444 Willis. — The Distribution of Species in New Zealand. 
at one end and going to the other, will form an ordinary rising and falling 
curve, rising somewhat more sharply at the beginning and falling likewise 
at the end, but flat in the middle. It will most often have only one 
maximum, but unless the endemics form rather more towards the centre 
than away from it, there will tend to be two maxima, with a slight 
depression between them. I am greatly indebted to Mr. E. G. Gallop, M.A., 
Mathematical Lecturer of Gonville and Caius College, for assistance in 
dealing with this somewhat mathematical problem. 
Now to turn to the facts. Having calculated out the matter in this 
way, I proceeded to count up the flora of New Zealand, expecting to find 
that the totals at any rate would show this gradual rise to and fall from 
a maximum, even if it were not very regular, and perhaps showed serious 
breaks in continuity. In actual fact the result was very much more exact 
than I had ventured to expect, as will be seen at once by a glance at the 
following table : 
Table III. 
North 
Island. 
South 
Island. 
Stewart 
Island. 
Endemic 
Dicotyledons. 
Monocotyledons. 
Total. 
Zone from o 
to 
100 miles 
x 74 
60 
234 
99 
IOI 
to 
200 
99 
213 
67 
280 
99 
201 
to 
300 
9 9 
254 
76 
330 
99 
3oi 
to 
400 
99 
280 
88 
368 
99 
401 
to 
500 
99 
3 °° 
86 
386 
99 
501 
to 
600 1 
99 
432 
105 
537 
99 
601 
to 
700 
99 
429 
103 
532 
99 
701 
to 
800 
99 
424 
103 
527 
99 
801 
to 
900 
99 
408 
108 
516 
99 
901 
to ] 
[,000 
99 
322 
92 
4 X 4 
99 
1,001 
to : 
0 
00 
0 
99 
98 
39 
137 
This is a very striking table, and shows clearly that natural selection 
at any rate cannot be responsible for the local range. I therefore followed 
it up by testing the individual families and genera separately, and obtained 
the truly remarkable result given in the next three tables. 
Ranunculaceae 
Magnoliaceae 
Cruciferae 2 
Violaceae 
Pittosporaceae 
Caryophyllaceae 
a 
o 
0 
w 
1 
o 
3 
2 
4 
1 1 
Table IV. 
North Island. 
South Island. 
Stewart 
Island. 
1 Includes a number of species confined to one, chiefly the South Island, which would, one 
would imagine, have spread to the North Island had they arrived at the north end of the South 
Island in time to get across before the separation of the two islands. 
2 Families showing one or more figures not in a regular progression to a single maximum. 
