The spatial pattern of Enchytraeidae (Oligochaeta)

Oecologia 9 Springer-Verlag1985

Oecologia (Berlin) (1985) 68:153-157

The spatial pattern of Enchytraeidae (Oligochaeta) Josef Chalupsk~, Jr. ~ and Jan Lep~ 2

1 Laboratory of Soil Biology, Institute of Landscape Ecology, Czechoslovak Academy of Sciences, Na s/tdkfich 7, 370 05 Cesk6 Bud~jovice, Czechoslovakia 2 Department of Biomathematics, Biological Research Centre, Czechoslovak Academy of Sciences, Branigovskfi 31, 370 05 Cesk6 Bud~jovice, Czechoslovakia

Summary. Spatial pattern of enchytraeids (Oligochaeta: En-

chytraeidae) was studied in an experimental plot in an apple orchard near Bavorov, South Bohemia, Czechoslovakia. A total of 450 soil cores were taken in 1982, all individuals were determined (juveniles to genus, mature individuals to species) and counted. In total, 17 species of 4 genera were found. Both juveniles and mature individuals exhibited a distinctly aggregated spatial pattern. The distribution of the number of individuals in a sampling unit may be effectively fitted by the negative binomial distribution. The fit of Neyman type A distribution was considerably poorer. Comparing juveniles and mature individuals of the same genus using Lloyd's index of patchiness we found mature individuals to be slightly more aggregated than juveniles. Comparing the observed distribution of species number with that expected under the assumption of independence we may conclude that individuals appear in multispecies aggregation centres. These two conclusions support the hypothesis that aggregations are environmentally conditioned (abiotic factors and/or food availability) rather than caused by the type of reproduction.

There are at least two reasons for ecologists' concern with spatial patterns - distribution of individuals in space. (We use the term spatial pattern and not the term distribution in this meaning in order to avoid confusion with distribution in statistical sense, cf. Pielou 1977, p. 117). (1) The type of statistical distribution of the number of individuals in sampling unit corresponds to the type of spatial pattern. This knowledge provides important information for proper sampling plan and data treatment. (2) Each spatial pattern type is caused by certain processes in the population or community and/or by influence of environment; the recognition of the spatial pattern type and particularly of its changes with time helps to determine these unknown processes. Three basic types of spatial pattern are usually distinguished in ecology: random, regular and aggregated. The last one is the most commonly found in both plant and animal populations in nature (e.g. Kershaw 1973; Southwood 1978). Generally, three main causes of this type of pattern may be distinguished: (1) The type of reproduction (e.g. eggs laid in clusters), (2) heterogeneity in the abiotic environment, and (3) the influence of other populations Offprint requests to: J. Lepg

(e.g. if one of two competing species exhibits an aggregated pattern, we may hardly expect the other one to be distributed randomly). Regular and random patterns are far less common. The regular pattern usually results from strong intraspecific competition, as has been documented for evenaged populations of plants (e.g. Ford 1975), marine spinoid polychaetes (Levin 1982) and others. Random pattern is usually interpreted as a consequence of lack of intraspecific interactions, although it may be found as a consequence of "equilibrium" between causes of aggregated pattern and intraspecific competition (Lepg and Kindlmann 1984). The aggregated pattern is rather typical for soil organisms. The clusters of individuals usually form the "aggregation centres", while the rest of space is scarcely populated. This type of pattern has been found in populations of soil fauna (see e.g. Murphy 1962; Axelsson et al. 1975) and is particularly well documented in enchytraeids (Nielsen 1954, 1955; O'Connor 1967; Peachey 1963; Nakamura 1979, 1982; Abrahamsen 1969; Abrahamsen and Strand 1970). Probable cause is the dependence of aggregation centres on the favourable physical conditions in a heterogeneous soil environment, on the food availability (particularly food in the suitable state of microbial decay or decomposition). The aggregation centres may also be caused by sudden breeding of young individuals from cocoons. However, aggregation centres were also found in populations of species with prevailing asexual types of reproduction (O'Connor 1967). The common appearance of different species in aggregation centres may be considered as evidence for environmentally induced aggregation. Methods

Of the two common types of sampling for spatial pattern determination, distance methods and counting individuals in sampling units (see e.g. Pielou 1977), the latter is obviously applicable in soil biology. There are two characteristics of aggregated pattern - grain and intensity. For the determination of grain, the use of odd-size sampling units or of a continuous grid or transect of sampling units is needed. Whereas this may be easily done in plant ecology (see pattern analysis of Greig-Smith 1964 and Kershaw 1973), in soil biology it would be very tedious. Hence, the intensity of clumping is usually studied by means of predetermined sampling units. In this account the enchytraeid census data, associated with the field ecological experiment on the influence of her-

154 bicide application on the density of soil organisms, have been involved. During 1982 an apple orchard near Bavorov (South Bohemia) was sampled with a total of 450 soil cores, taking 10 cm z of surface and going 10 cm down. After O'Connor's (1955) wet funnel extraction all live enchytraeid worms were counted and determined in each soil core. Mature individuals were identified to species; the immature specimens were referred to genus only. Seventeen species of 4 genera were found. Thus, the precise numbers of adults of all 17 species and of juveniles of the 4 genera became available for further statistical analysis. In the case of a random spatial pattern, the number of individuals in a sampling unit follows the Poisson distribution. Hence, the spatial pattern may be characterized by (1) comparison of properties of observed distribution with that of the Poisson and (2) fitting the observed distribution to some contagious distributions. We have used two of them that are adopted most frequently in ecology, the negative binomial (with parameters p and k, notation according to Gurgland and Hinz 1971) and Neyman type A (parameters 21 and 22). The negative binomial is usually interpreted in ecology as distribution of number of individuals, when individuals occur in clusters. Counts of dusters follow the Poisson distribution, and number of individuals in a cluster, the logarithmic. In short, the distribution may be referred to as Poisson-logarithmic. In a similar way, the Neyman type A may be referred to as Poisson-Poisson. It should be noted, that other than the above-stated models may lead to the above-distributions (e.g. Southwood 1978 listed five models leading to negative binomial distribution) and consequently the agreement between observed and fitted distribution should not be taken as verification of those models. The following procedures were used: 1) For the Poisson distribution the mean and variance are equal. Indexes based on comparison with Poisson distribution compare the sample mean (~) and the sample variance (sZ). We have used the following indexes (see Pielou 1969, pp. 90-98): the variance: mean ratio (s2/yc) and Lloyd's index of patchiness (s2-Y)/P~z+l. The first one does and the second one does not change its value when some of the population members are removed randomly. 2) Data were fitted to negative binomial distribution, using the maximum likelihood procedure of Bliss and Fisher (1953), and to both negative binomial and Neyman type A distributions, using the minimum Z 2 procedure of Gurland and Hinz (1971), with our own BASIC program on desktop calculator HP-9845. The moment estimates of parameters of both distributions (e.g. Weber 1964) are the easiest to calculate. However, they are usually less efficient than the minimum Z 2 or the maximum likelihood estimates. With the increasing availability of programable calculators their use seems to lose justification. The agreement between observed (O) and expected (E) frequencies in a given distribution were tested by Pearson's Z 2 (as recommended by Bliss 1971)

2 v'(O--E) 2 z=2

2

with N - 1 - Q degrees of freedom, where N is the number of ratios that are summed and Q is the number of estimated parameters of the distribution under consideration (Q = 2 for both the negative binomial and Neyman type A). In the same way, the agreement with the Poisson distribution

was tested (here Q = I ) . Observations in the tail were grouped to avoid very low frequencies. The variance: mean ratio and Lloyd's index of patchiness were computed for all populations separately. As genera only were determined in juveniles, the particular population of adults belonging to the same genus were thereafter lumped together to allow comparison of juveniles with adults. The distribution fitting was carried out for items with means higher than 0.1. Two approaches were used to evaluate the spatial relationships of particular populations (only adults were used). First, the independence of occurrence of each pair of species was tested using the 2 x 2 contingency table, as it is generally used for determination of "interspecific associations" in quantitative ecology (e.g. Kershaw 1973, p. 26). Species occurring in at least 10 sampling units were considered (14 species). Second, the distribution of species counts in sampling units was compared with that expected under the assumption of independence of species (Barton and David 1959). The procedure described by Pielou (1974, appendix 11.3) was kept. All species were considered. The dependence of variance on the mean within the set of 17 species of adults and 4 genera of juveniles was estimated. It was supposed, that the relationship obeys "Taylor's power law" (Taylor 1961), although it is originally intended for one species in different localities (here, different species from the same locality were used) : S2 = a" ~b,

where s 2 and ~ are variance and mean, respectively, and a and b are parameters. As both variables are not error-free, the relation was fitted by Bartlett's (1949) method (after log-log transformation of data) as recommended by Bliss (1971). Keeping Taylor's rules, the optimal transformation of data for stabilizing variance and "improving" normality should be transf ( x ) = x v, where p = 1 - b / 2 (Taylor 1961; Southwood 1978, p. 11). Obviously, for the Poisson distribution we obtain the square root transformation. It should be noted, that the statement in Odum's textbook (Odum 1971, p. 205) dealing with this point " I t should be recalled that random distribution is one that follows the so-called " n o r m a l " or bell-shaped curve on which standard statistical methods are based," is confusing. Results and discussion

Results of evaluation of spatial patterns of particular species and genera are in Table 1. For all items under consideration, the variance exceeds the mean indicating an aggregated spatial pattern. Comparing juveniles and adults of the same genus using the Lloyd's index of patchiness we found a very slight increase of aggregation intensity from juveniles to adults (see Table 1). It does not support the assumption, that the aggregations are caused by breeding from cocoons. The comparison of observed and fitted data is given for adults of Fridericia connata and juveniles of Fridericia spp. in Figs. 1 and 2. Clearly, the negative binomial fits best. In all cases with the density of more than 0.1 individuals per sampling unit, the Poisson distribution may be rejected (P..

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