A Quantitative Study of the Nocturnal Migration of Birds Part 4

When the nightly curves of density at the various stations are plotted as a function of time, a salient fact emerges--that the flow of birds is in no instance sustained throughout the night. The majority of the curves rise smoothly from near zero at the time of twilight to a single peak and then decline more or less symmetrically to near the base line before dawn. The high point is reached in or around the eleven to twelve o'clock interval more often than at any other time.

[Ill.u.s.tration: FIG. 27. Hourly station densities plotted as a percentage of peak. The curve is based only on those sets of data where observations were continued long enough to include the nightly peak. In each set of data the station density for each hour has been expressed as a percentage of the peak for the night at the station in question. All percentages for the same hour on all dates have been averaged to obtain the percentile value of the combined station density at each hour (CST).]

Figure 26, representing the average hourly densities for all stations on all nights of observation, demonstrates the over-all effect of these tendencies. Here the highest density is reached in the hour before midnight with indications of flights of great magnitude also in the hour preceding and the hour following the peak interval. The curve ascends somewhat more rapidly than it declines, which fact may or may not be significant. Since there is a great disproportion in the total volume of migration at different localities, the thought might be entertained that a few high magnitude stations, such as Tampico and Progreso, have imposed their own characteristics on the final graph. Fortunately, this idea may be tested by subjecting the data to a second treatment. If hourly densities are expressed as a percentage of the nightly peak, each set of observations, regardless of the number of birds involved, carries an equal weight in determining the character of the over-all curve.

Figure 27 shows that percentage a.n.a.lysis produces a curve almost identical with the preceding one. To be sure, all of the individual curves do not conform with the composite, either in shape or incidence of peak. The extent of this departure in the latter respect is evident from Figure 28, showing the number of individual nightly station curves reaching a maximum peak in each hour interval. Even this graph demonstrates that maximum densities near midnight represent the typical condition.

[Ill.u.s.tration: FIG. 28. Incidence of maximum peak at the various hours of the night in 1948. "Number of stations"

represents the total for all nights of the numbers of station peaks falling within a given hour.]

The remarkable smoothness and consistency of the curves shown in Figures 26 and 27 seem to lead directly to the conclusion that the volume of night migration varies as a function of time. Admittedly other factors are potentially capable of influencing the number of birds pa.s.sing a given station in a given hour. Among these are weather conditions, ecological patterns, and specific topographical features that might conceivably serve as preferred avenues of flight. However, if any of these considerations were alone responsible for changes in the numbers of birds seen in successive intervals, the distribution of the peak in time could be expected to be haphazard. For example, there is no reason to suppose that the cone of observation would come to lie over favored terrain at precisely the hour between eleven and twelve o'clock at so many widely separated stations. Neither could the topographical hypothesis explain the consistently ascending and descending pattern of the ordinates in Figure 28. This is not to say that other factors are without effect; they no doubt explain the divergencies in the time pattern exhibited by Figure 28. Nevertheless, the underlying circ.u.mstances are such that when many sets of data are merged these other influences are subordinated to the rise and fall of an evident time pattern.

Stated in concrete terms, the time frequencies shown in the graphs suggest the following conclusions: first, nocturnal migrations are not a continuation of daytime flights; second, nearly all night migrants come to earth well before dawn; and, third, in each hour of the night up until eleven or twelve o'clock there is typically a progressive increase in the number of birds that have taken wing and in each of the hours thereafter there is a gradual decrease. Taken at its face value, the evidence seems to indicate that birds do not begin their night migrations _en ma.s.se_ and remain on the wing until dawn and that in all probability most of them utilize less than half of the night.

Interestingly enough, the fact that the plot points in Figure 26 lie nearly in line tempts one to a further conclusion. The curve behaves as an arithmetic progression, indicating that approximately the same number of birds are leaving the ground in each hour interval up to a point and that afterwards approximately the same number are descending within each hour. However, some of the components making up this curve, as later shown, are so aberrant in this regard that serious doubt is cast on the validity of this generalization.

Because the results of these time studies are unexpected and startling, I have sought to explore other alternative explanations and none appears to be tenable. For example, the notion that the varying flight speeds of birds might operate in some way to produce a c.u.mulative effect as the night progresses must be rejected on close a.n.a.lysis. If birds of varying flight speeds are continuously and evenly distributed in s.p.a.ce, a continuous and even flow would result all along their line of flight. If they are haphazardly distributed in s.p.a.ce, a correspondingly haphazard density pattern would be expected.

Another explanation might be sought in the purely mathematical effects of the method itself. The computational procedure a.s.sumes that the effective area of the sample is extremely large when the moon is low, a condition that usually obtains in the early hours of the evening in the days surrounding the full moon. Actually no tests have yet been conducted to ascertain how far away a silhouette of a small bird can be seen as it pa.s.ses before the moon. Consequently, it is possible that some birds are missed under these conditions and that the effective field of visibility is considerably smaller than the computed field of visibility. The tendency, therefore, may be to minimize the densities in such situations more than is justified.

However, in many, if not most, cases, the plotting of the actual number of birds seen, devoid of any mathematical procedures, results in an ascending and descending curve.

[Ill.u.s.tration: FIG. 29. Various types of density-time curves.

(A) Near typical, Ottumwa, April 22-23; (B) random fluctuation, Stillwater, April 23-24; (C) bimodal, Knoxville, April 22-23; (D) sustained peak, Ottumwa, April 21-22; (E) early peak, Oak Grove, May 21-22; (F) late peak, Memphis, April 23-24.]

A third hypothesis proposes that all birds take wing at nearly the same time, gradually increase alt.i.tude until they reach the mid-point of their night's journey, and then begin a similarly slow descent.

Since the field of observation of the telescope is conical, it is a.s.sumed that the higher the birds arise into the sky the more they increase their chances of being seen. According to this view, the changes in the density curve represent changes in the opportunity to see birds rather than an increase or decrease in the actual number of migrants in the air. Although measurements of flight alt.i.tude at various hours of the night have not been made in sufficient number to subject this idea to direct test, it is hardly worthy of serious consideration. The fallacy in the hypothesis is that the cone of observation itself would be rising with the rising birds so that actually the greatest proportion of birds flying would still be seen when the field of observation is in the supine position of early evening.

It cannot be too strongly emphasized that the over-all time curves just discussed have been derived from a series of individual curves, some of which differ radically from the composite pattern. In Figure 29, six dissimilar types are shown. This variation is not surprising in view of the fact that many other causative factors aside from time operate on the flow of birds from hour to hour. Figure 29A ill.u.s.trates how closely some individual patterns conform with the average. Figure 29B is an example of a random type of fluctuation with no p.r.o.nounced time character. It is an effect rarely observed, occurring only in the cases where the number of birds observed is so small that pure chance has a p.r.o.nounced effect on the computed densities; its vacillations are explicable on that account alone. Errors of sampling may similarly account for some, though not all, of the curves of the bimodal type shown in Figure 29C. Some variation in the curves might be ascribed to the variations in kinds of species comprising the individual flights at different times at different places, provided that it could be demonstrated that different species of birds show dissimilar temporal patterns. The other atypical patterns are not so easily dismissed and will be the subject of inquiry in the discussions that follow. It is significant that in spite of the variety of the curves depicted, which represent every condition encountered, in not a single instance is the density sustained at a high level throughout the night. Moreover, these dissident patterns merge into a remarkably harmonious, almost normal, average curve.

When, at some future date, suitable data are available, it would be highly desirable to study the average monthly time patterns to ascertain to what extent they may deviate from the over-all average.

At present this is not justifiable because there are not yet enough sets of data in any two months representing the same selection of stations.

_Correlations with Other Data_

It is especially interesting to note that the data pertaining to this problem derived from other methods of inquiry fit the conclusions adduced by the telescopic method. Overing (1938), who for several years kept records of birds striking the Was.h.i.+ngton Monument, stated that the record number of 576 individuals killed on the night of September 12, 1937, all came down between 10:30 P. M. and midnight.

His report of the mortality on other nights fails to mention the time factor, but I am recently informed by Frederick C. Lincoln (_in litt._) that it is typical for birds to strike the monument in greatest numbers between ten and twelve o'clock at night. At the latter time the lights illuminating the shaft are extinguished, thus resulting in few or no casualties after midnight. The recent report by Spofford (1949) of over 300 birds killed or incapacitated at the Nashville airport on the night of September 9-10, 1948, after flying into the light beam from a ceilometer, is of interest in this connection even though the cause of the fatality is shrouded in mystery. It may be noted, however, that "most of the birds fell in the first hour," which, according to the account, was between 12:30 A. M.

and 1:30 A. M. Furthermore, birds killed at the Empire State Building in New York on the night of September 10-11, 1948, began to strike the tower "shortly after midnight" (Pough, 1948). Also it will be recalled that the observations of Stone (_loc. cit._), already referred to in this paper (page 410), show a situation where the flight in the early part of the night was negligible but mounted to a peak between ten and eleven o'clock, with continuing activity at least until midnight.

All of these observations are of significance in connection with the conclusions herein advanced, but by far the most striking correlation between these present results and other evidences is found in the highly important work of various European investigators studying the activity of caged migratory birds. This work was recently reviewed and extended by Palmgren (1944) in the most comprehensive treatise on the subject yet published. Palmgren recorded, by an electrically operated apparatus, the seasonal, daily, and hourly activity patterns in caged examples of two typical European migrants, _t.u.r.dus ericetorum philomelas_ Brehm and _Erithacus rubecula_ (Linnaeus). Four rather distinct seasonal phases in activity of the birds were discerned: _winter non-migratory_, _spring migratory_, _summer non-migratory_, and _autumn migratory_. The first of these is distinguished by morning and evening maxima of activity, the latter being better developed but the former being more prolonged. Toward the beginning of migration, these two periods of activity decline somewhat. The second, or spring migratory phase, which is of special interest in connection with the present problem, is characterized by what Palmgren describes as nightly migratory restlessness (_Zugunruhe_). The morning maximum, when present, is weaker and the evening maximum often disappears altogether. Although variations are described, the migratory restlessness begins ordinarily after a period of sleep ("sleeping pause") in the evening and reaches a maximum and declines before midnight.

This pattern agrees closely with the rhythm of activity indicated by the time curves emerging from the present research. Combining the two studies, we may postulate that most migrants go to sleep for a period following twilight, thereby accounting for the low densities in the early part of the night. On awakening later, they begin to exhibit migratory restlessness. The first hour finds a certain number of birds sufficiently stimulated so that they rise forthwith into the air. In the next hour still others respond to this urge and they too mount into the air. This continues until the "restlessness" begins to abate, after which fewer and fewer birds take wing. By this time, the birds that began to fly early are commencing to descend, and since their place is not being filled by others leaving the ground, the density curve starts its decline. Farner (1947) has called attention to the basic importance of the work by Palmgren and the many experimental problems it suggests. Of particular interest would be studies comparing the activity of caged American migrant species and the nightly variations in the flight rates.

_The Baton Rouge Drop-off_

As already stated, the present study was initiated at Baton Rouge, Louisiana, in 1945, and from the outset a very peculiar density time pattern was manifest. I soon found that birds virtually disappeared from the sky after midnight. Within an hour after the termination of twilight, the density would start to ascend toward a peak which was usually reached before ten o'clock, and then would begin, surprisingly enough, a rapid decline, reaching a point where the migratory flow was negligible. In Figure 30 the density curves are shown for five nights that demonstrate this characteristically early decline in the volume of migration at this station. Since, in the early stages of the work, coordinates of apparent pathways of all the birds seen were not recorded, I am unable now to ascertain the direction of flight and thereby arrive at a density figure based on the dimension of the cone and the length of the front presented to birds flying in certain directions. It is feasible, nevertheless, to compute what I have termed a "plus or minus" flight density figure stating the rate of pa.s.sage of birds in terms of the maximum and minimum corrections which all possible directions of flight would impose. In other words, density is here computed, first, as if all the birds were flying perpendicular to the long axis of the ellipse, and, secondly, as if all the birds were flying across the short axis of the ellipse. Since the actual directions of flight were somewhere between these two extremes, the "plus or minus" density figure is highly useful.

[Ill.u.s.tration: FIG. 30. Density-time curves on various nights at Baton Rouge. (A) April 25, 1945; (B) April 15, 1946; (C) May 10, 1946; (D) May 15, 1946; (E) April 22-23, 1948.

These curves are plotted on a "plus or minus" basis as described in the text, with the bottom of the curve representing the minimum density and the top of the curve the maximum.]

The well-marked decline before midnight in the migration rates at Baton Rouge may be regarded as one of the outstanding results emerging from this study. Many years of ornithological investigation in this general region failed to suggest even remotely that a situation of this sort obtained. Now, in the light of this new fact, it is possible for the first time to rationalize certain previously incongruous data.

Ornithologists in this area long have noted that local storms and cold-front phenomena at night in spring sometimes precipitate great numbers of birds, whereupon the woods are filled the following day with migrants. On other occasions, sudden storms at night have produced no visible results in terms of bird densities the following day. For every situation such as described by Gates (1933) in which hordes of birds were forced down at night by inclement weather, there are just as many instances, even at the height of spring migration, when similar weather conditions yielded no birds on the ground.

However, the explanation of these facts is simple; for we discover that storms that produced birds occurred before midnight and those that failed to produce birds occurred after that time (the storm described by Gates occurred between 8:30 and 9:00 P. M.).

The early hour decline in density at Baton Rouge at first did not seem surprising in view of the small amount of land area between this station and the Gulf of Mexico. Since the majority of the birds destined to pa.s.s Baton Rouge on a certain night come in general from the area to the south of that place, and since the distances to various points on the coast are slight, we inferred that a three-hour flight from even the more remote points would probably take the bulk of the birds northward past Baton Rouge. In short, the coastal plain would be emptied well before midnight of its migrant bird life, or at least that part of the population destined to migrate on any particular night in question. Although data in quant.i.ty are not available from stations on the coastal plain other than Baton Rouge, it may be pointed out that such observations as we do have, from Lafayette and New Orleans, Louisiana, and from Thomasville, Georgia, are in agreement with this hypothesis.

A hundred and seventy miles northward in the Mississippi Valley, at Oak Grove, Louisiana, a somewhat more normal density pattern is manifested. There, in four nights of careful observation, a p.r.o.nounced early peak resulted on the night of May 21-22 (Figure 29E), but on the other three nights significant densities held up until near twelve o'clock, thereby demonstrating the probable effect of the increased amount of land to the south of the station.

Subsequent studies, revealing the evident existence of an underlying density time pattern, cast serious doubt on the explanations just advanced of the early decline in the volume of migration at Baton Rouge. It has as yet been impossible to reconcile the early drop-off at this station with the idea that birds are still mounting into the air at eleven o'clock, as is implied by the ideal time curves.

C. MIGRATION IN RELATION TO TOPOGRAPHY

To this point we have considered the horizontal distribution of birds in the sky only on a very narrow scale and mainly in terms of the chance element in observations. Various considerations have supported the premise that the spread of nocturnal migration is rather even, at least within restricted s.p.a.cial limits and short intervals of time.

This means that in general the flow of birds from hour to hour at a single station exhibits a smooth continuity. It does not mean that it is a uniform flow in the sense that approximately the same numbers of birds are pa.s.sing at all hours, or at all localities, or even on all one-mile fronts in the same locality. On the contrary, there is evidence of a p.r.o.nounced but orderly change through the night in the intensity of the flight, corresponding to a basic and definitely timed cycle of activity. Other influences may interfere with the direct expression of this temporal rhythm as it is exhibited by observations at a particular geographical location. Among these, as we have just seen, is the disposition of the areas that offer suitable resting places for transient birds and hence contribute directly and immediately to the flight overhead. A second possible geographical effect is linked with the question of the tendency of night migrants to follow topographical features.

_General Aspects of the Topographical Problem_

That many diurnal migrants tend to fly along sh.o.r.elines, rivers, and mountain ridges is well known, but this fact provides no a.s.surance that night migrants do the same thing. Many of the obvious advantages of specialized routes in daylight, such as feeding opportunities, the lift provided by thermal updrafts, and the possible aid of certain landmarks in navigation, a.s.sume less importance after night falls.

Therefore, it would not be safe to conclude that _all_ nocturnal migrants operate as do _some_ diurnal migrants. For instance, the pa.s.sage of great numbers of certain species of birds along the Texas coast in daylight hours cannot be regarded as certain proof that the larger part of the nocturnal flight uses the same route. Neither can we a.s.sume that birds follow the Mississippi River at night simply because we frequently find migrants concentrated along its course in the day. Fortunately we shall not need to speculate indefinitely on this problem; for the telescopic method offers a means of study based on what night migrants are doing _at night_. Two lines of attack may be pursued. First we may compare flight densities obtained when the field of the telescope lies over some outstanding topographical feature, such as a river, with the recorded volume of flight when the cone of observation is directed away from that feature. Secondly, we may inquire how the major flight directions at a certain station are oriented with respect to the terrain. If the flight is concentrated along a river, for instance, the flight density curve should climb upward as the cone of observation swings over the river, _regardless of the hour at which it does so_. The effect should be most p.r.o.nounced if the observer were situated on the river bank, so that the cone would eventually come to a position directly along the watercourse.

Though in that event birds coming up the river route would be flying across the short axis of an elliptical section of the cone, the fact that the whole field of observation would be in their path should insure their being seen in maximum proportions. If, on the other hand, the telescope were set up some distance away from the river so that the cone merely moved _across_ its course, only a section of the observation field would be interposed on the main flight lane.

The interaction of these possibilities with the activity rhythm should have a variety of effects on the flight density curves. If the cone comes to lie over the favored topographical feature in the hour of greatest migrational activity, the results would be a simple sharp peak of doubtful meaning. However, since the moon rises at a different time each evening, the cone likewise would reach the immediate vicinity of the terrain feature at a different time each night. As a result, the terrain peak would move away from its position of coincidence with the time peak on successive dates, producing first, perhaps, a sustention of peak and later a definitely bimodal curve.

Since other hypotheses explain double peaks equally well, their mere existence does not necessarily imply that migrants actually do travel along narrow topographical lanes. Real proof requires that we demonstrate a moving peak, based on properly corrected density computations, corresponding always with the position of the cone over the most favored terrain, and that the flight vectors be consistent with the picture thus engendered.

_The Work of Winkenwerder_

To date, none of the evidence in favor of the topographical hypothesis completely fills these requirements. Winkenwerder (_loc. cit._), in a.n.a.lyzing the results of telescopic counts of birds at Madison and Beloit, Wisconsin, Detroit and Ann Arbor, Michigan, and at Lake Forest, Illinois, between 1898 and 1900, plotted the number of birds seen at fifteen-minute intervals as a function of the time of the night. He believed that the high points in the resulting frequency histograms represented intervals when the field of the telescope was moving over certain topographically determined flight lanes, though he did not specify in all cases just what he a.s.sumed the critical physiographic features to be. Especially convincing to him were results obtained at Beloit, where the telescope was situated on the east bank of the Rock River, on the south side of the city.

Immediately below Beloit the river turns southwestward and continues in this direction about five miles before turning again to flow in a southeastward course for approximately another five miles. In this setting, on two consecutive nights of observation in May, the number of birds observed increased tremendously in the 2 to 3 A. M. interval, when, according to Winkenwerder's interpretation of the data (he did not make the original observations at Beloit himself), the telescope was pointing directly down the course of the river. This conclusion is weakened, however, by notable inconsistencies. Since the moon rises later each evening, it could not have reached the same position over the Rock River at the same time on both May 12-13 and May 13-14, and therefore, if the peaks in the graph were really due to a greater volume of migration along the watercourse, they should not have so nearly coincided. As a matter of fact the incidence of the peak on May 12-13 should have preceded that of the peak on May 13-14; whereas his figure shows the reverse to have been true. Singularly enough, Winkenwerder recognized this difficulty in his treatment of the data from Madison, Wisconsin. Unable to correlate the peak period with the Madison terrain by the approach used for Beloit, he plotted the observations in terms of hours after moonrise instead of standard time. This procedure was entirely correct; the moon does reach approximately the same position at each hour after its rise on successive nights. The surprising thing is that Winkenwerder did not seem to realize the incompatibility of his two approaches or to realize that he was simply choosing the method to suit the desired results.

Furthermore, as shown in Part I of this paper, the number of birds seen through the telescope often has only an indirect connection with the actual number of birds pa.s.sing over. My computations reveal that the highest counts of birds at Beloit on May 12-13 were recorded when the moon was at an alt.i.tude of only 8 to 15 and, that when appropriate allowance is made for the immense size of the field of observation at this time, the partially corrected flight density for the period is not materially greater than at some other intervals in the night when the telescope was not directed over the course of the Rock River. These allowances do not take the direction factor into consideration. Had the birds been flying at right angles to the short axis of an elliptical section of the cone throughout the night, the flight density in the period Winkenwerder considered the peak would have been about twice as high as in any previous interval. On the other hand, if they had been flying across the long axis at all times, the supposed peak would be decidedly inferior to the flight density at 10 to 11:00 P. M., before the cone came near the river.

Admittedly, these considerations contain a tremendous element of uncertainty. They are of value only because they expose the equal uncertainty in Winkenwerder's basic evidence. Since the coordinates of the birds' apparent pathways at Beloit were given, I at first entertained the hope of computing the flight densities rigorously, by the method herein employed. Unfortunately, Winkenwerder was apparently dealing with telescopes that gave inverted images, and he used a system for recording coordinates so ambiguously described that I am not certain I have deciphered its true meaning. When, however, his birds are plotted according to the instructions as he stated them, the prevailing direction of flight indicated by the projection formula falls close to west-northwest, not along the course of the Rock River, but _at direct right angles to it_.

[Ill.u.s.tration: FIG. 31. Directional components in the flight at Tampico on three nights in 1948. The lengths of the sector vectors are determined by their respective densities expressed as a percentage of the station density for that night; the vector resultants are plotted from them by standard procedure. Thus, the nightly diagrams are not on the same scale with respect to the actual number of birds involved.]

[Ill.u.s.tration: FIG. 32. Hourly station density curve at Tampico, Tamaulipas, on the night of April 21-22, 1948 (CST).]

_Interpretation of Recent Data_

I am in a position to establish more exact correlations between flight density and terrain features in the case of current sets of observations. Some of these data seem at first glance to fit the idea of narrow topographically-oriented flight lanes rather nicely. At Tampico, where six excellent sets of observations were made in March and April, 1948, the telescope was set up on the beach within a few yards of the Gulf of Mexico. As can be seen from Figure 25 (_ante_), the slant of the coastline at this point is definitely west of north, as is also the general trend of the entire coast from southern Veracruz to southern Tamaulipas (see Figure 34, beyond). The over-all vector resultant of all bird flights at this station was N 11 W, and, as will be seen from Figure 31, none of the nightly vector resultants in April deviates more than one degree from this average. Thus the prevailing direction of flight, as computed, agrees with the trend of the coast at the precise point of the observations, at least to the extent that both are west of north. To be sure, the individual sector vectors indicate that not all birds were following this course; indeed, some appear to have been flying east of north, heading for a landfall in the region of Brownsville, Texas, and a very few to have been traveling northeastward toward the central Gulf coast. But it must be remembered that a certain amount of computational deviation and of localized zigzagging in flight must be antic.i.p.ated. Perhaps none of these eastward vectors represents an actual extended flight path. The nightly vector resultants, on the other hand, are so consistent that they have the appearance of remarkable accuracy and tempt one to draw close correlations with the terrain. When this is done, it is found that, while the prevailing flight direction is 11 west of north, the exact slant of the coastline at the location of the station is about 30 west of north, a difference of around 19. It appears, therefore, that the birds were not following the sh.o.r.eline precisely but cutting a chord about ten miles long across an indentation of the coast. If it be argued that the method of calculation is not accurate enough to make a 19 difference significant, and that most of the birds might have been traveling along the beach after all, it can be pointed out with equal justification that, if this be so, the 11 divergence from north does not mean anything either and that perhaps the majority of the birds were going due north. We are obliged to conclude either that the main avenue of flight paralleled the disposition of the major topographical features only in a general way or that the angle between the line of the coast and true north is not great enough to warrant any inference at all.

Consideration of the Tampico density curves leads to similarly ambiguous results. On the night of April 21-22, as is evident from a comparison of Figures 25 and 32, the highest flight density occurred when the projection of the cone on the terrain was wholly included within the beach. This is very nearly the case on the night of April 23-24 also, the positions of the cone during the peak period of density being only about 16 apart. (On the intervening date, clouds prevented continuous observation during the critical part of the night.) These correlations would seem to be good evidence that most of these night migrants were following the coastline of the Gulf of Mexico. However, the problem is much more complicated. The estimated point of maximum flight density fell at 10:45 P. M. on April 21-22 and 11:00 P. M. on April 23-24, both less than an hour from the peak in the ideal time curve (Figure 26, _ante_). We cannot be sure, therefore, that the increase in density coinciding with the position of the moon over the beach is not an increase which would have occurred anyway. Observations conducted several nights before or after the second quarter, when the moon is not on or near its zenith at the time of the predictable peak in the density curve, would be of considerable value in the study of this particular problem.

The situation at Tampico has been dealt with at length because, among all the locations for which data are available, it is the one that most strongly supports the topographical hypothesis. In none of the other cases have I been able to find a definite relation between the direction of migration and the features of the terrain. Studies of data from some of these stations disclose directional patterns that vary from night to night only slightly more than does the flight at Tampico. In three nights of observation at Lawrence, Kansas, marked by very high densities, the directional trend was north by north-northeast with a variation of less than 8, yet Lawrence is so situated that there seems to be no feature of the landscape locally or in the whole of eastern Kansas or of western Missouri that coincides with this heading. At Mansfield, Louisiana, in twelve nights of observation, the strong east by northeast trend varied less than 15, but again there appears to be no correlation over a wide area between this direction and any landmarks. And, at Progreso, Yucatan, where the vector resultants were 21 and 27 on successive nights, most of the birds seen had left the land and were beginning their flight northward over the trackless waters of the Gulf of Mexico. Furthermore, as I have elsewhere pointed out (1946: 205), the whole northern part of the Yucatan Peninsula itself is a flat terrain, unmarked by rivers, mountains, or any other strong physiographic features that conceivably might be followed by birds.

[Ill.u.s.tration: FIG. 33. The nightly net trend of migrations at three stations in 1948. Each arrow is the vector resultant for a particular night, its length expressing the nightly density as a percentage of the total station density for the nights represented. Thus, the various station diagrams are not to the same scale.]

In Figure 33 I have shown the directional patterns at certain stations where, unlike the cases noted above, there is considerable change on successive nights. Each vector shown is the vector resultant for one particular night. The lengths of the vectors have been determined by their respective percentages of the total computed density, or total station magnitude, for all the nights in question. In other words, the lengths of the individual vectors denote the percentile role that each night played in the total density. From the directional spread at these stations it becomes apparent that if most of the birds were traveling along a certain topographic feature on one night, they could not have been traveling along the same feature on other nights.