Robert R. Sokal

STATISTICAL METHODS IN SYSTEMATICS

From the biological viewpoint the tasks of systematics may be subdivided into analyses of infraspecific variation (both intra‐ and interpopulation studies), the separation of genetic from environmental effects on the phenotype, the definition of species (and possibly subspecies), the definition of supraspecific taxa, the measurement of similarity among taxa, life‐history stages or organs, the measurement of evolutionary rates, the evaluation of biogeographical relationships and information‐handling problems.

Typology and empiricism in taxonomy

The term typology has been used in taxonomy to imply procedures and philosophies of somewhat diverse meanings. Not all typological work meets every criterion suggested for such work by various authors. Some of these criteria are untenable when viewed in the context of modern biological theory, while others seem eminently reasonable in the light of present day knowledge. Mere reference to a work as typological will not convey to the reader or listener a clear idea why a reviewer has decided that it merits the term. Similarly, it would be improper to attach automatic derogatory implications to the adjective “typological”, since it is only those aspects of typological procedure which cannot be defended or maintained today that would merit such a connotation. The classificatory philosophy of many proponents of typology is based on a platonic idealism. To consider a taxonomic type as an abstract idea seems of doubtful utility at best and is certainly beyond the realm of scientific inquiry. The method by which types are obtained must be indicated without ambiguity. In classical typological work this is generally not done, and reconstructions relying on the metamorphosis of parts are often rather vague and controversial. Similarly, abstractions relying either on weighted or unweighted averages of the characters in the taxa to be studied are of questionable value. It would appear that character variation of individuals within taxa or of taxa within higher taxa must in some way be accounted for, if types are to be defined which will represent the natural order in the system. The choice of characters must also be clearly defined and defensible. A priori weighting or preference of some characters over others, based on either presumed phylogenetic importance or logical or functional primacy, is an unjustifiable procedure. Equal weighting and use of all characters leads directly into an empirical approach, which attempts to classify organisms on the basis of all available evidence, without preconceived notions about their arrangement. Such a procedure also arrives at a classification from which types may be abstracted, but does so by clearly defined and previously determined criteria, and does not rely on hypotheses based on certain preliminary conclusions in order to reinforce its argument. The empirical approach, the most notable example of which in recent years has been the development of numerical taxonomy, has definite typological aspects which, however, appear to this writer to be of value and preferable to the phylogenetic method. Smirnovs statistical method of constructing types is contrasted with results obtained by numerical taxonomy. The latter appear preferable from several points of view.

The fate of immature housefly populations at low and high densities

This study analyzes in some detail the fate of immature populations of the housefly (Musca domestica L.) at a low and a high density as shown by sequential censuses. Previous work in this laboratory (SULLIVAN and SOKAL, 1963, 1965; SOKAL and SULLIVAN, 1963; BHALLA and SOKAL, 1964) established the effects of increasing density on three biological parameters (percent survival to adulthood, dry weight of adults, and length of developmental period) for several strains of flies reared singly; in competition the effects were more complex. Different genetic strains showed important differences in these biotic properties and in their responses to changes in density. The results of these experiments are principally characterized by observations on adults, but the causes of the observed differences must be sought in the fate of the immature stages of these strains. Preliminary experiments by SULLIVAN and SOKAL (1963) showed that the greatest mortality of flies at higher densities took place late in larval life. Substantial numbers of larvae survived for at least eight days even at high densities. This study of the fate of immature houseflies at a near-optimal and a high density employed the OL strain (Orlando No. 1), a standard strain used in the previous studies. A subsequent paper (BRYANT and SOKAL, in preparation) will discuss the differences between OL and two other strains. Some of the questions which the present study attempts to answer are : When during larval development, does increase in density affect larval survival ? Similarly, when is growth and weight of larvae affected ? What shifts in the frequencies and developmental periods of the several immature instars are brought about by an increase in density ?

Thurstone's analytical method for simple structure and a mass modification thereof

The analytical method for simple structure proposed by Thurstone is applied to four separate cases and found to yield satisfactory results. The simple structure obtained by Thurstones method is found to match closely that obtained by other methods and corresponds to the true structure of the matrix in those cases where true structure is known. Difficulties about the choice of the correct trial vector led the writer to develop a modification of Thurstones method, useful where high speed computational facilities are available. Instructions are given for this so-called mass modification, and the procedure is illustrated with a 5-factor, 14-variable example. While the results do not fully correspond to a previous graphical solution, it can be argued that the results obtained by the new method show an improved simple structure. The modified method is applied to three other correlation matrices, yielding in each case a satisfactory simple structure.

Computing a population budget from sequentially sacrificed, replicated cultures

When a population budget must be obtained from censuses based on replicated, sacrificed cultures, it is difficult to obtain estimates of transition probabilities and of the errors of such estimates, because there is no logical basis for pairing successive census counts. In a study of this nature estimating a population budget of immature stages of the housefly, the problem was solved by a randomization treatment of the original census results obtained at two densities. One hundred randomly generated census matrices over all census times for each density were smoothed to remove the effects of sampling error and a population budget constructed according to defined rules. Transition probabilities computed from the population budget were plotted on triangular coordinate paper and mean probabilities, 95% confidence regions for these means, and 95% equal frequency ellipses computed. All computations and the graphing of the results were carried out on a digital computer. The computer program, available from the authors, is written in FORTRAN IV and could be easily modified for similar studies.

Genetic differences affecting the fates of immature housefly populations at two densities

This study contrasts the fates of immature populations of three strains of the housefly, Musca dornestica L., at a low and a high density. It completes a series of three publications. In the first (SoKAL and BRYANT, 1967), a method for analyzing census data from sequentially sacrificed, replicated cultures was outlined. This method was then applied in the second paper (BRYANT and SOKAL, 1967) to an analysis of the fate of immature populations o5 the OL strain, a standard wild type strain used in previous studies in this laboratory. These studies focus on the immature stages since it is believed that differences in survival, weight, and length of developmental period of adults observed in earlier work in this laboratory (SULLIVAN and SOKAL, 1963, 1965; SOKAL and SULLIVAN, 1963; BHALLA and SOKAL, 1964) can be interpreted in terms of critical differential phenomena during the preadult life history of the flies. The present study will investigate biological parameters and fates of immature populations of the green and brown strains employed in the cited earlier studies and contrast these with findings for the OL strain analyzed in the previous paper in this series.