A Quantitative Study of the Nocturnal Migration of Birds Part 3

Locating the position of a particular sector boundary now becomes a mere matter of subst.i.tuting the values in the equation (1) and reducing. The computation of the north point for 11 to 12 P. M. in the sample set of data will serve as an example. Since the north point reckoned west from the south point is 180, its [eta] has a value of 180.

[Ill.u.s.tration: FIG. 19. Method of plotting sector boundaries on the diagrammatic plots. The example employed is the 11:00 to 12:00 P. M. diagram of Figure 15.]

tan [theta]_{Npt.} = tan (180 - [psi]_{0}) / cos Z_{0}

Subst.i.tuting values of [psi]_{0} found on the form (Figure 18):

tan [theta]_{Npt.} = tan [180 - (-35)] / cos 50 = tan 215 / cos 50 = .700 / .643 = 1.09

[theta]_{Npt.} = 4728'

[Ill.u.s.tration: FIG. 20. Form for computing sector densities.]

Four angles, one in each quadrant, have the same tangent value.

Since, in processing spring data, we are dealing mainly with north sectors, it is convenient to choose the acute angle, in this instance 47 28'. In doubtful cases, the value of the numerator of the equation (here 215) applied as an angular measure from 6 o'clock will tell in which quadrant the projected boundary must fall. The fact that projection always draws the boundary closer to the 3-9 line serves as a further check on the computation.

[Ill.u.s.tration: FIG. 21. Determinationn of the angle [alpha]]

In the same manner, the projected position angles of all the pertinent sector boundaries for a given hour may be calculated and plotted in red pencil with a protractor on the circular diagrams of Figure 15. To avoid confusion in lines, the zones are not portrayed in the black and white reproduction of the sample plot form. They are shown, however, in the shaded enlargement (Figure 19) of the 11 to 12 P. M. diagram.

The number of birds recorded for each sector may be ascertained by counting the number of tally marks between each pair of boundary lines and the information may be entered in the columns provided in the plot form (Figure 15). We are now prepared to turn to the form for "Computations of Sector Densities" (Figure 20), which systematizes the solution of the following equation:

(220) 60/T (No. of Birds) (cos^2 Z_{0}) D = --------------------------------------- (2) (1 - sin^2 Z_{0} cos^2 [alpha])^0.5

[Ill.u.s.tration: FIG. 22. Facsimile of form summarizing sector densities. The totals at the bottom of each column give the station densities.]

[Ill.u.s.tration: FIG. 23. Determination of Net Trend Density.]

Some of the symbols and factors, appearing here for the first time, require brief explanation. D stands for Sector Density. The constant, 220, is the reciprocal of the quotient of the angular diameter of the moon divided by 2. T is Time In, arrived at by subtracting the total number of minutes of time out, as noted for each hour on the original data sheets, from 60. "No. of Birds" is the number for the sector and hour in question as just determined on the plot form. The symbol [alpha] represents the angle between the mid-line of the sector and the azimuth line of the moon. The quant.i.ty is found by the equation:

[alpha] = 180 - [eta] + [psi]_{0} (3)

The symbol [eta] here represents the position of the mid-line of the sector expressed in terms of its 360 compa.s.s reading. This equation is ill.u.s.trated in Figure 21. The values of [eta] for various zones are given in the upper right-hand corner of the form (Figure 20). The subsequent reductions of the equations, as they appear in the figure for four zones, are self-explanatory. The end result, representing the sector density, is entered in the rectangular box provided.

After all the sector densities have been computed, they are tabulated on a form for the "Summary of Sector Densities" (Figure 22). By totaling each vertical column, sums are obtained, expressing the Station Density or Station Magnitude for each hour.

An informative way of depicting the densities in each zone is to plot them as lines of thrust, as in Figure 23. Each sector is represented by the directional slant of its mid-line drawn to a length expressing the flight density per zone on some chosen scale, such as 100 birds per millimeter. Standard methods of vector a.n.a.lysis are then applied to find the vector resultant. This is done by considering the first two thrust lines as two sides of an imaginary parallelogram and using a drawing compa.s.s to draw intersecting arcs locating the position of the missing corner. In the same way, the third vector is combined with the invisible resultant whose distal end is represented by the intersection of the first two arcs. The process is repeated successively with each vector until all have been taken into consideration. The final intersection of arcs defines the length and slant of the Vector Resultant, whose magnitude expresses the Net Trend Density in terms of the original scale.

The final step in the processing of a set of observations is to plot on graph paper the nightly station density curve as ill.u.s.trated by Figure 24.

[Ill.u.s.tration: FIG. 24. Nightly station density curve at Progreso, Yucatan, on April 24-25, 1948.]

PART II. THE NATURE OF NOCTURNAL MIGRATION

Present day concepts of the whole broad problem of bird migration are made up of a few facts and many guesses. The evolutionary origin of migration, the modern necessities that preserve its biologic utility, the physiological processes a.s.sociated with it, the sensory mechanisms that make it possible, the speed at which it is achieved, and the routes followed, all have been the subject of some investigation and much conjecture. All, to a greater or less extent, remain matters of current controversy. All must be considered unknowns in every logical equation into which they enter. Since all aspects of the subject are intimately interrelated, since all have a bearing on the probabilities relating to any one, and since new conjectures must be judged largely in the light of old conjectures rather than against a background of ample facts, the whole field is one in which many alternative explanations of the established phenomena remain equally tenable.

Projected into this uncertain atmosphere, any statistical approach such as determinations of flight density will require the acc.u.mulation of great ma.s.ses of data before it is capable of yielding truly definitive answers to those questions that it is suited to solve. Yet, even in their initial applications, density a.n.a.lyses can do much to bring old hypotheses regarding nocturnal migration into sharper definition and to suggest new ones.

The number of birds recorded through the telescope at a particular station at a particular time is the product of many potential variables. Some of these--like the changing size of the field of observation and the elevation of flight--pertain solely to the capacity of the observer to see what is taking place. It is the function of the density and direction formulae to eliminate the influences of these two variables insofar as is possible, so that the realities of the situation take shape in a nearly statistically true form. There remain to be considered those influences potentially responsible for variations in the real volume of migration at different times and places--things like the advance of season, geographic location, disposition of terrain features, hourly activity rhythm, wind currents, and other climatological causes. The situation represented by any set of observations probably is the end result of the interaction of several such factors. It is the task of the discussions that follow to a.n.a.lyze flight densities in the light of the circ.u.mstances surrounding them and by statistical insight to isolate the effects of single factors. When this has been done, we shall be brought closer to an understanding of these influences themselves as they apply to the seasonal movements of birds. Out of data that is essentially quant.i.tative, conclusions of a qualitative nature will begin to take form. It should be constantly borne in mind, however, that such conclusions relate to the movement of birds _en ma.s.se+ and that caution must be used in applying these conclusions to any one species.

Since the dispersal of migrants in the night sky has a fundamental bearing on the sampling procedure itself, and therefore on the reliability of figures on flight density, consideration can well be given first to the horizontal distribution of birds on narrow fronts.

A. HORIZONTAL DISTRIBUTION OF BIRDS ON NARROW FRONTS

Bird migration, as we know it in daytime, is characterized by spurts and uneven spatial patterns. Widely separated V's of geese go honking by. Blackbirds pa.s.s in dense recurrent clouds, now on one side of the observer, now on the other. Hawks ride along in narrow file down the thermal currents of the ridges. Herons, in companies of five to fifty, beat their way slowly along the line of the surf. And an unending stream of swallows courses low along the levees. Everywhere the impression is one of birds in bunches, with vast s.p.a.ces of empty sky between.

Such a situation is ill-suited to the sort of sampling procedure on which flight density computations are based. If birds always traveled in widely separated flocks, many such flocks might pa.s.s near the cone of observation and still, by simple chance, fail to enter the sliver of s.p.a.ce where they could be seen. Chance would be the dominating factor in the number of birds recorded, obscuring the effects of other influences. Birds would seldom be seen, but, when they did appear, a great many would be observed simultaneously or in rapid succession.

When these telescopic studies were first undertaken at Baton Rouge in 1945, some a.s.surance already existed, however, that night migrants might be so generally dispersed horizontally in the darkness above that the number pa.s.sing through the small segment of sky where they could be counted would furnish a nearly proportionate sample of the total number pa.s.sing in the neighborhood of the observation station. This a.s.surance was provided by the very interesting account of Stone (1906: 249-252), who enjoyed the unique experience of viewing a nocturnal flight as a whole. On the night of March 27, 1906, a great conflagration occurred in Philadelphia, illuminating the sky for a great distance and causing the birds overhead to stand out clearly as their bodies reflected the light.

Early in the night few birds were seen in the sky, but thereafter they began to come in numbers, pa.s.sing steadily from the southwest to the northeast. At ten o'clock the flight was at its height. The observer stated that two hundred birds were in sight at any given moment as he faced the direction from which they came. This unparalleled observation is of such great importance that I quote it in part, as follows: "They [the birds] flew in a great scattered, wide-spread host, never in cl.u.s.ters, each bird advancing in a somewhat zigzag manner.... Far off in front of me I could see them coming as mere specks...gradually growing larger as they approached.... Over the illuminated area, and doubtless for great distances beyond, they seemed about evenly distributed.... I am inclined to think that the migrants were not influenced by the fire, so far as their flight was concerned, as those far to the right were not coming toward the blaze but keeping steadily on their way.... Up to eleven o'clock, when my observations ceased, it [the flight] continued apparently without abatement, and I am informed that it was still in progress at midnight."

Similarly, in rather rare instances in the course of the present study, the combination of special cloud formations and certain atmospheric conditions has made it possible to see birds across the entire field of the telescope, whether they actually pa.s.sed before the moon or not. In such cases the area of the sky under observation is greatly increased, and a large segment of the migratory movement can be studied. In my own experience of this sort, I have been forcibly impressed by the apparent uniformity and evenness of the procession of migrants pa.s.sing in review and the infrequence with which birds appeared in close proximity.

As striking as these broader optical views of nocturnal migration are, they have been too few to provide an incontestable basis for generalizations. A better test of the prevailing horizontal distribution of night migrants lies in the a.n.a.lysis of the telescopic data themselves.

[Ill.u.s.tration: FIG. 25. Positions of the cone of observation at Tampico, Tamps., on April 21-22, 1948. Essential features of this diagrammatic map are drawn to scale, the triangular white lines representing the projections of the cone of observation on the actual terrain at the mid-point of each hour of observation. If the distal ends of the position lines were connected, the portion of the map encompa.s.sed would represent the area over which all the birds seen between 8:30 P. M. and 3:30 A. M. must have flown.]

The distribution in time of birds seen by a single observer may be studied profitably in this connection. Since the cone of observation is in constant motion, swinging across the front of birds migrating from south to north, each interval of time actually represents a different position in s.p.a.ce. This is evident from the map of the progress of the field of observation across the terrain at Tampico, Tamaulipas, on April 21-22, 1948 (Figure 25). At this station on this night, a total of 259 birds were counted between 7:45 P. M. and 3:45 A. M. The number seen in a single hour ranged from three to seventy-three, as the density overhead mounted to a peak and then declined. The number of birds seen per minute was not kept with stop watch accuracy; consequently, a.n.a.lysis of the number of birds that pa.s.sed before the moon in short intervals of time is not justified. It appears significant, however, that in the ninety minutes of heaviest flight, birds were counted at a remarkably uniform rate per fifteen minute interval, notwithstanding the fact that early in the period the flight rate overhead had reached a peak and had begun to decline. The number of birds seen in successive fifteen-minute periods was twenty-six, twenty-five, nineteen, eighteen, fifteen, and fifteen.

Also, despite the heavy volume of migration at this station on this particular night, the flight was sufficiently dispersed horizontally so that only twice in the course of eight hours of continuous observation did more than one bird simultaneously appear before the moon. These were "a flock of six birds in formation" seen at 12:09 A. M.

and "a flock of seven, medium-sized and distant," seen at 2:07 A. M.

In the latter instance, as generally is the case when more than one bird is seen at a time, the moon had reached a rather low alt.i.tude, and consequently the cone of observation was approaching its maximum dimensions.

The comparative frequency with which two or more birds simultaneously cross before the moon would appear to indicate whether or not there is a tendency for migrants to fly in flocks. It is significant, therefore, that in the spring of 1948, when no less than 7,432 observations were made of birds pa.s.sing before the moon, in only seventy-nine instances, or 1.1 percent of the cases, was more than one seen at a time. In sixty percent of these instances, only two birds were involved. In one instance, however, again when the moon was low and the cone of observation near its maximum size, a flock estimated at twenty-five was recorded.

The soundest approach of all to the study of horizontal distribution at night, and one which may be employed any month, anywhere, permitting the acc.u.mulation of statistically significant quant.i.ties of data, is to set up two telescopes in close proximity. Provided the flight overhead is evenly dispersed, each observer should count approximately the same number of birds in a given interval of time. Some data of this type are already available. On May 19-20, at Urbana, Illinois, while stationed twenty feet apart making parallax studies with two telescopes to determine the height above the earth of the migratory birds, Carpenter and Stebbins (_loci cit._) saw seventy-eight birds in two and one-half hours. Eleven were seen by both observers, thirty-three by Stebbins only, and thirty-four by Carpenter only. On October 10, 1905, at the same place, in two hours, fifty-seven birds were counted, eleven being visible through both telescopes. Of the remainder, Stebbins saw seventeen and Carpenter, twenty-nine. On September 12, 1945, at Baton Rouge, Louisiana, in an interval of one hour and forty minutes, two independent observers each counted six birds. Again, on October 17, 1945, two observers each saw eleven birds in twenty-two minutes. On April 10, 1946, in one hour and five minutes, twenty-four birds were seen through one scope and twenty-six through the other. Likewise on May 12, 1946, in a single hour, seventy-three birds were counted by each of two observers. The Baton Rouge observations were made with telescopes six to twelve feet apart. These results show a remarkable conformity, though the exceptional October observation of Carpenter and Stebbins indicates the desirability of continuing these studies, particularly in the fall.

On the whole, the available evidence points to the conclusion that night migration differs materially from the kind of daytime migration with which we are generally familiar. Birds are apparently evenly spread throughout the sky, with little tendency to fly in flocks. It must be remembered, however, that only in the case of night migration have objective and truly quant.i.tative studies been made of horizontal distribution. There is a possibility that our impressions of diurnal migration are unduly influenced by the fact that the species accustomed to flying in flocks are the ones that attract the most attention.

These conclusions relate to the uniformity of migration in terms of short distances only, in the immediate vicinity of an observation station. The extent to which they may be applied to broader fronts is a question that may be more appropriately considered later, in connection with continental aspects of the problem.

B. DENSITY AS FUNCTION OF THE HOUR OF THE NIGHT

There are few aspects of nocturnal migration about which there is less understanding than the matter of when the night flight begins, at what rate it progresses, and for what duration it continues. One would think, however, that this aspect of the problem, above most others, would have been thoroughly explored by some means of objective study. Yet, this is not the case. Indeed, I find not a single paper in the American literature wherein the subject is discussed, although some attention has been given the matter by European ornithologists. Siivonen (1936) recorded in Finland the frequency of call notes of night migrating species of _t.u.r.dus_ and from these data plotted a time curve showing a peak near midnight. Bergman (1941) and Putkonen (1942), also in Finland, studied the night flights of certain ducks (_Clangula hyemalis_ and _Oidemia fusca_ and _O. nigra_) and a goose (_Branta bernicla_) and likewise demonstrated a peak near midnight. However, these studies were made at northern lat.i.tudes and in seasons characterized by evenings of long twilight, with complete darkness limited to a period of short duration around midnight. Van Oordt (1943: 34) states that in many cases migration lasts all night; yet, according to him, most European investigators are of the opinion that, in general, only a part of the night is used, that is, the evening and early morning hours. The consensus of American ornithologists seems to be that migratory birds begin their flights in twilight or soon thereafter and that they remain on the wing until dawn. Where this idea has been challenged at all, the implication seems to have been that the flights are sustained even longer, often being a continuation far into the night of movements begun in the daytime. The telescopic method fails to support either of these latter concepts.

[Ill.u.s.tration: FIG. 26. Average hourly station densities in spring of 1948. This curve represents the arithmetic mean obtained by adding all the station densities for each hour, regardless of date, and dividing the sum by the number of sets of observations at that hour (CST).]

_The Time Pattern_