata. If the elephant damage is random throughout your area then it becomes part of that natural variability of your population.

When designing forest/vegetation sample designs you usually define what it is you want to sample (age, size, volume) and design a sample to get you that metric. Then you look for logical stratum, and in your case elephant damage in your teak trees. If you can draw boundaries around your teak population as a stratum, and define areas of teak damage as a stratum, then you can estimate healthy teak volume and the damage (volume loss) caused by elephants or animals in general. Without knowing the spatial distribution of your populations and potential statum I probably cannot be more specific. As for each stratum you can use a stratified sampling design. But keep your sample design the same for each stratum (or the statistics get very convoluted and complex).

There are no rules in ecology or statistics, so you can choose :)

W.V. Tharindu Amarasinghe -

Your first sentence got my attention: "Some of the forest plantations do not show even growth (same age stands) due to different management or site problems."

Does that mean that management and site (elephant damage) problems were different within the same plantation, or between plantations. It sounded like the former, but it seems odd to have more than one management on the same plantation.

At any rate, it sounds as if just identifying all of the types of areas would be the first problem. It doesn't sound to me as if there would be any continuous auxiliary variable that could be used in a model-based approach. The "blocks" range substantially in size, but an unequal probability sample based on block size sounds like it would bias results if larger blocks tended to be managed differently than small ones. A little of that is fine if you can then look at fewer blocks to get the job done, but I am not experienced in forestry, so I would have to ask you about that problem. But it sounds like you expect (or expected, if this study has been done now) that there would be a great deal of difference between areas due to multiple characteristics.

People mentioned systematic sampling to make it easier, and stratified random sampling to try to more efficiently handle the various characteristics which change from one area to another, but I wonder, if you were to identify several types of areas which are not continuous areas, if you might do a cluster sample of equal size plots for each type, doing a simple random sample for each type, and censusing the plots selected?

It would be interesting to hear how this project has progressed, or progresses in the future.

Cheers - Jim