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This contribution is an attempt to present instances of population fluctuations in adventive plants, treating the subject from two viewpoints.
A.-Fluctuations in species populations in relation to period of domicile of the particular species in New Zealand
Consideration of the adventive flora of New Zealand (circa 1400 species) shows that the constituent species, in terms of abundance and probable period of domicile, fall into one or other of the groups or categories detailed below.

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The fundamental equation for the balance between incomings and outgoings of fish stocks in a fishery was first expressed by E. S. Russell in 1930: "stock this year equals stock last year plus growth during year plus recruitment of young fish during year mm.us natural mortality during year minus fish caught during year." The last, the fish caught, is the only one of these variables known to us from the start. The others must be determined by sampling.

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This paper (to be published in full in N Z.J. Sci.Tech) discusses plant fossils from Upper Tertiary and Pleistocene beds and shows that paleobotanical evidence supports Fleming's (1953) suggestion that the Nukumaruan and Castlecliffian stages, at present considered to be Pliocene, should be included in the Pleistocene. The significant points are, that Nukumaruan and younger floras lack many species that are important in underlying Tertiary beds, and that some Nukumaruan floras indicate markedly cooler climates.

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The gently sloping basaltic base of Rangitoto Island in Auckland Harbour shows stages in colonization by pohutukawa (M etroszderos excelsa) and the scoria cone above is covered with incipient pohutukawa forest. During a statistical investigation it became necessary to take the age of this vegetation into consideration in order to complete the picture.

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In the preparation of this paper an attempt has been made to gather together the opinions of as many zoologists as possible. Knowledge of most of the animals of the ash-shower country is, however, confined to observations on discontinuous areas, and the paper will serve mainly to show us how little is known.

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The soil-forming ash-showers of the central North Island as now defined cover, sometimes disjointedly, over 20 per cent. of the area of New Zealand. This size in itself is of great importance ecologically.

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