DEVELOPMENTAL PHASES OF THE * BY CLYDE E. GOULDEN

ACADEMY OF NATURAL SCIENCES OF PHILADELPHIA AND UNIVERSITY OF PENNSYLVANIA Communicated by G. Evelyn Hutchinson, January 31, 1969 Abstract.-Species number and diversity increase log-linearly with time during the early development of a biocoenosis. This period may be divided into three phases. In the first phase, diversity increases with the rapid immigration of species into the newly established . In the second phase, diversity in- creases as common species become less common and rare species less rare. This period ends with the attainment of a maximum diversity pattern. In the third phase, rare species continue to invade the habitat until it is saturated. In each phase there is a maximal number of species that can invade the habitat.

There are three aspects of species diversity: (1) number of species, S; (2) their relative abundances, commonly designated as H in the most-often-used diversity index; and (3) the pattern of relative abundances of all species. The second aspect is generally measured by the Shannon-Wiener information theory equation, H = - Xpi log Pi. The pattern of relative abundances for a taxocene (a set of closely related species) varies for different groups of , changing with the maturity of the association under study as shown below, and is probably related to the number of competing species composing the taxocene. We are concerned here with a description of the historical changes in species number and diversity characteristic of early developmental stages of the biocoen- Os's. The organisms considered here are all members of the Family Chydoridae (Order Cladocera, Class Crustacea). The species are found concentrated in weed beds in the littoral zone of lakes. All appear to feed on plant detritus, algae, and bacteria. Our initial studies indicate that the species have substrate preferences. All species produce recognizable chitinous exuviae that are pre- served in lake sediments. A single sample of surface sediment can be used to identify the entire chydorid of a lake,1 and samples from a single sediment core suffice to describe for a given lake age the relative abundances of the micro- fossil .2 We have shown elsewhere that the pattern of relative abundances of fossil chydorid that represent stable, mature periods of a lake's history tends to conform with predicted values from the MacArthur Type 1 distribu- tion3-5 (the fact that it fits this particular model is unimportant-any biological model will suffice for the present discussion). t Chydorid populations represent- ing the early stages of development of the lake biocoenosis tend to be poor fits to the Type 1 distribution, with successively better fits as the habitat "matures." This trend has now been found for five lakes: Aguada de Santa Ana Vieja, Guatemala ;5 Lago di Monterosi, Italy ;6 Esthwaite Water, England ;3 Lake Lacawac, Pennsylvania; and Lake Nojiri, Japan.7 1066 Downloaded by guest on September 29, 2021 VOL. 62, 1969 : C. E. GOULDEN 1067

After attainment of a good fit to the Type 1, additional species may be added- thus further increasing diversity-but the basic pattern of relative abundances remains the same. There appears to be an upper limit or asymptotic number of species, so that diversity H tends toward an asymptote. This can best be seen in Esthwaite Water, England, in which the association of chydorids remained essentially constant over the last 4000 years of the lake's history.8 However, if the environment is disturbed significantly, there is an immediate decrease in diversity and usually in number of species, with an accompanying poorer fit to the Type 1 distribution.5' 7 9 When this occurs, one species becomes superabundant while the other species become rather rare. As long as the dis- turbance persists, the number of species and diversity H will remain low. But at its cessation, assuming that the habitat is not totally destroyed, diversity and the number of species will again increase as in the early stages of biocoenosis develop- ment.

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FIG. 1.-Changes in species S _ number S and diversity H with H 0 regression line for chydorid Cla- docera in sediment core from the Aguada de Santa Ana Vieja, 0 l l l Guatemala. DC". I0 20 DEPTH

To illustrate and describe the changes occurring during the early stages of biocoenosis development, I have plotted the logarithm of number of species S and of diversity H against sediment depth (Figs. 1 and 2); sediment depth was mea- sured in centimeters from the bottommost sample in which reliable population sizes were encountered. The increases in both species numbers and diversity appear to be almost log-linear, and in fact give significant linear regressions, as measured by the F test. It is apparent that the points do not form a straight line if connected and are more convex curvilinear. Part of the explanation for this is that an error is in- troduced in the time scale used, which in this case is sediment levels. Without an absolute dating scale we must assume that the sedimentation rate is constant. This is a weak assumption. We do have an almost absolute time scale based on Downloaded by guest on September 29, 2021 1068 ZOOLOGY: C. E. GOULDEN PRoc. N. A. S.

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-I.0 0 20 40 60 DEPTH FIG. 2.-Changes in species number S and diversity H for chydorid Cladocera in sediment core from Lake Lacawac, Pennsylvania. Solid line represents linear regression for all points; dashed line, linear regression for points above 30 cm; dotted line, esti- mated regression for points below 5 cm. closely spaced radiocarbon dates for Lago di Monterosi, Italy (Fig. 3), and have compared the increase in diversity during and following a period of Roman dis- turbance of the drainage basin with both the sediment-level time scale and the absolute time scale. The regression of diversity on time is slightly more signif- icant (with a higher F-test value) than that of diversity on sediment depth. Since this is a semilogarithmic plot, we would conclude that both species num- ber and diversity increase exponentially, but tend toward an asymptote. If we assume diversity and species number to be in equilibrium with the environment, then these changes must reflect structural changes in the environment probably associated with decreasing unpredictability of the environment.10 One more point can be added to Figures 1 and 2, a point representing the earli- est of lake development, just before animals migrated into the newly formed lake. Downloaded by guest on September 29, 2021 VOL. 62, 1969 ZOOLOGY: C. E. GOULDEN 1069

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FIG. 3.-Changes in diversity H .50 H for chydorid Cladocera with sediment depth and time (see text for explanation) in Lago di ______Monterosi, Italy. 0 cs 20 DEPTH This point would be to the left of zero on the abscissa, since the zero represents the first point where microfossils were encountered in sufficiently large numbers to be counted. In Figure 2 we have added a dotted line on the left, a suggested re- gression line, that could be extrapolated back to the time when the lake lacked a cladoceran fauna. We have added a dashed line that represents the linear re- gression for diversity H and species number S values minus the initial set of points. These two "regression" lines (as given in Fig. 2) describe the data much better than would a single line since they suggest that there are in fact two phases of biocoenosis development and that both are probably exponential.t The first phase is associated with the immigration of species into the newly formed habitat. The increase in species occurred very rapidly, so rapidly that our techniques are not sensitive enough to measure it. This increase may be exponential, which would correspond with the suggestion by MacArthur and Wilson" that immigra- tion onto islands occurs at an exponential rate. The second phase, as indicated in Figures 1, 2, and 3, has a more gradual slope covering a much longer period of time and is not associated with as significant an increase in species numbers. The increase in diversity results not only from an increase in species numbers but also from the rearrangement of the relative abundance of species in which the common species become less common and the rare species less rare. This should lead to the ultimate, most equitable division of the environment wherein all species are equally common; however, this rarely, if ever, occurs in nature. Instead, as mentioned above, the relative abundance of species in this case attains a pattern similar to that described in MacArthur's Type 1 distribution or similar models suggested by Cohen.'2 This pattern appears to represent the "most equitable" diversity of resources that can occur in nature.'3 We can see this more clearly in Figure 4. Here we have put together all data for species number and diversity available from our own studies and from one study by Frey'4 on Schleinsee, Germany, from which the data could readily be obtained. Essentially all the points in Figure 4 are concentrated between two Downloaded by guest on September 29, 2021 1070 ZOOLOGY: C. E. GOULDEN PRoc. N. A. S.

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t.0 2.0 3.0 H FIG. 4.-Relationship between species number S and diversity H for fossil populations of chydorid Cladocera from different lakes. See text for explanation. lines. The concave curved line on the right, which is the maximum diversity H attainable for a given number of species, represents the theoretical diversity for associations of different species numbers, all of which fit the Type 1 distribution.'5 The more sigmoid-shaped line across the top of the data points is a least-squares polynomial fit of the maximum number of species found for a given diversity. As this line approaches the origin, it tends to coincide with a calculated line (dashed line, left) which represents diversity for associations of different species numbers with one superabundant species and varying numbers of rare species; each of the latter arbitrarily composes exactly 1 per cent of the fauna. In this graph there are several points of interest that follow from our earlier discussion. First, there is a maximum number of species that can invade and exist in the environment. This number is much lower for disturbed and "imma- ture" biocoenoses than for undisturbed or "mature" biocoenoses. It is the asymptotic number of species discussed before. Furthermore, since the mini- mum diversity line diverges strongly to the right of the graph above about ten species, there would appear to be a limit to the number of rare species that can occur in a given habitat. Second, it is easier to expand upward along the ordinate in the graph than to move to the right. The minimum diversity line suggests this as does the clump- ing of points; all those on the left-hand side of the graph represent disturbed or Downloaded by guest on September 29, 2021 VOL. 62, 1969 ZOOLOGY: C. E. GOULDEN 1071

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1.0 2.0 3.0 H FIG.S.-Changes in species number S and diversity H during early developmental stages of Lake Lacawac, Penn~sylvallia. D~ashed line as in Fig. 4.

"immature" . As shown in Figure 4, the rate of addition of species, and thus the expansion along the ordinate, is primarily limited by the immigration rate of species that can live under the given environmental conditions, whereas Figures 1, 2, and 3 indicate that expansion to the right of the graph is limited by time. This would support the earlier conclusion that there are two phases of development. Third, the minimum diversity line in Figure 4 suggests that as diversity in- creases in the second phase, additional species may be added. The further addi- tion of species occurs Ilot only during the shifting phase of the relative abundance pattern but also after attainment of a set pattern. This is shown in Figure 5, which depicts the changing relationship between species-number increase and diversity with respect to the theoretical maximum diversity line. Ideally, the approach to maximum diversity should be log-linear, but postglacial climatic changes would undoubtedly affect the productivity of the basin, which would in turn cause slight changes in the number of species and diversity. The increase in species following attainment of a set pattern of relative abundances, shown in Figure 5 and suggested by the minimum diversity line of Figure 4, should be recognized as a separate phase by itself. Thus there appear to be three phases in the development of the biocoenosis. Phase A: The immigration rate of species most tolerant of the existing environ- ment is rapid, but is later limited by the number of rare species that can become Downloaded by guest on September 29, 2021 1072 ZOOLOGY: C. E. GOULDEN PROc. N. A. S.

established in the habitat (this does not include nonestablished species passing through in migratory stages, as Patrick"6 has found in diatoms). Phase B: The common species become less common, the rare species become less rare. (Additional species may invade the biocoenosis during this phase but at a much slower rate than in phase A, because as the rare species of phase A become less rare, additional rare species can enter the habitat). Time is the major limiting factor in phase B, assuming that there is a stable environment with relatively little fluctuation of productivity. Phase C: Species are added up to the limiting number for a given , in our case a lake. Dr. Leigh Van Valen has suggested that the low maximum number of rare species observed here would not be seen in a "less restricted environment." Species area curves would indeed suggest this. Lake biocoenoses are more com- parable to those of islands than of continents. After these three phases, little change in the biocoenosis should occur, barring caused by climatic changes, geological events, biological succession such as would occur during the senescent stages of a lake, or cultural changes, i.e., those caused by man. I should like to express my sincere appreciation to Drs. Wayne Moss of the Academy of Natural Sciences and Neville Kallenbach of the University of Pennsylvania for their very helpful comments during the course of development of this study. A General Electric 235 time-sharing computer was used for the statistical analyses. This study was supported by National Science Foundation grant GB-6152. * This paper is dedicated to George Gaylord Simpson. t Sandersl7 has found in his samples of deep-sea benthic organisms that a fit to the Type 1 distribution is dependent upon the number of individuals in the sample, with a good fit when few individuals are counted and an increasingly poorer fit with increased sample size. We have not found this to be true. Instead, counts of several hundred individuals generally give slightly better fits than do smaller counts. I The hiatus in Figure 2 resulted because the sediment levels studied extendedlover two suc- cessive core sections. A modified Livingstone piston corer was used to collect the core, and inevitably a small segment of the upper portion of each core section was lost. This is ex- tremely unfortunate because the segment missing should include the period when the initial increase in species stopped and the second phase began. We shall obtain a second core that should allow a more detailed study of this critical period. 'Frey, D. G., "The ecological significance of cladoceran remains in lake sediments," , 41, 684-699 (1960). 2 Mueller, W. P., "The distribution of cladoceran remains in surficial sediments from three northern Indiana lakes," Invest. Ind. Lakes Streams, 6, 1-63 (1964). Goulden, C. E., "Interpretative studies of cladoceran microfossils in lake sediments," Mitt. Intern. Ver. Limnol., in press. 4MacArthur, R. H., "On the relative abundance of bird species," these PROCEEDINGS, 43, 293-295 (1957). 5 Goulden, C. E., "La Aguada de Santa Ana Vieja: An interpretative study of the clado- ceran microfossils," Arch. Hydrobiol., 62, 373-404 (1966). 6 Goulden, C. E., "Lago di Monterosi: The fossil and fauna," manuscript in prepara- tion. 7Tsukada, M., "Fossil Cladocera in Lake Nojiri and ecological order," Quaternary Res., 6, 101-110 (1967). 8 Goulden, C. E., "The history of the cladoceran fauna of Esthwaite Water (England) and its limnological significance," Arch. Hydrobiol., 60, 1-52 (1964). 9 Goulden, C. E., "The history of Laguna de Petenxil: The animal microfossils," Acad. Arts Sci. Mem., 17, 84-120 (1966). 10 Levins, R., Evolution in Changing Environments (New Jersey: Princeton University Press, 1968), 120 pp. Downloaded by guest on September 29, 2021 VOL. 62, 1969 ZOOLOGY: C. E. GOULDEN 1073

11MacArthur, R. H., and E. 0. Wilson, The Theory of Island (New Jersey: Princeton University Press, 1967), 203 pp. 12 Cohen, J., "Alternate derivations of a species-abundant relation," Am. Naturalist, 102, 165-172 (1968). 13 Lloyd, M., R. F. Inger, and F. W. King, "On the diversity of reptile and amphibian species in a Bornean rain forest," Am. Naturalist, 102, 497-515 (1968). 14 Frey, D. G., "Developmental history of Schleinsee," Verhandl. Intern. Ver. Limnol., 14, 271-278 (1961). 16 Lloyd, M., and R. J. Ghelardi, "A table for calculating the 'Equitability' component of species diversity," J. Animal Ecol., 33, 217-225 (1964). 16 Patrick, R., "The effect of invasion rate, species pool, and size of area on the structure of the diatom ," these PROCEEDINGS, 58, 1335-1342 (1967). 17 Sanders, H. L., "Marine benthic diversity: A comparative study," Am. Naturalist, 102, 243-282 (1968). Downloaded by guest on September 29, 2021