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Remember that the variance is calculatedĪs a squared deviation from the mean. What kinds of values can throw the variance away from the "expected"?įor our cases with mean 0.25 any values out at high numbers per cell will (reasonable, given that we are talking about unitary animals or plants In our observed vector of animals/quadrat (approximately a one in 10,000),īut that expectation rounds down to 0 because I am using integer math. There is a small probability of having 5 individuals Note also that anything beyond the last value given Those far-from-the-mean values would drive up the variance, leading to a high variance. It would also have a deficiency of zeros (not much open space).Ī clumped distribution with this mean would have lots of zeros and more quadrats with high numbers of animals (that is there would be few quadrats with 4s and 5s, the values close to the mean). For a more uniform distribution, we would have more values near the mean (more 4s and 5s) and fewer farther from the mean (fewer zeros and fewer high numbers).ĭeviations from the random (Poisson) expectation:Ī uniform distribution with a mean of 4.3 would tend to have lots of values close to the mean (4s and 5s), leading to a low variance. Note that the shape is different from other Poissons with different means. Histogram of frequency distribution of number of animals per quadrat under a Poisson ( random) expectation with a mean of 4.3 animals per quadrat (variance is therefore also 4.3). Prussian army battalion - Simon Poisson, 1781-1840, was a French mathematician "hits" per trial, if the "hits" are randomly distributed (in our case, number of animals per quadrat - the originalĮxample was the number of soldiers killed by horse kicks per Given a mean (our case is 0.25) it tells us the expected number of Like this can be fitted to the discrete Poisson distribution.
![dispersio patters of of orgaisms dispersio patters of of orgaisms](https://us-static.z-dn.net/files/d50/fd0594cc9a590018ae8be8df04297c4c.png)
The probability distribution of number of animals per quadrat? Any problem Quadrats with no animals, some with one, some with two, and on up. When we really get out there, we will have So, for this example, the mean occurrence or density Number of animals per quadrat? Just the number of animals divided by the Say we have 25 animals in a 10X10 plot (100 quadrats). Consider that we divide our study area up into subplots. Start with the expectation under a randomĭistribution. We say about these patterns in a quantitative way? Not that a random distribution will tend to have some clumps (as in the lower right) as well as very sparsely occupied areas (as in the upper right). By dividing the area into (invisible) quadrats, and counting the number of organisms per quadrat, we can assess the mean and variance of the number of organisms per quadrat, and thereby have a quantitative basis for deciding whether the observed dispersion is best described as random, uniform or clumped. Patterns of dispersion for organisms in a study area. Let me give a little background.įirst, remember that the three primary patterns that concern us are clumped, random, and uniform.įig. Homework: The first part of the homework deals with analyzing patterns of dispersion. Go to Lecture 14 (lognormal distribution of ending sizes for stochastically varying population matrix projections)ĭownload Excel spreadsheet to generate the "expected" distribution for HW2ĭispersion (for Homework # 2 and with reference to Lecture 6 - population characteristics). Go to Lecture 6 (where patterns of dispersion is mentioned as a population characteristic) PopEcol Dispersion/Poisson Lecture notes for ZOO 4400/5400 Population Ecology