# Scattered vs. Random

1. Sep 24, 2007

### Soley101

Context: just wondering

If I said the dispersion type of a certain animal is that incorrect to the term the animal has a random dispersion type. To clarify, is scattered a type of dispersion. Thnxs.

2. Sep 24, 2007

To answer your question--no--scattered is not a type of population dispersion. There are three types of dispersion (1) uniform (aka regular), (2) contagious (aka clumped, aggregated), (3) random. A scatter plot is used in statistical analysis (such as regression analysis) to show data points on an x-y graph. However, perhaps you really mean dispersal as a type of scattering--such as seed dispersal by wind ? Take for example puffball, which can release as many as 7.0 x 10+12 spores, which are distributed by the wind (scattered) and can have a specific dispersion pattern (perhaps random) when they hit the ground. Perhaps this is how you relate scattering and random--not clear from your post ?

3. Sep 25, 2007

### Staff: Mentor

FWIW - there are papers that claim random is really a non-linear dynamical system.
Especially with regard things like spores and pollen. But Rade's repsonse is a good one and is correct. And your definitions are fuzzy.

4. Sep 25, 2007

### Chris Hillman

"Random is a non-linear dynamical system"? No!

I assume jim just choose his words badly, but I urgently recommend that anyone who actually believes this should immediately read:

J. D. Murray, Mathematical Biology, 2nd Ed., Springer, 1993. Note the many examples of nonlinear dynamical systems which model highly structured geometric phenomena such as coat patterns.

E. Atlee Jackson, Perspectives on Nonlinear Dynamics, two volumes, Cambridge University Press, 1994. A wonderful picture book, full of excellent information, which provides a superb portrait of modern dynamical systems and which even includes some biological examples.

About dispersion patterns: the "scattered" versus "random" distinction is terribly crude by mathematical standards, but there is a mathematically valid intuition underlying this distinction.

When we speak of "choosing a position at random", we always must have in mind--- to use the language of mathematics--- some probability measure. When we have in mind a geometric setting, such as a metric space, we usually will want to choose a measure which is "compatible" with the topology of our space, a so-called Borel probability measure. In this case we probably have in mind something like a uniform measure induced from Lebesgue measure on a rectangle. If so, roughly speaking, "independently and randomly choosing many positions" using such a measure will result in a pattern in which some of the "random positions" happen to be quite close to each other. But if we are using some other means to generate our positions, the positions may tend to keep some minimal distance apart from each other (for example in a model of birds sitting on a telephone wire).

In a nonmathematical example which will nonetheless probably be familiar to most biologists: "pseudorandom number generators" are algorithms which attempt to mimic the behavior of "random and independent choice of positions" on the unit interval $\left[ 0,1\right]$. A common problem with naive algorithms is that statistical tests reveal that an algorithm produces positions which are "too scattered" to mimic the behavior of the Borel probability measure induced by "normalizing" Lebesgue measure on the unit interval.

Last edited: Sep 25, 2007
5. Sep 25, 2007

### Staff: Mentor

Yes, L-systems, for example, conform to what Chris mentioned. So we don't run afoul of my choice of words, let's stop here. Mine was a "Biological" repsonse. Sorry for the confusion.

Chris is an expert in dynamic systems - I just play with fractal modeling of ecological systems- already have a copy of Atlee and Peitgen, Jürgens, and Saupe as well and a few other primary sources back to 1986.

6. Sep 26, 2007

### Chris Hillman

Just curious

Do you find the book by Atlee Jackson as helpful as I would hope?

I probably shouldn't agree to be called anything more impressive than "a former expert on one small area of symbolic dynamics" (the subject of my diss). Although it's hard to discourage people from flattering me

Last edited: Sep 26, 2007
7. Sep 26, 2007

### Soley101

Thanks guys, you answered all my question and I congratulate you for answering what I meant, even though I don't understand what my own post was asking :S.