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Gleason (1926) describes a natural plant community as 'representing the selection of a certain environment acting on a given population of species'. In a climax community it is to the local variation in this environment itself that some at least of its internal vegetational variation, that is, variable success and incidence of its constituent species, is attributable. Further, the incidence of a definite type of plant community (which implies incidence of its characteristic species, e.g. Calluna in heathland) appears in some cases to correspond to the distribution of some environmental factor, e.g. heathland on acid sandy soils (Ashby, 1935). It appears probable, therefore, in cases where the incidence and success of a species appears to be noticeably correlated with variations in some environmental factor, that a quantitative investigation into the causes of such variations as they occur locally, together with some means of assessing the relative importance of the effects of such causes on local distribution and success of the species investigated, could be used to predict the wider incidence and success of such species in respect to this factor. Anything which enhances a knowledge of the physiological requirements of the species will increase the accuracy of any prediction of the habitat best likely to meet these requirements. For example, the wider the range of local variation in the factor investigated, and the closer the analysis of the causes of this variation, the more likely is the prediction of distribution and success, drawn from local investigations, to be correct. As for the causes which cannot be investigated locally, e.g. climatic variation, their effects can often be predicted qualitatively from experience. Generally, it is the edaphic factor which is the primary environmental factor influencing species success and distribution in a given climatic area, and since its influence can be approximately assessed from determinations of pH, organic content, and moisture contentin themselves easily determinable functions of a wide range of heterogeneous effects, such as slope, incidence of tree cover, exposure, base exchange capacity, and the like-it is the factor which will be considered in assessing the value of the above conclusions. We may point out here the essential similarity of the above concept to that which has led Boyko (1947) (of whose latest paper we were unaware at the time of our experiments) to his conclusion: 'The specific topographical distribution (micro-distribution) of an ecotypic plant species is a parallel function of its general geographical distribution (macrodistribution), since they are both determined by the same ecological amplitudes.' Boyko is dealing with the variables which together constitute climate, and while we appreciate his conclusion, we can commend a more rigorous analysis of the results. 11. The following experiment, then, is a preliminary attempt to assess the relative importance of the effects of the causes of local edaphic variation on local distribution and success of Holcus mollis and Deschampsia flexuosa. From the results we shall attempt to

In their paper 'Some observations on the relations between H-ion concentration of the soil and plant successsion', Emmett & Ashby (1934) proposed a sampling method for separating the frequency distribution of a species over an area from that of soil acidity over the same area. It is unforttnate that the statistical test used in the analysis of their data was incorrect and consequently the hypothesis that the two species Pteridium aquilinum (L.) Kuhn and Vaccinium myrtillus L. occurred with the same frequency at every pH value within their respective pH ranges was accepted when in fact there is significant evidence to the contrary. We propose to discuss in detail the data which were given in Table 1 of that paper, and are reproduced in Table 1 below.

Evaluation of erythropoietic function by the use of radioactive labels is discussed in relation to the capturerecapture method for investigating changes in wild animal populations. Mathematical equations are derived and applied to experimental data. It is shown how estimates of the rate of creation at isolated instants may be made without actually fitting the differential equation for population growth, and without assuming the form of the mortality function of the cells. The methods proposed are based on the comparison of the value and gradient of radioactivity of samples of cells immediately before and after a number (possibly one) of successive injections, and minimize the number of injections necessary. (H.H.D.)

The comparison of numbers of successes and failures in two treatment groups by the usual chi-squared criterion with one degree of freedom becomies invalid if the groups are heterogeneous, falling into categories with different success rates in propoitions which differ systematically for the treatments. If these nuimbers are adjlusted beforehand by a simple procedure of the type used in stanclarlising mortality rates the validity of the criterion is restored, subject to multiplication by aii inflating factor which exceeds unity by an amouint which is usually so small that it may be neglected.

A widening of the concept of stationarity leads to the concepts of smooth heteromorphy and local homomorphy in stochastic series, obviating much of the need for the introduction of trend into structural specifications of statistical data. It is shown that formulae for sampling properties of local statistics in stationary stochastic series are applicable as they stand to series having these less restricted properties.

for the binomial distribution is an incomplete Beta integral. The cumulative probability function for the F distribution is also an incomplete Beta integral. The purposes of this note are to demonstrate that this is more than a mathematical coincidence and to show how the standard tables of Fmay be used to evaluate partial binomial sums. 2. Suppose that random events are occurring at a long-run rate of one per unit of time, and that each event independently has a probability p of being of one type, called E-events, and a probability q( = 1 -p) of being of a second type, called E-events. Then in any set of n successive events the number r of E-events will have a binomial distribution, the probability that r is at least equal to any specified value ro being given by (1). Furthermore, the sequence of E-events may itself be regarded as a sequence of random events occurring at a long-run rate of p per unit time, and the sequence of E-events as an independent sequence of random events occurring at a long-run rate of q per unit time; this is a consequence of the randomness of the original sequence coupled with independent occurrence of type at each event. When random events are occurring, the time interval from an arbitrary instant to the instant of occurrence of one such event (or equally between the instants of occurrence of two such events) is an exponentially distributed variate, the mean of the distribution being the reciprocal of the rate of occurrence (v. Jowett (1958)). Since the X22 distribution is in fact an exponential distribution with mean 2, it follows from the additive property of the x2 distribution and the independence of the sequences of E-events and E-events that the time interval T(m) from an arbitrary instant to the mth E-event is distributed as (x2m2)/2p, and the time interval T'(m) to the mth E-event is independently distributed as X2m2/2q. If r > ro, by the time that the nth event has happened, at least 55

W. J. Youden: Statistical Methods for Chemists. New York: John Wiley & Sons; London: Chapman & Hall, 1951. Pp. x + 126. 24s.

J. Mounsey: An Introduction to Statistical Calculations. London: English Universities Press, 1952. Pp. 351. 15s.

H. C. Fryer: Elements of Statistics. New York: John Wiley and Sons; London: Chapman and Hall, 1954. Pp. vi + 262. 38s.

M. S. Bartlett: An Introduction to Stochastic Processes. Cambridge University Press, 1955. Pp. xiv + 312. 35s.