Hi everyone,
There's a huge and long-standing literature on nearest-neighbor
statistics. A starting point within ecology is Clark and Evans (1954,
Ecology 35:445-453).
In general, you cannot calculate the actual mean nearest neighbor
distance from the density, because density is not sufficient to define
the distribution of neighbor distances. (Just imagine two fields of the
same density, but one with a very clumped and one with a very
over-dispersed distribution.)
If you assume that the distribution is random, then there is a simple
formula for mean (and other moments) of the nearest neighbor distance.
See, e.g., Pielou (1969, Introduction to Mathematical Ecology, pp.
111ff. for a concise description). In the case of a random
distribution, the mean distance from an individual to its nearest
neighbor is
1/(2*sqrt(density))
If you just want an index of distance relative to density, this would
work, but it wouldn't give you what the bees are actually experiencing.
For that, you would need more detailed spatial distribution information.
Hal Caswell
PS --- distances from a random point to the nearest plant are not the
same as distances from a random plant to its nearest neighbor unless the
distribution is random.
On 4/25/12 11:12 AM, Dixon, Mark wrote:
I haven't worked through this mathematically, but could the average distance
vary for the same value of density? I would think that the median could
differ, but I'm not so sure about the average. The point-centered quarter
method for estimating stem density relies explicitly on the square of the
average distance (1/d2) to individual trees from the point. But, the
assumption of that method is (I believe) that plants are randomly distributed
in relation to one another, which of course may not be the case.
Mark D.
-----Original Message-----
From: Ecological Society of America: grants, jobs, news
[mailto:[email protected]] On Behalf Of Basil Iannone
Sent: Wednesday, April 25, 2012 8:40 AM
To: [email protected]
Subject: Re: [ECOLOG-L] estimating distance between points from density?
Nic,
Can you give us more context. Are you trying to use average distance as a
predictor of some other variable? If so, why not just stick with density?
Converting density to an average distance seems to me that you are just making
up numbers, i.e., in reality the average distance could vary considerably for
the same value of density. So it seems to me that your density measure is
actually reflective of the level of precision that you collected your data at
and should be used rather than average distance.
On Wed, Apr 25, 2012 at 4:15 AM, Nic Charlton<[email protected]>wrote:
Hi Ecologgers,
I am trying to estimate the average distance between flowers from
their density (flowers per square metre) and have not been able to
find a simple and satisfactory method for this.
At first I assumed that if the flowers were distributed evenly, I
could use the square root of the density to find the number of flowers
in a straight line per metre, and use this to estimate the distance
between the nearest two flowers.
Does any one know a better way to estimate average distance between
points or prey items (in my case flowers for foraging bees) from their
density (preferably without a lot of maths)?
Thank you,
Nic Charlton
PhD student
University of Bristol, UK
--
Basil Iannone
University of Illinois at Chicago
Department of Biological Sciences (MC 066)
845 W. Taylor St.
Chicago, IL 60607-7060
Email: [email protected]
Phone: 312-355-3231
Fax: 312-413-2435
http://www2.uic.edu/~bianno2
--
Hal Caswell
Senior Scientist
Biology Department MS-34
Woods Hole Oceanographic Institution
Woods Hole MA 02543
USA
508-289-2751 (office)
508-457-2134 (fax)
