PT. I, CH. viii] AGE AND AREA. INVASIONS 77 



occurs in real life, but by taking groups of ten allied species one 

 may cancel out many of the effects of chance differences. This 

 dispersal is indicated by drawing a right-angled triangle, which 

 expands regularly till after a certain time it reaches both ends 

 of New Zealand. As it does so, and covers more country, JV is 

 supposed to give rise casually to new species (shown at every 

 increase of 200 miles of range, their locations of origin obtained 

 by dra^ving numbers at random). These new species, El to 10, 

 spread like the parent, as is shown by the similar triangles, so 

 that when W reaches and 1000, E 1 reaches 120 and 920. 



If noAv we divide New Zealand into ten zones by drawing a 

 vertical line at every 100 miles, and count in every zone the 

 number of endemics found there (derived directly or indirectly 

 from W), we find the number small at each end, and with a 

 maximum (or at times two or more) near the middle. In the 

 present case, for instance, the numbers in each of the zones from 

 left to right are: 0, 3, 5, 8, 9, 8, 7, 3, 2, 2. 



If we obliterate the left-hand half of the diagram, we get the 

 result of entrance of W at one end of New Zealand, and find the 

 maximum near that end; it always tends to be near the point 

 of entry. If the entrance be not at a jjoint, but at a zone, e.g. 

 from 300 to 700 miles, at the level of E 2 and 3, then, if one 

 omit -E 1, 2, and 3, one finds that the remainder give the figures: 

 0, 1, 3, 5, 6, 5, 4, 1, 0, 0, a similar but shorter curve. 



Occasionally, with a casual development of new endemic 

 species, it so happens that the cur^'c may show two, or even 

 more, maxima with a slight drop between them, but to have one 

 maximum only is the general rule. 



One might therefore j^redict that one would find the endemic 

 species of any genus in New Zealand to form such a curve, and 

 this proved to be the case for every genus in the flora. A few 

 examples are here given; 



