Fróðskaparrit - 01.01.1998, Side 25

EIN OYGGJALÍVLANDAFRØÐILIG GREINING AV FLORUNI í FØROYUM
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APPENDIX
The mathematical background
For each of the 294 species Kjeld Hansen
lists the frequency at which they are found
in a total of 237 locations.
The basis of the null hypothesis is the as-
sumption that the probability of finding
species no i within an area unit E is a con-
stant Sj . The best estimate for s( must be:
_ number offinding places for specie no i
237
The probability of finding species no i
within an area AE is then
l-( l-Sj)A = 1 -eAu(i),
in which u(i) = ln( 1 -s;)
The anticipated number of species in an is-
land of an area AE is thus:
294 294
1) N(A) = X(1 -f eA«(‘))=294 -r XeA«(‘)
i=i i=i
For a fixed area, A, the variance of N is:
294
2) Var(N) = X(l = tAu(if)tAu(i)
i=i
In this model the z-value depends on the
area, A:
z(A) =
‘/(ln(V))
di\n(A))
A vt4
t, Xn( i)eAu<‘>
i= 1
The area unit E is defined in such a way that
the species-area-graph and the 17 measur-
ing points observed correlate best (the
method of least squares) and E becomes 5
km2.