Annals of the Missouri Botanical Garden 34(4): 353-432 (Nov 1947)
Some Dynamics of Leaf Variation in Asclepias tuberosa
Robert E. Woodson, Jr.


One day many years ago, as a young student, I paid my first visit to the Smithsonian Institution in Washington. When noontime arrived, I was taken in tow by my new friend, E. P. Killip, to the Smithsonian's unofficial "Lunch Mess" in the kitchen of an old house around the corner. There I was awed by my inclusion within a jovial group of biologists previously known to me only by their eminence. Killip announced me as a budding authority on the Asclepiadales, an order of Flowering Plants including the milkweed genus, Asclepias. Instantly the late Dr. F. V. Coville fixed me with a baleful glare and thundered: "All right, then tell us what is wrong with Asclepias tuberosa!" I was dumb-struck. I knew A. tuberosa in the field about my home in St. Louis, but it had never occurred to me that anything was "wrong" with it; and besides, I was having troubles of my own with my dissertation topic, the exasperating genus Apocynum.

At any rate, when my taxonomic studies finally brought me to Asclepias shortly before the outbreak of the recent World War, I already was prepared to find something "wrong" with A. tuberosa. And I did. The species, as is usual in the genus, is beautifully distinguished by sharply defined floral and vegetative characters; it is easily keyed from its congeners. But within the species extraordinary variation is rampant, particularly in the leaves. By overworking my taxonomic intuition, at length I was able to distinguish three subspecies, which went far toward resolving the difficulty. But I could not escape the knowledge that something still was "wrong," particularly at the peripheries and commissures of the subspecific distributions. Nevertheless, but for the outbreak of the war I probably would have been content to let well enough suffice.

Every taxonomist is all too familiar with the professional handicaps imposed by a world conflict. Even for those who fortunately are left at home, special duties demand attention. Furthermore, necessary facilities for research are curtailed, such as the exchange of authentic or type specimens. Nor can one overlook the difficulties of publication itself, thanks to wartime industrial disturbances. Anticipating this prospect, I decided to take advantage of international catastrophe by familiarizing myself with some of the more recent tools of biological systematics to the end of applying them to the special problems presented by Asclepias tuberosa.


Asclepias tuberosa is familiar to practically any one who is interested in wild flowers from Sonora to Massachusetts and from Minnesota to Florida. Throughout approximately the eastern half of the United States it is a common roadside plant, conspicuous to any passer-by because of its clusters of stems about knee-high, each surmounted in midsummer by showy trusses of smallish but intensely brilliant orange, scarlet, or yellow flowers. The plants are long-lived perennials of easy culture, and are prized by many horticulturists because of their dependability, long season of bloom, and dramatic dashes of color.

Not the least interesting feature of the flowers is their apparently irresistible appeal to insects, particularly Hymenoptera, which are their chief pollinating agents. Butterflies, as well, are almost constantly hovering above blooming plants, and are responsible for their most familiar popular name of butterflyweed. Coralweed also is an appropriate name for them. Fortunately less familiar are the names pleurisyroot and chiggerweed.


A fully developed butterflyweed usually is a rather massive plant. The perennial portion consists of a woody tap root as much as three feet long and eight inches in circumference, surmounted just below ground level by a tightly branching crown from which a few to as many as a hundred herbaceous flowering stems may arise each year. Plants attain blooming age two to three years after germination of the seed and may persist for as long as twenty years or more. It would be difficult to estimate the age of a large plant upon a single examination because of the numerous stems produced each season and their crowding at the crown.

Some botanists would refer to the perennial plant body which has just been described as a "clon," and the term has been applied to the essentially similar structure in the Viorna Section of Clematis (Erickson, 1945). It should be borne in mind that in butterflyweeds, as in other similar plants, the communities of clustered stems have no greater degree of individuality than have the separate twigs of a tree. They are connected organically to the same tap root, and are ramifications of a single embryonic plumule. In butterflyweeds there are no vegetatively reproducing stolons, rhizomes, gemmiferous roots, nor other special propagulae. It is conceivable that accidental or purposeful operation might result in the successful division of the crown into two or more parts, although I have not been successful in the attempt. But such division in nature, if it occurs at all, must be contrary to the habit of the species, since I have observed no instance amongst the several thousand living plants which I have examined.

It so happens that in certain other species of Asciepias, as in the common A. syriaca, adventitious buds upon special gemmiferous roots habitually succeed in multiplying single plants. These compose true clons such as those of Hemerocallis, Iris, Robinia, and other spontaneously vegetative-propagating plants. To call the plant of butterflyweed a clon in my opinion not only is misleading but destroys the contrast of the vegetative propagation of such a species as A. syriaca. It is difficult to imagine a plant which under some unusual circumstance might not become divided into two or more. If a term is allowed to become a quibble, its significance is lost.

The herbaceous stems of butterflyweed range approximately from one to three feet in height. They normally are unbranched save at the terminal region of inflorescence, although occasional axillary branches may be encountered most frequently as the traumatic result of early decapitation. It must be emphasized at this point that the herbaceous sterns are produced at one time at the beginning of each season, and are of essentially identical age. They are remarkably similar in height and rate of development, as well as in number and relative size of parts. These factors are of obvious advantage in the random collection of leaves for statistical analysis.

The stems of butterflyweed are determinate, ending in an umbelliform cyme of approximately one to two dozen pedicellate flowers. In most fully developed plants the terminal cyme is subtended by two or more leafy-bracted, scorpioid branches studded at the nodes with umbelliform cymules developing in acropetal succession. These branches obviously are the homologues of the branches of a dichasium. The determinate inflorescence character of A. tuberosa is an anomaly amongst the American species of Asclepias. It is an extremely fortunate one from the standpoint of these investigations, since it further facilitates the collection of leaves of nearly identical physiological age, which would be a precarious operation upon an indeterminate axis.

The leaves are simple, entire, and are irregularly alternate or spirally arranged. The number, shape, and size of leaves are extremely important characters in the distinction of the subspecies, and will be discussed in later paragraphs of this section. Obviously, the leaf variability is such that it forms the subject matter for these investigations.


The flowers of Asciepias are classical examples of entomophily and are equalled in complexity only by those of the orchids. In the present connection it will probably suffice to recall only those features immediately concerning pollination and the production of seed. In the center of a butterflyweed flower, as in other milkweeds, there arise five cornucopia-shaped bodies which are petalaceous, and are in fact often mistaken for the corolla. These are the hoods, the nectar-secreting bodies which are the goal of the insect visitors. The hoods actually are outgrowths of the staminal filaments, the smaller anthers of which they virtually conceal.

The anthers themselves are closely connivent in the form of a cylinder or truncated cone about the stigma. Each anther contains two pollen cavities. A remarkable feature of milkweed pollen is that it is borne within small, flat bags, or pollinia, the confining membrane being derived from the tapetum. Still more remarkable is the fact that the pollinia of adjacent anthers are joined together in pairs by means of a delicate yoke-apparatus (translator) surmounted by a padlock-shaped body known as the corpusculum.

The corpusculum bears upon its outer face a more or less conspicuous cleft. It is well known that pollination is initiated when a strong insect, such as a wasp, accidentally thrusts its barbed legs between the anthers while scrambling about the center of the flower in search of nectar. If a barb of the insect's leg wedges into the cleft of the corpusculum, a stout pull of the member usually succeeds in withdrawing the pair of pollinia from the anthers. It is a common sight to see wasps or bees flying about a blooming butterflyweed, their legs laden with pollinia.

Robertson (1892) has enumerated 15 species of Lepidoptera, Hymenoptera, and Diptera collected while bearing on their bodies pollinia of Asclepias tuberosa in the neighborhood of Carlinville, Illinois. Amongst these is Apis mellifera, the common honey bee, which is known to have a flight radius of one-half rarely to five miles. It is difficult to secure data concerning the radius of flight of the other possible pollinators, although the phenomenal migrations, some hundreds of miles, of certain Lepidoptera are well known.

I do not wish to over-emphasize the efficacy of the floral mechanism of Asciepias with regard to insect visits, since it does not appear to be very high. Certainly less than 1 per cent of the flowers normally set fruit, except in A. incarnata, the swamp milkweed, in which sets may amount to 25 per cent. An additional factor to recall, in connection with insects as pollinators of Asclepias, is that the pollinia appear to be highly irritating to the carrier. On several occasions I have trapped wasps of the genus Chlorion in transparent bags, when they invariably appear to be more anxious to divest themselves of the pollinia than to escape.

The stigma of the milkweed flower is surrounded by the connivent anthers and is a rather complex structure. The receptive surface is not at the flat top, but actually is divided into five concave surfaces which alternate with the anthers and are closely protected by them. In order that a stigmatic surface be pollinated, it is necessary to introduce a pollinium between the flanged, cartilaginous, marginal wings of the anthers, an extremely delicate and nerve-wracking operation for a human experimenter. That the feat is accomplished at all by the chance movements of an insect seems nothing short of marvellous, and that so few fruits usually are observed upon a single plant is quite understandable.

Size and shape of pollinia, corpuscula, anther wings, and stigmatic chambers vary greatly amongst the species of Asclepias. Hense it is not surprising that interspecific hybridization within the genus is very infrequent. After over a decade spent in studying it, I doubt whether I have observed many more than a dozen instances of putative hybrids amongst the approximately 80 species.

The only record of a successful experimental cross between distinct species is that of A. speciosa x syriaca, first performed by Stevens (1945). In crosses involving other species, Moore (1946a) occasionally observed preliminary swelling of the ovary, followed by abortion. This he interprets as due to somatoplastic sterility. Although successful self-pollinations have been reported by several authors for certain species of Asclepias (notably Stevens, 1945), similar experiments by Moore (1946b) were unsuccessful. My friend F. K. Sparrow has told me that his extensive pollinations with A. syriaca reveal clonal self-sterility. My own limited experiments at self- and cross-pollinations involving A. tuberosa have been notably futile. I suspect that special mechanical factors may account for the difficulty in milkweed pollinations, such as the degree of desiccation of the tapetal membrane, which must split to allow the emission of the pollen tubes.

Fig. I . Somatic metaphases from young leaves of Asclepias tuberosa in different parts of its distribution: 1, Stillwater, Okla.; 2, Glendale, Mo.; 3, Westport, Conn.; 4, Snail Lake, Minn.—All figures X 1500.

The fruit of butterflyweed consists of solitary, or infrequently paired, narrow, fusiform follicles up to 15 cm. in length. Upon dehiscence as many as 100 compressed, oval seeds approximately 0.4 cm. long are released, each provided with the micropylar parachute of silky hairs so diligently studied and collected as a substitute for kapok during the recent war. The silky parachute, technically called the coma, is extremely bouyant, and is doubtless capable of conveying the attached seeds for long distances, even approximate estimates of which, however, are unavailable.

I have found during the course of progeny tests that viability of the seeds is fairly high as a rule, but that germination is very irregular, proceeding in some samples for well over a month. Although I am not yet ready to publish conclusions upon these tests, they indicate at the present writing that the various leaf modifications encountered in different parts of the species' distribution have a genetic basis and are maintained within sufficient limits under cultivation in my test plots.

Reproductive mechanism of Asclepias tuberosa: 1, flower; 2, gynostegium with hoods removed, showing connivent anthers with one pollinium protruding; 3, two anthers as seen from within, showing pollinia; 4, carpets with stigma head, showing two stigmatic surfaces; 5, Chlorion sp. bearing pollinia on feet; 6, pollinia enlarged, attached to barb of insect's foot; 7, follicles with comose seeds.


Chromosome counts for Asclepias tuberosa made by various workers, notably Moore (1946), agree in the figure n = 11. This is also the base number for all other Asclepiadaceae investigated. Polyploidy has not been reported in Asclepias, although tetraploids occur in certain other genera, particularly in the Orient. Somatic metaphases from young leaves of A. tuberosa in various parts of its range are reproduced in fig. 1. The chromosomes are small (about 2 μ long) and relatively uniform, and are poor subjects for configuration or structural studies.


In its geographical distribution from southern peninsular Florida to northern Sonora and from the Ottawa River to the Black Hills of South Dakota, Asclepias tuberosa demonstrates its wide climatic adaptability (Map 1) . It is clear from the map, as well as substantiated by my field observations, that the species is best adjusted to its environment in the mesothermal and southern microthermal climatic regions of North America. Where it is found in the western steppe climates it is probably as a scattered relic of former mesophytic times.

Something of the climatic preferences of butterflyweed can be deduced from a comparison of the distribution map of the species with standard climatic charts of North America. At least in general outline, it appears that the July mean temperature is critical in relation to density of population of the plants, a normal mean surface temperature of 68° to 86° F. indicating roughly the optimal limits. Precipitation appears to be more critical than temperature, however, suggesting general requirements of an annual mean of over 20 inches. It is very striking, when traveling eastward across Kansas in midsummer, to find the butterflyweed suddenly emerge from more sheltered positions as a common roadside plant on the outskirts of Topeka, near the boundary of the tall-grass prairies and the short-grass plains.

In the opinion of some, Asclepias tuberosa should be considered as a prairie type, or even as an emigrant from the dry plains or deserts of northern Mexico. To my mind it accords more closely with the facts of distribution to regard it as indigenous to the glades and open woodlands of the southern hardwood forests, from which it has spread to the southeastern longleaf, loblolly, and slash pine forests, and to the southwestern pinyon-juniper-ycllow pine woodlands. When one considers that approximately the northeastern third of the species' present distribution has been available for plant colonization only since the Pleistocene, it is clear that establishment of populations is taking place to the northeast much more rapidly than to the southwest.

Butterflyweed is found at elevations from near sea-level to about 6000 feet altitude. In the western states progressive desiccation of the plains appears virtually upon the point of eliminating the species except upon the well-watered highlands. In the plains the plant must seek the protection of ravines and canyons, or larger neighboring plants.

The wide distribution of A. tuberosa bespeaks its tolerance for a broad range of edaphic conditions. Horticulturists are in the habit of prescribing for it a sandy soil, upon which it undoubtedly flourishes, but scarcely more so than upon the exceptionally tight clays known as "crawfish soil." Although I have made no attempt to determine its pH preferences, they probably are circumneutral since I have found fine colonies of plants growing impartially upon dolomitic limestone, argillaceous shale, and granitic detritis. An unusually large colony was found on an alkaline flat in western Texas, but the plants appeared depauperate. Good soil drainage appears essential for optimal growth, and a "poor" soil is generally preferable to a "rich" one. I do not remember ever having found it growing on alluvium.

Butterflyweed is found occasionally as single plants, but more frequently in colonies of three or four to well over a hundred individuals. Distance between colonies varies notably with respect to local climatic and vegetational conditions. Roughly east of the 96th meridian the species is a common roadside plant, as has been discussed before. Through eastern Kansas and Missouri the colonies may be encountered at intervals averaging about ten miles apart.

Through the prairies of south-central Illinois, on the other hand, I was able to find only three colonies along the route of about 150 miles between St. Louis and the Wabash River. From southern Indiana to West Virginia the colonies become somewhat more frequent, and reach their greatest frequency, somewhat more than in Missouri, from West Virginia to the coast of Virginia. The brief account of this transect summarizes observations made during a collecting trip in the summer of 1946. Statistical details will be presented in a subsequent chapter.

Roughly west of the 96th meridian butterflyweed is scarcely ever encountered along roadsides through the Great Plains. The plants are found, if at all, only along the infrequent water courses, particularly at the heads of ravines. The size of colonies is considerably smaller than is customary in the East, and the distances between them is far greater. It is only in the pinyon-juniper-yellow pine highlands of the southwestern states that butterflyweed again becomes a fairly frequent plant.

I believe that colonies usually develop from seedlings of a single parent plant. This is indicated not only by their considerable degree of isolation, but by the centering of leaf variation amongst individual plants about more or less distinctive colonial means for the various characters measured.

Map I. Distribution of Asclepias tuberosa: each symbol represents a single county record. Large dots: A. t. interior; small dots: A. t. tuberosa; hollow circles: putative hybrids A. t. tuberosa x interior; half-circles: A. t. Rolfsii.


Ordinary herbarium methods disclosed at the outset of these investigations the presence of three subspecies of Asclepias tuberosa (Woodson, 1944): A. t. tuberosa, with leaves typically obovate to linear-oblanceolate, the base usually cuneate or rounded; A. t. interior, with leaves typically ovate to ovate-lanceolate, usually with cordate or truncate base; and A. t. Rolfsii, with leaves essentially as in ssp. tuberosa but predominantly with more or less conspicuous hastate or cordate dilation toward the base and with the margins more or less crisped. Map I shows the known distribution of the three subspecies and indicates the probability that the centers of modern dispersal, if not of actual origin, may be regarded as the Paleozoic land masses Appalachia and Ozarkia, and the early Mezozoic "Orange Island," now north-central Florida, respectively.

It is difficult to indicate with such a map the variation and intergradation of taxonomie units, since in this case only three types of symbol are employed. In addition to the symbols for the separate subspecies, however, a fourth, the hollow circle, has been introduced to indicate intergradations of A. t. tuberosa and A. t. interior. A fifth type of symbol might further be used to show intergradation of A. t. Rolfsii, particularly with ssp. tuberosa, since as it stands the map rather implies that Rolfsii is genetically more isolated than the other two subspecies.

As a matter of fact, such is far from being true. The distribution of hollow circles suggests that in southern Alabama and southern Georgia one might expect to find intergradations of all three subspecies. This actually appears to be the case, and the practical limits of such a map stand revealed. A fifth symbol is not used for intergradations of Rolfsii simply because I cannot distinguish the separate roles of the three subspecies satisfactorily.

Almost the first glance at Map I will show that although ssp. tuberosa, indicated by small dots, is distributed roughly from the western Appalachian foreland to the coast, with interior, indicated by large dots, to the west and north, the hollow circles, which indicate subspecific intergrades, extend from the commissure of the subspecies completely through the distribution of ssp. tuberosa. It is clear even from routine examination of herbarium specimens that tuberosa, situated unstrategically between interior and the sea, is in the process of genetic dissolution.

This situation appeared so interesting that a biometric study of natural and artificial populations of A. tuberosa was begun early in 1942. Begun as a side-line to my more orthodox systematic studies, my hobby soon grew to occupy the majority of my research. So many additional topics of interest arise as time passes, and so many new lines of attack suggest themselves, that the study might possibly be continued as long, if scarcely so profitably, as the classic investigations of Sumner on Peronyseus.


The disadvantages of the type of distribution map which has just been presented in the previous chapter are the simple consequence of the use of a discontinuous scale with too few intervals. Nevertheless I do not wish to minimize its use. In dealing with a genus of many species, such as Asclepias, it is ordinarily the only type practicable. It at least states the known range of one or more taxonomic units and perhaps suggests the region of any intergradation. To an imaginative mind one of its virtues may be that it asks more questions than it answers.

When a continuous scale is available, however, measurements of a large series of specimens may allow the accumulation of equally spaced means and their accompanying measures of variability, and the result is a "phenocontour map" such as that advocated by Huxley (1938). As yet few phenocontour maps have been published. Possibly the most familiar examples are those of Alpatov (1929) for Apis mellifera, the common honey bee, in European Russia. These, in my opinion, suffer chiefly because of the relatively few and irregularly distributed localities into which the many samples fall. A better instance is provided by Pearson's (1938) geographic study of melanism in the Tasmanian bush opossum, Trichosurus vulpecula fulginosus, in which definite contour lines ("isophenes") were obtained. In a class by itself is the world chart of human blood groups presented by Boyd (1939).

From a phenocontour map benefits may accrue from several directions. The biogeographer may plot with a degree of mathematical precision the migrations and environmental adjustments of which he now speaks in more general terms. The cytogeneticist may be given wholesale data of population dynamics upon which to apply a gamut of attractive theory much of which still requires exemplification. Last, but not least, opportunity finally is given the customarily inarticulate systematist to prove the detail of his observations to a disbelieving world. The inexorable accumulation of specimens to catalogue for the benefit of others may allow but one such opportunity, and it should be taken.


There can be little doubt that systematic botany has contributed far less to recent advances in the study of evolution than has systematic zoology, and one reason for this has been its neglect of modern statistical methods. Yet for ready collection of data, ease of manipulation, and wealth of museum material, plants in general are much more favorable subjects for study than are animals. No one has appreciated these advantages more than did Charles Darwin, who bequeathed a part of his estate for the founding of the 'Index Kewensis,' the herbarium taxonomist's most indispensable single tool.

Herbarium specimens are not a perfect substitute for living plants, but they offer incalculable advantages for the interpretation of field studies. Not all plant materials are adequately preserved by the usual herbarium methods of pressing and drying, but an astonishing percentage is. In the herbarium of the Missouri Botanical Garden is a collection of several hundred dried plants assembled by one Georg Rudolph Boehmer as material for his 'Florae Lipsiae Indigena,' published in 1750. The appearance of some of these plants is almost as though they had been pressed and dried but a few months ago. All are perfectly recognizable, and we have in them a detailed record of the distribution of plants around Leipsic two centuries ago.

In the early days of botany it was customary to have represented in the herbarium only one or two specimens of each species. Nowadays any of the several major herbaria of the world may include a thousand specimens of a single widespread species from all parts of its range, gathered in all stages of its growth at all times of year by faithful collectors, living and dead, for at least a century. When several such collections of a group of plants are united for one's study, the very mass of it is most impressive. The accumulation of material so representative of variation in time and space obviously is beyond the powers of an individual. It is a unique evolutionary heritage.

A false impression widely current among non-taxonomists is to the effect that herbarium specimens usually are collected because of some abnormality which attracts the fancy of the collector. The accusation reveals such prejudice that one is baffled for an effective retort. Perhaps a denial that falls far short of revealing the sincerity of a plant collector but may impress the critical outsider is the fact that plant collections habitually are made in multiplicate sets bearing identical serial numbers for purposes of sale or exchange amongst the numerous botanical institutions of the world. It would be difficult indeed for even an unusually perverse individual to pursue his passion under such adverse circumstances. The chief danger in plant collecting actually is that of choosing too many "normal" specimens. The statistical errors from such likelihood, however, should be ineffective.

"Mass collections," which I prefer to call "local population samples," have been advocated recently by Anderson (1941) and others as an aid to the solution of certain systematic and cytogenetic problems. This method of sampling local variation surely is a very useful one, and a tool which I have used in part in my own work. Certain attendant disadvantages should be discussed, however.

It is known, for example, that the phenotypic responses to the fluctuations of climate may vary from year to year in a given place, as Lewis (1947) recently has shown with respect to Delphinium. Population statistics obtained from a given locality for a given year may not be compared safely with samples from other localities at another time, perhaps even during the same year. Employing only local population samples, the task of effectively covering the entire range of a single widespread species, in the case of Asclepias tuberosa about 1,500,000 square miles, assumes fantastic proportions.

The most reliable statistics concerning plant populations over a wide area must be made not during a single season but over a span of years, and the samples must be randomly selected and as widely distributed as only generations of differently tempered naturalists can accumulate them. It is possible to meet these requirements only by the use of herbarium collections. It is not a new convenience: plant taxonomists have been enjoying it since long before the birth of Linnaeus.

The advocate of "mass collections" may retort that even though herbarium samples may cover distribution in time and space more effectively, the samples are smaller at best than those specially made by his methods. The statistical fallacy of this argument is obvious. The reader should not infer that I am condemning the use of local population samples. I am merely attempting to point out what I consider to be their limitations and to defend my use of herbarium specimens. I have obtained quite interesting results through using both methods coordinately.

Perhaps this will be an appropriate place to caution firmly against the inconsiderate use of herbarium material for statistical work. Being an herbarium custodian myself I can anticipate the angry protests which will arise from my colleagues at the prospect of their precious charges being plucked, petal by petal, or for that matter, leaf by leaf, by increasing numbers of "biosystematists." We may not treat herbarium specimens as we would living plants having the power of regeneration of lost parts. Type or other authentic specimens must remain sacrosanct for the use of posterity. Only abundant parts of herbarium specimens should be sampled in studies such as these, and then only by an experienced student upon express permission of the proper authority.

Being an herbarium man, my first impulse in beginning my study of leaf variation in Asclepias tuberosa was to turn to the herbarium of the Missouri Botanical Garden where I am employed. There I found several hundred sheets of specimens representative of the entire range of the species. Nearly all the sheets I found to bear at least one entire stem of the plant. The leaves of each, habitually numerous, I found to be well preserved, being somewhat leathery in texture. Since they were so abundant, I discovered that at least some had escaped being glued to the paper and could be removed without appreciably damaging the specimen.

After experiment I adopted the procedure of selecting a "random" leaf from about the middle of a single flowering stem of each specimen, if it included more than one stem, and recording the locality (state and county for reasons which will develop) from whence it came. I soon found also that it is desirable to keep a record of the various collectors' numbers in order to avoid statistical bias from measurement of duplicated specimens so prevalent in large herbaria. This entails no unusual inconvenience, being a common monographie practice. The leaves were boiled in water, separately, until completely exhausted of air. Their outlines were then traced upon paper with a sharp 2-H lead drawing pencil, using an illuminated tracing table.

For tracing, I have found best adapted to my needs the large sheets of millimeter grid paper printed by Keuffel & Esser of New York. The 5- and 10-millimeter lines are specially accentuated on this paper, which facilitates both orientation of the tracings and subsequent measurement. The grid paper may be protected from the moistened leaf by placing between them a small piece of wax paper.

To some, I might appear to have been more scientific had I used sonic photographic means of transferring the leaf outlines. There are several advantages of the tracings, the first of which is the millimeter grid itself, special advantages of which will be indicated. A second advantage is that the tracings can be added to the large grid sheets consecutively as they accumulate, assigning a special sheet to each local population sample, or particular geographic division. In short, the tracings appeared to be more convenient and photographs or blueprints unnecessarily complicated and time-consuming. In measuring smaller objects, greater accuracy doubtless would be obtained by the latter methods. The degree of accuracy obtained through tracing will be discussed presently; I believe that it will be found sufficient for my needs.


It has been explained in previous paragraphs that the chief, if not the only, criteria distinguishing the three subspecies of A. tuberosa are found in differences of leaf shape. Size, as measured by median length and width, is of minor taxonomic importance except perhaps in providing abstract universe values. This is usually true because size, although it has a genetic basis, is more directly influenced by environment and age of organism than is shape.

It is easily seen in fig. 2, which consists of very small random samples of leaves, that leaves of ssp. tuberosa may be said to be of greatest average width and those of ssp. interior of greatest average length, while those of ssp. Rolfsii average least in both regards. But an experienced plant systematist probably would prefer to point out that the leaves of tuberosa tend to be broadest above the middle (obovate to oblanceolate) with rounded or tapered base, those of interior broadest below the middle (lanceolate to ovate-lanceolate), usually with 2-lobed (cordate) base, and those of Rolfsii more or less fiddle-shaped (pandurate) and with crisped margins.

Determined to find a suitable continuous scale with which to measure leaf shape in Asclepias tuberosa, I finally recognized that the differences in shape, at least those distinguishing ssp. tuberosa and ssp. interior, resolve themselves into relative differences in width at two points, at approximately one-quarter the median length from the apex and the same distance from the base, respectively. It was obvious that in tuberosa the greater width typically is at the upper quarter and in interior at the lower quarter. The intergrades usually are found to bear essentially oblong or elliptic leaves, their widths at the upper and lower quarters being approximately equal. For some time thereafter I measured leaf widths at exactly the upper and the lower quarters of median length, hoping that by the ratios I might be able to distinguish quantitatively the leaves of the two subspecies with respect to unity as represented by the oblong or elliptic leaves of intergrades. This activity ceased when I realized that ratios such as those I was employing are functions of length. Another disillusioning discovery was that both ratios and their reciprocals afford warped scales, and furthermore the warping of the two scales is unequal. I mention these points for the consideration of any who may contemplate using similar ratios in biometric studies.

Fig. 2. Representative leaf types of three subspecies of Asclepias tuberosa.

The methods which I finally adopted for measuring shape are illustrated in fig. 3. In the diagram to the left of the figure, AOB represents the frame by which leaf outlines are oriented at equal distances upon my large grid sheets. The base of the leaf blade, where it joins the petiole, is placed at O and the tip vertically above in the position designated as B. After tracing the outline about the frame AOB, it is a very easy matter, since 1-, 5-, and 10-mm, distances are indicated on the grid itself, to measure median length to the nearest millimeter as the distance OB, rounding to the nearest even figure. Median width, MM', is measured also to the nearest millimeter, at the point midway between 0 and B, rounding as before. It appears unnecessary to read these distances to fractions of a millimeter in the light of what we shall learn concerning the experimental error involved.

It will be recalled that leaf shape differences of the two subspecies are found not only in the relative width of the blade at the upper and lower quarter lengths but also in the fact that the blade predominantly is cuneate in A. t. tuberosa (fig. 3, center figure) and cordate in A. t. interior (fig. 3, right figure). To measure either character it is found desirable to draw a horizontal line at right angles to the median line OB at one quarter the distance of its length from the apex (XX') and base (YY'), respectively.

Fig. 3. Methods for measuring leaf shape in butterflyweeds.— Explanation in the text.

In order to measure the direction and extent of apical taper of the leaves two chords now are drawn, XY and X'Y'. Using a standard protractor the two angles XYY' and X'Y'Y are measured to the nearest degree, rounding to the nearest even figure, and their mean is entered as the statistic hereafter to be known as L A.

In fig. 3 it will be seen that measurements of L A are 94.5° and 85° (treated as 85.0° in computations) for A. t. tuberosa and A. t. interior respectively. By use of this type of measure, a plant taxonomist will recognize that a leaf of ovate type will always have an angular reading of less than 90°, a leaf of obovate type one of more than 90°, and a leaf exactly of oblong type a reading of exactly 900.

An angular measure to distinguish different types of leaf base in butterflyweed was obtained after it was recognized that in cordate leaves the tip of the basal lobe usually occurs at a point about midway between O and Y on the one side, and between O and Y' on the other. Consequently, I now drop two perpendiculars PZ and P'Z' at points on YY' midway between OB and the margin of the leaf as indicated in the diagrams to the left of fig. 3. The angles ZOB and Z'OB are now read by protractor as before, and the mean rendered as L B, the measure of the leaf base. In the diagrams to the center and right of fig. 3 it is seen that the example for the cuneate base of ssp. tuberosa has an L B value of 40° while the equivalent value for the cordate base of ssp. interior is 110°. A truncate base would have an L B of 90°. In computations these figures are recorded as though significant to one decimal.

It will occur to the reader that the values L A and L B actually refer to hypothetical leaf halves and thus are not real variables. Such is doubtless the case, but their other virtues will probably save them from being condemned by the practical statistician. In addition, my recording of the mean angles to one decimal in excess of significant digits is open to criticism although I believe it will be allowed since subsequent computations are limited to one decimal. In practice the process of averaging, besides halving the scale intervals, has the effect of halving the experimental error.

Although L A and L B have been very satisfactory as measures for shape in A. t. tuherosa and A. t. interior, I must confess that they are wholly inoperative with respect to A. t. Rolfsii. This has been a great disappointment, although to be anticipated since one could scarcely expect to differentiate three value ranges and all their intermediates upon a linear scale. This is an unfortunate consequence of the biological reality of Rolfsii. It might be possible to exclude Rolfsii from the absolute comparison of tuberosa and interior and yet to contrast it with both by means of an additional system of arbitrary scores, say for the crisped margin of the leaf. This would mix a discrete with four continuous scales, however, and the result probably would not be very helpful.

There can be little doubt that Rolfsii interbreeds with both tuberosa and interior upon the southeastern coastal plain, and it would be interesting to be able to measure the phenomenon accurately. It is possible to do so only indirectly according to my methods. In further studies we shall not forget the role that Rolfsii undoubtedly plays, particularly with regard to introgression with the other two subspecies, but we will be able to deal with it only through inference.


The methods just described at one time appeared so crude to me, compared to the technical refinements of others, that I spent some effort in obtaining estimates of the experimental error involved. Despite the risk of being tedious, I am reporting the results in some detail because I believe that exercises of this sort should be published more frequently. As a matter of fact, I know of only one other published estimate of experimental error of measurements used in population studies, that of Sumner (1927), in which the author was chiefly interested in variation of measurement amongst different observers.

In the summer of 1945 ten leaves of Asclepias tuberosa interior were collected along a roadside near Valley Park, St. Louis County, Missouri. They were placed in numbered envelopes and subsequently measured with respect to length, width,

L A and L B, while in the fresh condition. After measurement, each leaf was returned to its proper envelope and dried under pressure for a week. For ten consecutive days thereafter the leaves were drawn and measured, being returned to their proper envelopes each time, but the order of the envelopes changed by shuffling. After the tenth dry measurement the leaves were boiled separately and measured a last time. In this experiment extra precaution was taken against unconscious bias in that I personally traced the outlines on each occasion, while my friend Richard W. Holm performed the actual measurements independently.

Table I contrasts the measurements of the ten leaves in the fresh condition and after having been boiled after drying. Table II presents the results of measuring the ten leaves upon ten different occasions. The first is designed to show, as far as this case is concerned, how comparable statistics obtained from fresh leaves and those from soaked herbarium specimens may be. The second is a gage of accuracy in the tracing and measuring process itself, and also provides something of a guide to the statistics of Table 1.

(Means, standard deviations, and coefficients of variation; angles n degrees, length and width in millimeters)

    L A L B Length Width
  N s V s V s V s V
Fresh 10 85.0 0.5 0.6 120.0 1.6 1.6 77.3 1.4 1.8 19.7 0.5 2.5
Soaked 10 85.2 0.4 0.5 120.6 2.1 1.7 76.1 1.3 1.7 19.3 0.5 2.6

Since I have no similar exercises with which to compare, it is hard to evaluate the results recorded in Table II. I was surprised indeed, however, when the error appeared to be so small, in view of my rather crude instruments, ranging from 0.4º or 0.4 per cent for L A to only 1.5º or 1.3 per cent for L B. The metric error likewise appears to be small. In comparing Table I with the discussion of Table II it is seen to be immaterial, as far as the two angles are concerned, whether the leaves are measured fresh, dry, or soaked, since all three means for both lie within the experimental error estimated in Table II. In length and width, on the other hand, the three means lie at distances greater than that provided for by the estimate of error, particularly in width. This is disquieting, but there is no recourse since it would be impossible to measure all leaves while fresh. Statistics of length and width, however, will play a role subordinate to those for the two angles in the studies which follow, since they are not important systematically.

(Means, standard deviations, coefficients of variation, means of means, means of standard deviations, and means of coefficients of variation; angles in degrees, length and width in millimeters)

No. s V s V s V s V
1 85.2 0.2 0.2 118.9 1.2 1.0 76.0 0.0 0.0 20.0 0.0 0.0
2 85.2 0.4 0.5 117.2 2.0 1.7 75.2 0.4 0.5 18.0 0.0 0.0
3 85.1 0.3 0.4 119.1 1.9 1.6 75.9 0.4 0.5 18.6 0.5 2.7
4 85.3 0.3 0.4 121.5 1.4 1.2 75.4 0.5 0.7 19.0 0.0 0.0
5 85.4 0.4 0.5 119.6 2.7 2.2 75.6 0.5 0.7 18.7 0.5 12.7
6 85.2 0.6 0.7 114.0 1.2 1.0 75.2 0.4 0.5 19.0 0.0 10.0
7 85.5 0.4 0.5 117.2 1.1 0.9 74.0 0.0 0.0 18.1 0.3 1.7
8 85.1 0.2 0.2 120.6 1.5 1.1 77.1 0.3 0.4 19.1 0.3 1.6
9 85.1 0.5 0.6 115.9 1.6 1.4 75.3 0.5 0.7 18.1 0.3 1.3
10 85.1 0.3 0.4 121.8 1.0 0.8 72.6 0.8 1.1 18.0 0.0 0.0
85.2 0.4 0.4 118.4 1.5 1.3 75.0 0.4 0.5 18.7 0.2 1.0



Phenocontour mapping is such a recent biological technique that it may be worth while to combine the account of my own practice with some general comments. The subject may be divided into several considerations which impinge upon one another so closely that they form a sort of continuum. In beginning an investigation of this kind, the first thing to be done is to become familiar with the systematic morphology of the organism chosen for study. Without a clear understanding of the critical characters of the species, for example, much time may be spent measuring size which might be spent more profitably measuring shape. In plant subjects, recourse should be had to a large, well‑ordered, general herbarium where the problem in all likelihood can be viewed in perspective and plans made for the most promising direction of attack.

Having selected a problem and noting the most advantageous direction of attack, suitable biometric measures must be devised as the sine quo non of all that is to follow. A measure must be found which expresses numerically the phenomena judged as biologically most significant. Any given measure will only infrequently be found effective for more than the organism for which it was invented. My method of measuring leaf base in Asclepias tuberosa, for example, may be quite useless in measuring that of another species.

A good measure should be duplicable, sensitive to organic variation, and should provide an unwarped scale. These are rather complex attributes to discuss briefly. They discriminate, in my opinion, against various types of discontinuous scales encountered in arbitrary scoring. In some cases, as in presence‑or‑absence criteria, scoring is the only sensible procedure. In others, the varying characters may be so complex that scores at first would appear as the only recourse. But scores almost inevitably are the product of the personal equation and should be used only when standard scales, such as the linear and the angular, are unavailing. The statistical advantages of fixed continuous scales are expressed most succinctly by Miss Walker (1943): "In order to know how much of a trait an individual has or to say that one thing is twice another, it is necessary not only to have equality of units but also to establish a zero point. Only when these two conditions are met can scores properly be spoken of as measures."

The area chosen for mapping preferably should include the entire range of the species or other taxonomic unit under investigation. This sometimes will be very large and impose considerable handicap in the gathering of data. But as a general rule the biological interest will be proportional to the area because of the relative number of factors allowed to operate. When I commenced this study of butterflyweed several years ago, I seriously considered following a suggestion of Huxley and confining my efforts to a single profile across the distribution of the species. Luckily my taxonomic training insisted that the distribution be treated as a whole; several unsuspected topics of interest emerged as a result.

Equal to the importance of adequate measures is that of adequate sampling. The prime requisite of sampling is that it be random. In biometric work of this kind, one cannot use the word "random" in quite the same sense in which it is employed in ordinary statistics; one cannot make use, for example, of the published lists of random numbers commonly employed in sampling. It is necessary to avoid the selection of cases which exhibit injury or manifest growth abnormality. It is necessary also to select cases at equivalent stages of development; therefore I have selected leaves from about the middle of a flowering stem rather than leaves at a given node from the top or bottom of the stem, for some stems produce a larger number of nodes during the course of their development than do others. Above all, one must not allow himself to select what he chooses to call "typical" eases in the hope of deriving therefrom the benefits of random sampling.

It does not seem quite possible to deal with questions of bias here in the ordinary way. In my own studies I think of bias as being intellectual, accidental, or biological. The intellectual bias is understood easily as the more or less subconscious desire to vindicate a predisposition. Perhaps its best antidote is to remember that truth may be stranger than fiction. Accidental bias may be occasioned by the paucity of specimens available for study in a given population. If herbarium specimens are in use it may be occasioned by duplicated specimens frequently encountered. Protection is taken against this by keeping a list of collectors' numbers as in ordinary monographic work. A variety of other sources of accidental bias come to mind.

Biological bias is a phenomenon which is less easy for a mathematical statistician to anticipate. In plants, if a species forms true clons it may be difficult if not impossible to tell whether one actually is sampling a number of genetic individuals or offshoots from a single plant. Fluctuations of climate are known to have a pronounced effect upon phenotypic expression (Lewis, 1947), and a sampling made during any given season or year may be biased as a result. Sampling made for convenience along roadsides or in occupied areas may present a very special bias (Wiegand, 1935). On first consideration it might be thought possible to escape physiological bias if sampling of an organism were made at random stages of its seasonal growth. But if any sample is allowed to consist chiefly of cases collected during a given stage of development, it may be biased with respect to others made during another stage. I have limited my sampling of butterflyweed to plants in full anthesis.

The number of samples and number of cases included is secondary in importance to the degree of randomness obtained. However, it may be worth while to emphasize that an adequate sampling is dependent more upon the number and randomness of samples than upon the number of included cases. Of course I do not overlook the fact that reliability of means and their derived statistical measures of variability increases as a rule with sample size; but size alone is not an indication of randomness and hence of reliability. Adequacy of sample size is determined by the unique degree of variability of each organism and can be determined in each case only after special observation.

Adequate sampling of the vast distribution of such a species as Asclepias tuberosa, an area of approximately 1,500,000 square miles, is clearly beyond the power of a single individual since we require randomness of climate, time, and environment. In an earlier section of this paper I have explained how herbarium collections would appear to satisfy these conditions. The argument may be advanced, however, that the relatively small numbers of specimens available in herbaria is insufficient for an adequate sampling distribution. Superficially it appears small indeed. Its adequacy with regard to butterflyweed may be judged by fig. 7 of this paper, in which statistics of two sets of samples are compared: one from the herbarium, consisting of 117 cases distributed along an approximately 1200-mile profile from Topeka, Kansas, to Norfolk, Virginia, and the other of 994 cases collected personally by myself and two friends in June, 1946, along roadsides between those two cities. The close correspondence and consistency of the two samplings are striking.

If I may extend my comments on sampling a bit further, I should like to call attention again to the area inhabited by A. tuberosa: approximately 1,500,000 square miles. First impulse might be to obtain statistics from whatever source and to combine them for the supposed benefits of larger samples. I am obliged to confess that for this vast area I have been able to collect and measure only approximately 12,000 cases in the time at my disposal, or about 1 per 115 square miles. At first glance this appears inadequate indeed, and it minimizes the true situation since the cases could not, for practical reasons, be distributed uniformly. Actually my samples fall into three rough categories: cases obtained from herbarium specimens, those collected along roadsides, and those obtained in hit-or-miss fashion throughout the whole species distribution, largely through the kindness of interested friends.

Cases obtained from these three sources surely cannot be combined, since they have been accumulated under different conditions, and their discrepant numbers would constitute a serious bias. Consequently I have kept them separate although using all for comparison according to the special values accrued from each. At the risk of over-emphasis, I should like to repeat that of these three categories of samples, I consider that obtained from herbarium material by far the most representative biologically although they are also the smallest numerically, numbering only about 3,000 cases, or somewhat less than 1 per 470 square miles of the specific distribution. As shocking as this ratio will appear, I believe the derived statistics, on the whole, to be biologically reliable, and I have used them in constructing my phenocontour maps to the exclusion of other data.

The projection of data upon a phenocontour map is a rather complex matter which depends upon such factors as amount of available statistics, size and character of the area involved, and nature of the information which it is desired to convey. In his study of pelage melanism in the Tasmanian bush opposum, Trichosurus vulpecula fuliginosus, Pearson (1938) employed relative percentages two class scores, black and gray, although he mentions unmeasured variation in both. By using commercial pelt records of approximately 105,000 cases distributed amongst 48 more or less equally spaced stations, a ratio of about 5 cases per square mile, he was able to plot a series of four contours ("isophenes" of Huxley) approximately separating areas including 0-25 per cent, 25-50 per cent, 50-75 per cent, and 75-100 per cent of gray pelts. His conclusions are chiefly historical.

Few biologists will be able to equal the volume of Pearson's data. To be as representative of distribution for Asclepias tuberosa, my records would have to embrace over 7,000,000 cases, instead of the approximately 3,000 which I have! Another advantage of Pearson's data is the distribution of cases amongst 48 rather equally spaced stations.

Readers familiar with the composition of a general herbarium already are aware that the geographical distribution of exsiccatae, even in the United States, is far from uniform. Greatest concentrations of specimens occur as a rule about well-established cities where botanists long since have resided. Next come states which have undergone systematic botanical surveys, and there is a gratifying number of these. Thirdly, there are regions of peculiar scenic or biological interests, such as our national parks, which attract appreciable numbers of plant collectors. But we cannot disregard areas, sometimes of considerable extent, where a lamentable hiatus of herbarium records is encountered. There is no fixed pattern to this mosaic, and it presents the major obstacle in phenocontour mapping from herbarium collections.

The projection of data upon a phenocontour map presumably should require the imposition of equidistant statistics from equal areas. I have accomplished this by dividing the species distribution into quadrats of equal areas for which I have combined the data secured from the various localities included within each. This, of course, creates a system of artificial (in contrast to natural) populations from which the desired statistics are computed.

The quadrat area chosen clearly depends upon the geographic plasticity of the species and the nature of the information desired. If the species is very responsive to altitude or ecology, the size of the quadrat will need to be much smaller than if the organism is not so sensitive. This may be a very serious obstacle in mapping a large area. Fortunately, Asclepias tuberosa appears to be rather indifferent in these respects, and the size of the quadrat depends chiefly upon the necessity of obtaining artificial populations equally distributed and yet of sufficient numbers for statistical analysis. This amounts to a certain guise of "gerrymandering," but is legitimate since the same quadrat area is employed throughout.

In this study of butterflyweed I have manipulated quadrat area to the end of obtaining populations of at least five cases in critical but poorly collected regions. The quadrats in this instance are approximately 120 miles square, and there are 136 within the range of A. t. tuberosa and A. t. interior—many fewer than I would wish. Even with these large areas, it will be seen that certain of them have failed to yield as many as five cases. After recording the quadrat data, isophenes may be drawn, if desired or possible, either connecting equal statistics or according to arbitrary ranges, as practiced by Pearson.

The nature of statistics projected upon the map will vary with individual problems and with the inclination of investigators. If scores are used, Pearson's system, already explained, would appear admirable. If a continuous scale has been employed in measurement, it will be natural to compute the mean; and from it may be derived any of the familiar measures of dispersion such as the standard deviation and the coefficient of variation. These may be entered on the map together with the mean. A measure of variability frequently will be necessary in order to interpret the geographical distribution of means.

Of course there is a vast number of statistical formulae which may be used for the analysis of biological measurement, and if one has a taste for mathematics the possibilities are endless. In my own study, after some dalliance, I have limited myself, as a rule, to the simple calculation of means, standard errors, standard deviations, and coefficients of variation, the second and fourth largely for the sake of convention. An outstanding example of another point of view is afforded by Czeczottowa's (1933) remarkably painstaking study of variation in beech leaves, to which Dr. M. K. Elias kindly has called my attention.

In the phenocontour maps which follow, quadrats containing five or more cases are indicated with the mean in large bold face type and the associated standard deviation in large italics. Means of quadrats containing less than five cases are printed in small Roman type. The standard deviation is used instead of the coefficient of variation because there appears to be no need for percentage comparison; also the former adapts itself more readily to my procedure, and the latter appears too sensitive to the relative magnitudes of the means, in addition to other disadvantages (cf. Kesteven, 1946).



Before turning to the phenocontour maps, it may be well to consider very hastily certain details of the paleogeography of eastern North America which will have a bearing on our interpretations of the population dynamics of Asclepias tuberosa. The discussion is illustrated by Map 11.

It is generally recognized that many of the principal families of Flowering Plants were established by the close of the Mesozoic era, possibly before the Lower Cretaceous. Although I know of no indubitable fossil remains of Asclepias, numerous records of Late Cretaceous and Mesozoic imprints, such as the form genus Apocynophyllum, are known which may well represent, at least in part, ancestors of our modern milkweeds, if not records of extant species. At any rate, present distributions of many species of Asclepias correspond so closely to what is known of Cretaceous geography that I feel we may hypothesize rather safely much the same speciation in those times as that with which we are familiar at present (cf. Woodson, 1947).

The Cretaceous has been called "the age of greatest submergence of the continents and the most extensive epeiric seas the Earth has known (Schuchert & Dunbar, 1933)." The complex submergences and resulting isolation of floras probably were of the utmost importance to the meteoric evolutionary diversification of Angiosperms during this time, and are reflected in present speciation.

Late Cretaceous saw the climax of the dissection of North America with the submergence of the Rocky Mountain trough from the Caribbean to the Arctic. This was accompanied by submergence of the southeastern coastal plain, particularly north of the Gulf of Mexico, a deep embayment extending up the present Mississippi valley as far as southern Illinois. This embayment separated the ancient Appalachian and Ozark plateaus, including the extension of the latter to the Llano uplift in central Texas, and is recalled in our present vegetation by numerous vicarious species and subspecies. Amongst these may be mentioned Asclepias t. tuberosa and A. t. interior, respectively.

Map II. Ozarkia, Appalachia, and Orange Island, with reference to the Cretaceous and early Mesozoic seas, and Pleistocene glaciation. Explanation in the text.

Of equal interest in this connection is the probably fluctuating emergence of low islands in what is now northern Florida, culminating in the early Cenozoic in the appearance of the more sizable "Orange Island," separated from the Georgian coast by the Suwanee strait (Schuchert, 1935). On these islands possibly developed many or most of the Floridian endemics of Appalachian affinity, including A. t. Rolfsii and numerous other milkweeds.

Withdrawal of the Cretaceous seas during the early Cenozoic effected the reunion of the Appalachian and Ozarkian lands in Oligocene, and of emergent Orange Island to the continent in Pliocene. By Pliocene, therefore, there apparently were no geographic barriers to reunion of the disjunct distributions of the three subspecies of Asclepias tuberosa, if indeed they existed at that time.

Pleistocene brought the continental ice sheets approximately to the present valleys of the Missouri and Ohio rivers, virtually to the head of the old Mississippi embayment of Cretaceous and early Cenozoic times. This undoubtedly provided a partial secondary separation of the putative ranges of A. t. tuberosa and A. t. interior. It is well known that four glacial periods occurred during Pleistocene, interspersed by warm interglacials longer, indeed, than the present day is removed from the last withdrawal of the ice. The time since the retreat of the Wisconsin ice sheet usually is reckoned at about 25,000 years.