where Pe equals percentage of adults and Qe equals percentage of immatures in the entire sample.
[3] Probability of error; i. e., a P of .01 means there is one chance in 100 that the difference observed does not represent an actual difference in nature.
Upon the application of statistical methods it soon became evident that, unless changes in ratio between two samples are marked, large samples would be required in order to reach conclusions of high statistical significance in a single study of the present type. In this case (see Table 2), the Lincoln Sparrow and Orange-crowned Warbler, though represented by only moderate-sized series, show marked changes in age composition over the period studied, and the statistical treatment indicates a high degree of probability that these changes are real. Assurance that the lesser changes observed in the Nashville Warbler and Yellow-throat are real, on the other hand, is much less, even though the samples are larger. Few if any of the samples here discussed are as large as might be desired. Therefore, conclusions based upon them (see below) are to be regarded as tentative. Many other, future, samples will perhaps also be insufficient in size in themselves. There are, however, statistical advantages to repetition which will serve to make the repeated analysis even of small samples significant and valuable.
Certain of the samples not treated statistically show ratios that can be seen by inspection to be probably significant. For example the almost complete absence of adults from the three samples of Red-eyed Vireos (Fig. 1E) cannot be disregarded in view of the size of the whole sample of the species. The same applies to the high percentage of adult females and the near absence of adult males in the sample of the Dickcissel (Fig. 1F). The continuity in direction of changes observed in the three samples of the Mourning Warbler (Fig. 1G) and Red-eyed Vireo is likewise probably significant, even though some of the samples compared are small. It seems to us that the application of statistical methods to these species should await the accumulation of more material. For anyone desiring to treat them statistically now, the data are inherent in this paper.
We have not computed the standard errors of the ratios of sexes within age groups (except experimentally in a few cases). This can easily be done, however, and the significance of a given ratio determined, on the assumption (perhaps sometimes dubiously justifiable) that the sex-ratio in the species concerned is one:one. Obviously there is no point in computation of the standard errors of adult-immature ratios in single samples (such as that of the Dickcissel) until the actual ratio prevailing in the species in nature at the season in question is known for comparison with the observed ratio. Our formal statistical treatment, therefore, has been limited to an examination of the significance of the changes between adult-immature ratios in samples of the same species taken a number of days apart.
The samples suggest several patterns of differential migration of sex- and age-classes. Indeed, the important consideration brought out—in our opinion not hitherto sufficiently emphasized in literature—seems to be that in generalizing about adults and immatures, one must be careful to take sexes into account, and conversely, in generalizing about males and females, one must consider also age. In other words, there are really four classes to be considered. This poses additional problems in analysis and introduces the need for still larger samples in order to reach significant conclusions. To illustrate: an adult-immature ratio of 40:20 (N = 60) may be satisfactorily significant, while within the 40 adults a ratio of 25 males:15 females may not be. Were the original sample 80:40 (N = 120) with male adults 50 and female adults 30, it is obvious that the significance of the latter ratio would be greater. The same applies in reverse if the greater emphasis is placed on sex and the lesser on age. Because of the moderate size of the samples this problem has been felt in the present study in respect to sex ratios within age groups, many of which must at present be regarded as of tentative significance.
In short, what the earlier ornithologists regarded as a simple problem is in reality a complex one. There are only two patterns in what may be called the Brewster-Gätke argument: adults first or immatures first (with of course the further possibility of both at the same time). Both patterns occur, as is now known, at least to some extent. But actual patterns, as suggested by our samples, are more complex when all classes are considered. It will readily be seen that, if adult males, immature males, adult females, and immature females be regarded as units, each with certain migratory characteristics, the combinations of these units in various orders of migratory precedence are potentially numerous. In fact, of course, they do not behave strictly as units (or perhaps very rarely so), but our data strongly indicate that the tendency exists in many cases. This may be stated another way. The present samples may be reduced to two basic patterns, fitting the classic early American (adults first) and early European (immatures first) theories. But, either such simple arrangement is compounded in some, perhaps in truth in all, instances by differential migration of the sexes within each age class. This proposition can also be stated backwards: the samples show differential times of migration of the sexes, compounded by differential times of migration of the age groups within each sex. The order in which these matters are approached depends on what one is trying to find out. Influenced by the literature, in which most emphasis has been placed on age, we have approached the problem from that standpoint. The data and figures here given, however, can be juggled if one wishes to place first emphasis on the order of sexes in migration.
Bearing in mind what has just been said, particularly in respect to sizes of samples necessary for significance, let us consider the patterns of migration suggested by the Topeka sample. These are as follows:
(1) An early migration largely composed of adults, giving way later on to a preponderance of immatures. Regardless of variations among them, samples showing this basic pattern are in line with the opinions of Brewster (1886) and his followers. This pattern is here shown by the Lincoln Sparrow, Yellow-throat, Nashville Warbler, Catbird (one sample only), and Red-eyed Vireo (Fig. 1, A, B, C, D, E). The evidence of these and all other samples would admittedly be more conclusive if the samples were further apart in time or, better still, were there more of them. There is evidence that differences in migration of the sexes, within age classes, influence this pattern, sharply in some instances. In the later samples of Lincoln Sparrow, Yellow-throat, and Red-eyed Vireo (Fig. 1, A, B, E) there are relatively fewer males, both adult and immature, than in the earlier samples and this may be true also of the Catbird, judging from the single sample. The Red-eyed Vireo (Fig. 1, E) is characterized by small number, or absence of, males in each sample but the samples are not significantly different, and can be regarded as one. Although the samples of the Dickcissel and Mourning Warbler (Fig. 1, F, G) show a somewhat different over-all pattern and are discussed further on, they also contain few adult males. Since these samples are from a period that is near the end of the migration of Red-eyed Vireos, Mourning Warblers, and Dickcissels, it may be assumed tentatively that the adult males have already migrated. Meinertzhagen (1930:56) postulated that in many species there is an earlier or more rapid migration of adults, particularly males, and the data for the above species in our sample tend to support his assumption. But our data suggest in addition that in some species immature males migrate earlier, or more rapidly, than do immature females, just as adult males precede adult females in some instances. Within this general pattern (adults first) another variation is shown by the Nashville Warbler (Fig. 1, C) in which the later sample of adults is heavily weighted towards males, even though an increasing over-all proportion of immatures is evidenced. In this case, and contrary to Meinertzhagen's suggestion, it would seem that adult females have preceded or outstripped adult males in migration.