QUADRATS

199. Uses. In its simplest form, the quadrat, as the name implies, is merely a square area of varying size marked off in a formation for the purpose of obtaining accurate information as to the number and grouping of the plants present. As indicated above, it was first used for determining the abundance of the various species of a formation. This made it possible to ascertain the relative rank of the species of layers and formations, and enabled one for the first time to gain some idea of the minute structure of a bit of vegetation. The results were at once applied to the task of establishing a numerical basis for abundance, and of working out a new system of abundance to correspond. The quadrat method was also used to determine the character of seasonal aspects, and to yield a knowledge of the exact differences in diverse areas of the same formation. Incidentally, the determinations of abundance were made the basis of an actual census of certain alpine formations. This, while it was extremely interesting to find that a square mile of alpine meadow contained approximately 1,500,000,000 plants, was confessedly destitute of ecological value. The most important applications of the quadrat idea were made by Clements[[21]] in the chart, the permanent and the denuded quadrats. The development of these was due to the fact that zones or formations permit of comparison upon floristic as well as physical grounds, and that a detailed record of their structure is necessary for this purpose. Similar comparisons are necessary for the consocies, zones, and patches of the same formation, and the quadrat becomes an indispensable means for studying alternation and zonation. For the investigation of invasion year by year, and especially for succession, the method of permanent quadrats is imperative, and the denuded quadrat an invaluable aid. Changes, which would otherwise be incompletely observed and imperfectly recorded, are followed in the minutest detail and recorded with perfect accuracy.

200. Possible objections. The use of the quadrat has led to the criticism that it is needlessly detailed and thorough, and that, after all, the space covered is but a minute part of the entire formation. The first objection is one that has also been urged against the use of instruments of precision in the habitat. It is always brought forward by those who have not used instruments, and as witnesses they are of necessity incompetent. No one who is familiar with the instrument or the quadrat by actual practice has felt that the methods based upon them were too thorough. In no case has the writer ever listed or mapped a quadrat without discovering some new fact or relation, or clearing up an old question. It can not be denied that quadrat methods require both time and patience, but this is true of any kind of research work that is at all worth while. Every ecologist, moreover, that has the interests of his field at heart and deprecates the present slipshod work, will appreciate the necessity of methods which seem like drudgery to the mere dabbler.

The second objection, that the quadrat is at best but a small bit of the area under investigation, seems at first to be a valid one. It can not be gainsaid that the actual space studied is insignificant as compared with the whole formation; still, it must be obvious that even a single quadrat can add at least some facts of value, which can never be obtained by the best of general methods. Furthermore, if the formation be an actual and not an imaginary one, a single quadrat will be in some measure representative. In the more homogeneous ones, it will have much the same value that a type specimen bears to the species established upon it. In formations which are less uniform, its value is correspondingly reduced, so that in formations which show marked zones, consocies, or patches, it becomes necessary to locate a quadrat in each. In the matter of representation alone, the graphic method of the quadrat map with its close-focus detail photograph, is far superior to anything that can be obtained by the ordinary description and photograph. Finally, the scientific study and recording of succession, and particularly of competition, is an impossibility without the aid of the permanent and denuded quadrat. The stoutest champion of the practice of walking through a formation, and jotting down impressions, can not avoid their use if he would attack these problems, and, once familiar with the quadrat, his objections to the drudgery of thoroughness will soon vanish.

Kinds of Quadrats and Their Use

201. Size and kinds. The unit size of quadrat is the meter, and when the term is used without qualification, it refers to the meter quadrat. To make them strictly comparable, and exactly divisible, unit quadrats are always grouped in squares; thus a major quadrat is a square of four units, and a perquadrat one of sixteen units, or four meters square. Quadrats of greater size are necessary in woodland and forest, where the rule, however, is that the woody plants alone are recorded for the whole quadrat, the herbaceous growth being listed or mapped for but one or two representative units. For special purposes, quadrats of 3, 5, 6, etc., meters may be used, but they are much less convenient. Quadrats are further distinguished with respect to their use. A list quadrat is one in which the plants are merely listed and the number of individuals of each species indicated. Chart quadrats are those in which the area concerned is accurately mapped on plotting paper. Both list and chart quadrats are rendered permanent by careful labeling, so that their changes can be followed from year to year. The greater value of the chart causes practically all permanent quadrats to be of this type, and for the same reason only permanent chart quadrats are converted into denuded ones.

202. Tapes and stakes. The lines for marking out quadrats are made of strong white tape, ⅝ inches wide. This is doubled and sewed firmly at both edges. Under moderate stretching, the tape is carefully marked off into decimeters, and eyelets 5 mm. in diameter are set in at each end and at the marks. This can readily be done by any shoemaker at slight expense. The usual lengths are one and two meters, as these are most frequently used, and they can also be easily combined to make larger quadrats. The tapes are slightly longer than one meter in order that the distance between the end eyelets may be exact. The tapes of the larger forest quadrats should be divided into lengths of one meter, as these permit ready plotting and also make it possible to interpolate a meter quadrat for the study of the undergrowth at any point. The intervals of the tape are numbered from left to right, as conspicuously and clearly as possible. For this a waterproof ink or paint is very desirable. For holding the tapes in position, hatpins, nails, and meat-skewers have been used with more or less satisfaction. The ideal stake, however, is one which holds the tape close to the ground, and can be readily moved. It is merely a stout wire, 3 mm. in diameter and 8 inches long, looped at the top, sharpened at the tip, and with a small ring of solder 3 inches from the tip.

203. Locating quadrats. In staking a quadrat, the end tapes are invariably placed so that the numbers read from left to right, and the side tapes so that they read down. In mapping, a fifth tape is stretched parallel to the top, and as each decimeter strip is marked, the outer tape is shifted to delimit the new strip. Indeed, the side tapes can be placed alone, and the plotting tapes moved down one at a time as the mapping proceeds, but it is usually more satisfactory to locate the quadrat exactly and to square it first, a task most easily done by enclosing the whole quadrat, and then using a fifth tape. In the case of list quadrats in open vegetation, the measuring strip is unnecessary, but as a rule it facilitates counting, as well as mapping.

Fig. 50. Mapping a major quadrat on Mount Garfield at 3,600 m.

The List Quadrat

204. Description. This, as the simplest form of quadrat, is employed primarily to ascertain the abundance of species in a formation or during a particular aspect of it. Since this can be obtained readily from the chart, the list quadrat has fallen more and more into disuse, except where it is desired to determine abundance alone, or to aid in deciding whether a chart is really representative. The size depends almost wholly upon the nature of the vegetation. When the number of trees is to be determined, a quadrat of 10 or 50 meters is necessary. In ordinary herbaceous formations, the usual size is 2 meters, while the meter quadrat is used when the plants are especially small and crowded, as in alpine meadows. The location of the quadrat is based upon the general rule, but since its especial task is the determination of the greatest variable in vegetation, viz., number, it is necessary to use more quadrats, and to place them in areas which show the greatest differences in the mixture of species. For example, it was found that a half dozen list quadrats, when carefully located in the prairie formation, gave results almost identical with those obtainable from a larger number. With a little experience, the various degrees of mixture can be picked out superficially, and the corresponding number of quadrats established. If a single list quadrat is to be made for a formation or station, such a time should be selected as will make it possible to cover the greatest number of plants. Fortunately, this usually falls near the middle of the summer, when the remains of spring plants are still in evidence, and the autumn ones are sufficiently developed to be recognizable. In taking the census of different aspects, the quadrat should be made as near the middle of the period as is possible.

205. Manner of use. In listing a quadrat, i. e., counting the individuals of each species, the plan followed is to list the smaller, less conspicuous plants first, since they are apt to be tramped down. As a rule, the outside tapes and the taller species afford sufficient landmarks. When this is not the case, the measure tape is used, and the individuals of all species are checked as they are found, while in the first method one species, rarely two, is taken at a time. In cases of peculiar difficulty, it may be permissible to pull or break plants as they are counted, but ordinarily this can and should be avoided. Clusters, and bunches of stems from the same root are counted as single plants, and the number of stems indicated by an exponent. In the case of bunch grasses, each bunch counts as one plant.

206. Table of abundance. The species are arranged in the final list in the order of their numerical importance, and are divided into groups which correspond to the different degrees of abundance. The latter are arranged in two series, based upon the fact that association is by groups or by individuals. The table of abundance, based upon a 2–meter quadrat rather than upon the 5–meter one, by means of which the earlier results were obtained, is as follows:

Social exclusive, no other species of vascular plants present
social inclusive, above 100
gr1 gregarious1 100–50 copious1 cop1
gr2 gregarious2 50–25 copious2 cop2
gr3 gregarious3 25–10 copious3 cop3
sg subgregarious 10–5 subcopious sc
vg vixgregarious 5–1 sparse sp

It is obvious that the above outline is faulty inasmuch as it takes no account of the height and width of the individuals. This is a serious defect, and it constitutes one of the many reasons why the list quadrat should be replaced by the chart quadrat. The prairie formation affords an unusually striking illustration of this. A single quadrat may be filled by ten plants of Psoralea floribunda, and at the same time contain 22,000 plants of Festuca octoflora. Yet the former is conspicuous and controlling, the latter plays an altogether insignificant role. This difference is readily shown by comparing a plant of each. The one is 3 × 3 feet, the other 3 × ¼ inch. Such figures furnish a valuable check upon mere number, but make the brief, graphic designation of abundance difficult. An attempt has been made to solve this problem by roughly determining the space occupied by the plant, by means of the formula, height (πR2) × abundance. This would give Psoralea a value of 210, and Festuca one of 1.6, which much more nearly represents their real importance in the formation. Abundance or numerical value is a floristic concept entirely, and has little place in ecology unless checked in the way indicated. The whole problem, ecologically, depends upon an intimate knowledge of competition, and its solution in consequence is at present impossible.

The Chart Quadrat

207. Description and use. The detailed labor required in mapping makes it advisable to use the meter quadrat. An additional reason of much importance is furnished by the desirability of securing a detail photograph of the quadrat. This is impossible with field cameras, which should not exceed 6½ x 8½ inches, and are indeed most serviceable in the 4 × 5 size, if the area be larger. In open formations, the major quadrat of 2 meters can be used if necessary, but this is very rarely the case. Forest quadrats of ten meters square are easily charted, but detail photographs can not be made of them. Larger quadrats are impracticable; they can be counted but not mapped to advantage. The location of the chart quadrat must be decided by the structure to be studied. Its greatest service is in connection with zones and societies of the same formation, which can be easily compared in the chart form. In fact, the chart quadrat may well be regarded as the fundamental method for inquiry into zonation and alternation. It is an important aid in delimiting areas from the contiguous formations, and in determining the relationships of mixed formations. It is also used to record the character of the different aspects, but this is done more satisfactorily by the permanent quadrat.

208. The chart used is a decimeter square, and the scale is consequently 10 : 1. It is outlined on centimeter plotting paper, and the centimeter squares are numbered at the edges to correspond to the intervals of the quadrat, i. e., the top and bottom lines are numbered from left to right, and the side lines from top to bottom. These outlines are ruled in quantity and used as needed, or the forms can be furnished by the printer. In practice, a special quadrat book the size of the chart has been used. The need of a second book may be avoided by outlining two charts on the plotting sheet, and filing the latter in the field record book. In the few cases where 2–meter quadrats are desirable, four charts are used, care being taken to label them so that they can be combined whenever necessary. Ten-meter quadrats are recorded on the decimeter chart also, each meter interval corresponding to a centimeter, i. e., the scale is 100 : 1.

Fig. 51. Permanent chart quadrat, Andosacile, Carex-Campanulacoryphium.

Fig. 52. Chart of the quadrat shown in figure 51. Legend: a, Androsace chamaejasme; c, Carex rupestris; t, Tetraneuris lanata; p, Potentilla rubricaulis; as, Arenaria sajanensis; ar, Artemisia scopulorum; ag, Agropyrum scribneri; sa, Silene acaulis; st, Sieversia turbinata; d, Dasyphora fruticosa; al, Allium reticulatum; o, Oreoxis alpina.

209. Mapping is invariably begun at the upper left-hand corner of the chart, and is carried across the strip marked off by the plotting tape, decimeter by decimeter. As soon as this strip is completed, a second one is formed by moving the top tape to a position one decimeter below the plotting tape, which then becomes the upper one. This is repeated until the last strip is reached. Little difficulty is experienced in locating each plant exactly, as the decimeter interval is small, and the centimeter square which corresponds is divided into twenty-five tiny squares. Each plant is put in whenever possible, but mats, turfs, and mosses are merely outlined in mass if the individuals are not distinguishable. This holds true of all large rosettes and mats, even when they are single plants. Symbols were formerly used for indicating the various species. They have the advantage of requiring little space on the chart, and the disadvantage of necessitating constant reference to the legend. They are at present replaced by initials. By this plan, the decapitalized first letter of the generic name is used if no other genus found in the quadrat begins with the same letter. If, however, two or more genera begin with a, for example Agropyrum, Anemone, and Allium, the most abundant one is indicated by a, and the others by the first two letters, as an, al. In case two species of the same genus are present, the species initial is used in connection with that for the genus, as ac and ar for Agropyrum caninum and Agropyrum richardsonii respectively. It is rarely necessary to exceed two letters for any species. Plants which regularly have several stems from the same root are indicated by the initial and an exponent as a3. Seedlings are represented by a line drawn through the letter. Usually the chart sheet affords sufficient space below the chart for the legend. When the list of species is long, the back of the sheet is used.

210. Factors and photographs. Each chart is numbered, and the formation, station, and date indicated. The constant factors, altitude, slope, and exposure are ascertained and recorded on the sheet. The variable factors are read in each quadrat whenever possible, and in addition to being preserved in the record book, are noted on the chart sheet along with the base reading in the formation for the same time. This facilitates the interpretation of the differences found when two or more charts are compared. Chart quadrats are regularly photographed. For this purpose a long focus 4 × 5 camera with a telephoto lens is used. At the proper distance this will make a view of the same size as the chart, thus making possible an exact comparison of the two. The chart and photograph serve as mutual checks, as well as complements, since the former shows number, position, and arrangement, and the latter, height, form, position, and arrangement. The view is usually made by placing the camera directly in front of the middle of the lower tape, at such a distance that the side tapes fall just within the limits of the ground glass. The swing is always used in order that the focus may be uniformly sharp. Surface views of the quadrat can be taken by means of a device which permits the camera to hang downward from the tripod, or by means of a tripod with a swinging platform. Such views are especially valuable for the study of competition, since they give a clear idea of the spread and density of the various plants. They are difficult to make unless the vegetation is low and nearly uniform in height. The usual photograph is much more serviceable in regular quadrat work.

The Permanent Quadrat

211. Description and uses. As stated heretofore, either list or chart quadrats may be rendered permanent in order that they may be followed from season to season or from year to year. As a matter of fact, however, an area which is to be studied repeatedly really demands charting, and in practice chart quadrats alone are made permanent. This is done simply by driving a labeled stake at one corner of the quadrat, and locating the latter definitely in relation to a conspicuous landmark. When one is in residence for several years, practically all chart quadrats are converted into permanent ones, since the work already done in the chart quadrat is so much accomplished towards the permanent one. This is not necessary when one wishes merely to compare different areas of stable formations. As a rule, however, some change is constantly being wrought by invasion or competition, and the amount and direction of this can only be revealed by the permanent quadrat. The latter has a fundamental value for all kinds of invasion, but it is absolutely indispensable in studying complete invasion or succession, and in discovering and recording the gradual effects of competition. It is in the detailed investigation of these dynamic phenomena that the paramount importance of the quadrat is most evident. If the experience of several years be taken as conclusive, no other method is capable of revealing the minute changes as they are occurring.

Fig. 53. Permanent quadrat, Polygonile (Polygonum bistortoides) Ruxton Park; mapped and photographed July 22, denuded September 8, 1903.

The permanent quadrat is regularly 1 meter square, a size determined both by the exigencies of charting and photographing. When ecograph batteries are used, the quadrat is located as close to the latter as is possible. Otherwise, the quadrat itself should constitute a station for making factor observations. This connection is absolutely essential, since the quadrat is used expressly to determine the structural changes, which are produced by physical factors, and the reaction of vegetation upon them. Permanent quadrats are established in different formations or stages of a succession to trace the invasion of new species and the dropping out of old ones in response to competition. They serve to distinguish the proper formation, which represents a particular stage of development, from the mixed formations which precede and follow, and also to determine the exact course as well as the rapidity of the change that follows each reaction. When applied to different examples of the same stage, and to all the different stages of a succession, the whole development of the latter may be minutely traced and definitely recorded. The importance of following the changes from aspect to aspect is much less, since these are periodical rather than dynamic. They are an essential feature of structure, however, and it has been the practice to make at least one series of aspect charts from each permanent quadrat.

For tracing the invasion and competition of lichens and mosses, which play a primary role in initial formations, a subquadrat is used. The size varies, but it is usually smaller than the quadrat, although the latter is entirely available in the case of the large foliose lichens. For the crustose and smaller foliose forms, a subquadrat 2 decimeters square is used, and for the larger forms and tufted mosses, one of 5 decimeters. In the case of ground forms, tapes are employed, and the quadrat is permanently staked. On rocks and cliffs, where moss and lichen stages are most common, tapes are impracticable, and the quadrat is permanently outlined with paint. Charts of lichen quadrats are made to the usual scale of 10 : 1.

212. Manner of use. Permanent quadrats are mapped and photographed in exactly the same way as chart quadrats. As soon as this has been done, a labeled stake is driven at the upper left-hand corner, so that its edge indicates the exact position of the quadrat stake, and a smaller one is placed at the opposite corner to facilitate the task of setting the tapes accurately in later readings. The label stake bears merely the number of the quadrat and the date when it was first established. It is firmly fixed and allowed to project just enough to enable it to be located readily. Its position requires careful landmarking when the quadrat is to be visited year by year. In forest formations, this is readily done by blazing, but in grassland it is necessary to have recourse to compass and pacing, or to erect an artificial landmark. After several charts have been made, a permanent quadrat attains a high value, and every precaution must be taken to prevent losing its exact location. At the second reading of a quadrat, whether in the succeeding aspect or year, the tapes are placed with reference to the stakes, and a chart and photograph are made in the usual manner. These are labeled and dated like the original ones, but they are numbered to indicate both the quadrat and the series, e. g., 152 indicates the second chart, and photograph made of quadrat 15. The date indicates whether the readings are by the aspect or the year, though this may be shown also in the name of the series itself. It is clearly an advantage to have the two successive charts of a quadrat upon the same sheet, and to file all the charts and photographs of the same permanent quadrat together, and in the proper order.

Since much of the value of a permanent quadrat depends upon its use as a station for observing physical factors, it is unprofitable to establish a large number. The results of invasion and competition can be ascertained by the quadrat alone, but these should be merely preliminary to seeking for their causes. Clearly, a quadrat should be established for each battery of instruments, while additional ones should be located only in so far as they can be visited often enough to give an insight into the factors that control them. In view of the fact that the most important factors, water-content and light, are less variable than humidity, temperature, and wind, it will suffice if visits are made once a week. This is especially true when it is possible to refer the more variable factors to the continuous records of a base station. While all the results determined for permanent quadrats are preserved in the field record, a record of them is also kept on the reverse of the chart sheet for convenience in interpreting the different charts.

The Denuded Quadrat

213. Description. This is primarily a permanent quadrat from which the plant covering has been removed, after it has been charted and photographed. What is practically the same thing is obtained by establishing a permanent quadrat in a new soil, or in one recently laid bare and not yet reclothed with plants. These, however, are merely permanent quadrats, in which the first chart and photograph furnish a record of the habitat alone. They are of great importance in succession, and will be more fully discussed under experimental vegetation. The denuded quadrat is of the usual size, 1 meter, though the smaller lichen quadrats are also denuded. The location is subject to the conditions already indicated, especially with reference to physical factors. The denuded quadrat, however, is particularly adapted to the study of invasion and the resulting competition. Consequently, when migration is markedly from one direction, a series of denuded quadrats throws a flood of light upon the actual steps in invasion. Denuding is a valuable aid in succession, but it must be clearly recognized that, while permanent quadrats register the exact course of the succession, denuded ones can merely furnish facts as to the probable courses of stages not now in evidence.

Fig. 54. Denuded quadrat; this is the quadrat shown in figure 53; photographed September 7, 1904.

214. Methods of denuding and recording. Permanent quadrats may be denuded at any time during the time they are under observation. The best results, however, are to be obtained by establishing the two side by side, or at least close together. In this way, they are mutually supplementary, and furnish the most evidence possible with regard to the procedure of invasion and competition. Another advantage is found in that the same observations of climatic factors will do for both, though water-content and soil temperatures are necessarily different. A quadrat which is to be denuded is first mapped, photographed, and labeled exactly like a permanent quadrat. The vegetation is then destroyed. This is usually done by removal, though it may also be burnt, destroyed by flooding, or in some other manner. The method will depend upon the use which the quadrat is to serve. If it is to throw light upon the vegetation of an area in which denudation has affected the surface alone, the aerial parts only are removed by paring the surface with a spade. When the disturbance is to be more profound, the upper seed-bearing layer is removed, and the underground parts dug up. In the interpretation of a secondary succession, the denuding cause is made use of in a fashion as nearly natural as possible. Ordinarily, the plants are removed just below the top of the ground by a spade, leaving the underground parts undisturbed. This method has yielded very interesting results.

Quadrats have been denuded in the fall after the majority of the plants have completed their growth. This is largely owing to the fact that other field work is less pressing at this time. Denudation can be done as well in the spring, though the invasion will be slower in this case, since the seeds which have accumulated will be partly or entirely removed. During the first season the denuded quadrat should be mapped every month, and, if the invasion be rapid, photographed also. In open formations, especially those of a xerophytic nature, a single chart and photograph made at the end of the season are sufficient. In a few cases of this sort, indeed, no invaders have appeared until the second year. Beginning with the second season, a single record taken near the close of the growing period will suffice. Denuded quadrats are labeled, dated, and filed exactly as other permanent quadrats, but it should be noted that the first member of the chart and photograph series is that which records the original vegetation of the area denuded.

215. Physical factors. When denuded quadrats are single, their physical factors must be observed in the usual way. If they are associated with permanent ones, the ordinary readings are made for the latter, and those factors which are affected by exposing the soil are alone taken for the denuded area. These are the water-content, soil and surface temperatures, and in some stations at least the humidity near the surface. As everywhere, water-content is the most important, but the temperature at or near the surface has a marked effect upon germination. Because of its bearing upon the latter, the surface water-content is usually determined also. This has been done by taking a surface sample 2 inches square and 1 inch deep. Denuded quadrats naturally show considerable differences from year to year as the action of the invaders becomes more pronounced. To this fact is due much of their value as aids in interpreting succession.

Aquatic Quadrats

216. Scope. The preceding discussion of quadrat methods is based wholly upon their use in terrestrial formations. Wet meadow and dry bog are the wettest places in which quadrats have been used. It is clear, however, that with certain necessary modifications, quadrats can be used as successfully, though not as conveniently, in many water formations as in land ones. The tapes need to be raised above the surface of the water by longer stakes, and photographs often taken from a boat, but otherwise the usual methods apply, at any rate for bogs and shallow bodies of water. In lakes or streams the tapes might be attached to buoys or floats. The determination of factors is made as usual. Permanent quadrats are feasible in many cases at least, and denuded quadrats are not altogether impossible.