What is Area-Weighted Mean Patch Size?March 4, 2013 9:53 AM   Subscribe

I'm in a graduate-level Landscape Ecology course and keep running across/having to use the metric of Area-Weighted Mean Patch Size. We compute it in Fragstats but the professor uses the term in lecture, too. Can you explain what it means?

I asked the professor and because of the language barrier, he just read the definition from the textbook. Looking it up online and in Landscape Ecology books has made me feel like I understand it enough to use the phrase in a lab report but I'm not really getting it. Also, I don't have any experience with statistics, which it seems those explanations rely on.
posted by thewestinggame to education (4 answers total) 2 users marked this as a favorite

Mean patch size is the arithmetic mean of the patch sizes. The area-weighted mean patch size, on the other hand, is a weighted mean, where the weights are based on the size of the patch. I think the only stats background you'll need is an understanding of the difference between an arithmetic mean and a weighted mean. The wikipedia article on weighted means might be helpful.

Area-weighted statistics are useful because they give a "landscape" perspective, so you can calculate things like e.g. the probability that an animal is in a patch of a certain size.
posted by JumpW at 10:43 AM on March 4

I don't know much about ecology, but the formula here and explanation is pretty good. The weighting is a mathematical way of saying "the bigger patches are more important" by including a multiplier which is the proportion of the total area of that kind of patch that that particular patch occupies.

If you think about a meteor hit from space, and you want to know the mean size of the country it hits (given that it hits a country and not the sea), you don't want the mean size of the countries in the world, because that's the answer to "if I pick countries at random from the index of the atlas, what's the average size?". You need to adjust for the fact that the meteor doesn't have an equal chance of hitting Russia and Lichenstein, because Russia is much bigger. The Area Weighted Mean Size would be the answer to the question "If a meteor hits a country, what's the average size of that country going to be?".

(Assuming that a meteor hits a random point on Earth, which may or may not be true)

They're mentioning stuff about "sensitivity" to smaller patches, which means that a few extra teeny-tiny patches won't affect the weighted mean as much as they'd affect the mean.
posted by Wrinkled Stumpskin at 10:48 AM on March 4

Another way of thinking of the same issue is "What is the average class size?" Say you have a school with one intro section of 1000 people and 50 other courses with 10 people, and students only take one course because morality.

The straight up arithmetic average is 1500/51=29 students. And this might be valid from the perspective of the university -- we offer 51 courses, and our average class size is 29. With a very large sigma.

But that doesn't capture the experience of an average or otherwise representative student. After all, 1000 of the 1500 students are in that class of 1000. Run that way, as a weighted average, the average student has a class size of 670.
posted by ROU_Xenophobe at 11:11 AM on March 4

I view it as a way of converting from a per patch basis to a per area (in a patch) basis.

Sometimes you can count the frequency of a species in a patch, but you may need the areal coverage in a habitat, particularly one that changes, say seasonally. The AWMPS allows conversion from a per patch basis to a per landscape basis (and vice versa).

The mean over all patches, for example, tells you what the average patch is like. The AWMP tells you what the average per square metre of landscape (or acre or ha or whatever) is like.
posted by bonehead at 11:45 AM on March 4

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