Microb. Ecol. 6: 27-34(1980)
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M i c r o s p a t i a l H e t e r o g e n e i t y in the D i s t r i b u t i o n o f C i l i a t e s in a S m a l l P o n d William D. Taylor* and Jacques Berger Depa~mentof Zoology,Universityof Toronto,Toronto,Ontario,CanadaM5S IA I
Abstract. Five transects of contiguous samples from the surface of a small pond and one transect from its bottom were collected in order to quantify microspatial heterogeneity in the distribution of c iliated protozoa. Examination of the frequencyabundance relations for these transects suggests that they can be approximated by negative binomial distributions with a common k of 1.87. Contagiousness or crowding increases with population density. Mean patch size and mean interpatch distance were measured for 4 transects as 1.5 to 2 cm and 3 to 4 cm, respectively. This heterogeneity is suggested to arise from behavioral aggregation about discrete food sources and be very ephemeral. Blocking of adjacent contiguous samples was used to investigate the effect of sample size on the apparent correlation between the numbers of pairs of taxa. In all cases examined, taxa were relatively independent in their distribution at small sample sizes and became more negatively or positively associated as samples were combined. This may reflect that the small scale patches are essentially monospecific. Introduction Spatial heterogeneity in the distribution of aquatic microbes is easily observed by placing a small drop of pond water on a slide and examining it under a microscope. Clouds of bacteria surround dead algae or animal material. Feeding on these aggregations may be various ciliates, flagellates, and rotifers. Similarly, examination of the walls of an aquarium containing enriched natural waters may reveal clonal patches of sessile ciliates expanding about their founding members. In field studies, this spatial heterogeneity results in observations that samples collected close together in space may be quite dissimilar in their microfauna [2, ! 2]. It may also explain the paradox that numerical response curves generated for microscopic * Presentaddress: Departmentof Biology,Universityof Waterloo,Waterloo,Ontario, Canada, N2L 3GI. 0095-3628/80/0006-0027501.60 9 1980 Springer-Verlag New York Inc.
28
w.D. Taylorand J. Berger
predators in the laboratory generally suggest that required prey densities are rather high relative to what one would commonly find in a field sample. The purpose of this report is to describe microspatial heterogeneity in the distribution of ciliates in a small pond in terms of the frequency-abundance relationship, patch size, and interpatch distance and to note some resultant effects of scale on the measurement of species associations.
Materials and Methods The small pond used in this study has been described elsewhere [I 1, 12]. All of the samples described here were taken in the morning (9 to 11 a . m . E . D . T . ) in 1975. Counting was performed by placing the contents of the samples into a hemispherical watchglass or small petri dish and removing the live animals singly with a micropipet while viewing a stero dissecting microscope (6.4 to 40• magnification). Counting proceeded sequentially along the transects and was completed within 4 h of collection. Two sampling methods were employed. The first used the apparatus illustrated in Fig. 1, which holds 64 glass tubes with 5 mm I.D. protruding 31.6 mm below the frame of the apparatus. When lowered into the water until the frame just touches the surface film, it encloses 64 samples, 1 ml each, along a transect 0.45 m in length. It can be closed by screwing down the upper bar, which has a gasket of dried silicone sealant greased with petroleum jelly. When the sampler is removed and inverted, the samples remain at the open end of the tubes and the sampler can be carded back to a field station. The samples were removed from the sampler tubes with a Pasteur pipet. This method was used to collect samples of surface water near the pond's margin. The second method was used to collect samples of bottom sediment in a shallow (15 cm) area of the pond. A 30 cm length of the same 5 mm I.D. tubing was used to collect a transect of 20 " c o r e " samples, I ml each, at 2.5 cm intervals to a depth of approximately 3 cm into the benthos. The cores were removed while the upper opening was covered by an index finger and the sediment "pipetted" into small screw-capped vials. Since some mixing of sediment and water column occurred, we excluded the aerobic taxa Stentor, Strobilidium, Stokesia, and Lembadion from the counts, although these comprised relatively few individuals.
Results
Faunistic Description of the Transects Five transects were collected with the apparatus illustrated in Fig. 1. The first was collected on August 19 and contained principally Strobilidium gyrans (31% of the total) and Halteria grandinella (21%). It also contained many rotifers, mostly Keratella sp. The second transect was taken on August 20 and contained an abundance of an unidentified hypotrich (possibly Oxytricha sp.), which accounted for 30% of the total fauna as well as Ophryoglena sp. (21%) and Frontonia acuminata (17%). The hypotrich and F. acuminata probably were living on the surface film. Transect 3 was obtained on September 21 and was dominated by Stentorpolymorphus (60%). H. grandinella (5%)
Heterogeneity in Ciliate Distribution Fig. 1. The sampling apparatus used to collect contiguous samples from the surface of the pond. See text for description and dimensions.
29
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and S. gyrans (3%) were again present in this sample. The fourth transect was taken on October 11 and contained small numbers of S. gyrans (78%) and Stokesia vernalis (22%). The fifth transect was also collected on October ! ! and contained mostly the same hypotrich as transect 2 (88%) and the usually benthic Spirostomum teres (I 2%). The benthic transect was collected on November 22. It was dominated by Dexiotricha colpidiopsis (75%) but also contained significant numbers of Metopus spp. (15%).
Relationship Between Densi~ and Degree of Clumping The mean number of ciliates per sample varied between 0.34 and 9.98 for the surface transects and was 13.35 for the benthic transect. To compare the heterogeneity of these transects, the mean crowdmg (m) was calculated for each as N
r * m=
Xi(X i - 1)
i=1 N
i=1
where N is the number of samples and Xi is the number o f ciliates in the ith sample [8]. The index m has several useful properties as an index of contagiousness [6, 10]. When m*"ts equal to the variance and the mean (x). For the the X i follow a Potsson . . dmtnbutlon, . . six transects, r~ is linearly related (r z -- 0.995) to k-with a slope greater than one, suggesting that these transects follow negative binomial distributions with a common k parameter (Fig. 2). The slope (b = 1.53) furnishes an estimate o f k = l/(b - 1) = 1.87 [81. The intercept of the regression of ~ on m, called the "index of basic contagion" (a), provides an estimate o f the mean number of individuals per non-empty sample at low densities. The zero-truncated mean equals a + i. That the regression fits approximately through the origin (n~ = 1.53 .'7 - 0.11) indicates that there is no clumping of ciliates at very low densities. Put another way, the model that ciliates always occur in patches o f a certain size distribution, and therefore that density is determined by the frequency o f patches, is contradicted by the fit of the regression of r~ on ~- through the origin. Patchiness increases with density. To evaluate the regression of m on x as a method for fitting k, X 2 goodness of fit tests were performed for the transects with enough classes and samples (transects I, 2, 3, and 5). Satisfactory fits (0.25 < P < 0.65) to k = 1.87 were obtained.
Patch Size and lnterpatch Distance The patch size and interpatch distance of a transect, i.e., the " s c a l e " of spatial heterogeneity, can be made more easily discernible by calculating the autocorrelation
b/(
30 22 20" 18. 16-
W. D. Taylor and J. Berger
|4-
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m
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t
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420
function or correlogram for that transect. This is simply the correlation (product moment correlation coefficient) between the numbers ofciliates in samples as a function of the distance between the samples or lag (K). N-K
Z
i=1 N
Z
i=l
Thus the correlation between the number of ciliates in adjacent samples is rl, in samples separated by one sample it is 1"2,etc. If patch size is large relative to the diameter of a sample, then adjacent samples will tend to have similar numbers of ciliates, and rl will be positive. As K increases past the mean patch size, rr will decrease. At a distance of half the interpatch distance, rK will be minimal, as sample pairs K units apart will tend to fall "in and out of patch." At a value of K equal to the mean interpatch distance, rr will increase again. The autocorrelation function should fluctuate about zero with a periodicity equal to the interpatch distance as it dampens. Two problems can eomplicate interpretation of the autocorrelation function. The first is when patch size is small relative to the sample size. If the patch size is less than or equal to the sample size, the autocorrelation function will be negative at K = 1, as adjacent samples will often be in and out of a patch. When a patch is about 2 sampling units wide, the autocorrelation function may be weakly positive at K = !. The second difficulty that may arise is a trend across the transect or low-frequency oscillations. These may result in uniformly high correlations at small values of K and a failure of the autocorrelation function to dampen. These trends may be eliminated by
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Heterogeneity in Ciliate Distribution
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Fig. ;3. Histograms indicating the number ofciliates in samples from transects I, 2.3. and 5 (top to bouom). Adjacentto the histograms are their corresponding autocorrelation functions (correlograms)before (solid lines) and after (broken lines) differencing for K -- I to 16.
h.ln.,_ ,. n, ! .I,._g_lL L =
L 9
t7 l
repeating the analysis replacing the actual number of ciliates in each sample with the difference in numbers between adjacent samples. (For example, the sequence l, 4, 7, 6, 3 would become 3, 3, - l, - 3.) This does not change the periodicity of the transect, but reduces low-frequency fluctuations in the running mean. Differencing affects the apparent size o f the patches, as the autocorrelation function becomes negative sooner. If the patch size is 2 units and the undifferenced function is positive at rl, it will become negative. This reflects that samples at the "shoulders" of a patch, which have similar ciliate numbers, will become opposite in sign after differencing. For further discussion o f these techniques the reader may consult [ ! ]. The total numbers ofciliates in the samples of transects 1,2, 3, and 5, along with their aut0correlatidn functions before and after differencing, are shown in Fig. 3. For transect l, r~, r 2 , and ra are positive before differencing and r~ is positive after differencing, indicating a patch size of about 3 sampling units or 2 era. Peaks in autocorrelation at K = 4, 10, and 16 indicate an interpatch distance of about 5 or 6 sampling units or about 4 cm.
32
W.D. Taylor and J. Berger
The autocorrelation function for transect 2 is positive at K = ! before differencing and negative after differencing, indicating a mean patch size of about 2 units or 1.5 era. Inspection of the transect reveals that although there are some larger patches of 3 or 4 units, some patches are single"spikes." Peaks at K = 6 and 12 indicate a periodicity of 6 sampling units or about 4 cm. Transect 3 contains a coarse patch which causes the undifferenced autocorrelation function to be positive until high values of K are reached. The initially negative differenced autocorrelation function and the drop in the undifferenced autocorrelation function between K --- 1 and 2 suggest a patch size of about 2 units or 1.5 cm superimposed on the coarser trends. These small patches can be seen to have a pronounced periodicity of about 4 units or 3 cm, which is easily discerned even without examination of the autocorrelation functions. Transect 5 again has a patch size of about 2 units (1.5 cm) with a periodicity of about 6 units (4 cm). In summary, fine scale patches are frequently 1.5-2.0 cm in diameter and on average are about 3 or4 cm apart. The failure of the autocorrelation functions to damp reflects the presence of larger-scale trends in mean and variance within the transects. That the autocorrelation functions fluctuate around zero, rather than staying positive, indicates that areas of high ciliate density tend to be adjacent to areas of low ciliate density.
Effect of Spatial Heterogeneity on the Measurement of Species Association Patchiness in species' distributions may cause scale-dependent changes in their apparent spatial relationship. These scale-dependent changes can be examined by repeatedly combining or "blocking" adjacent samples frorrl the transects and recalculating similarity measures on the smaller set of larger samples. Some examples of spatial relationships (measured by linear cross-correlation coefficients) between taxa from the transects are given in Fig. 4. Figure 4A contains three examples of associations that become increasingly positive with blocking. The crustacea are primarily Cladocera and copepod nauplii while the rotifers are mostly Keratella sp. Figure 4B illustrates an opposite effect of blocking on the apparent correlation between numbers of Halteria grandinella and Strobilidium gyrans from 2 transects. In all cases, correlations between the abundance of taxa are weaker at smaller sample sizes. This observation is consistent with the fine-scale microfaunal patches being essentially monospecific, but independently distributed and overlapping. Repulsed monospecific patches would give rise to negative associations which would become less so with blocking. Contagious monospecific patches (i,e., mixed patches) would lead to strong positive associations at fine scales.
Discussion Visual inspection of the transects presented in Fig. 3 reveals that there are large differences among them in the abundance of ciliates. Within some of the transects there are coarse trends as well. Superimposed on these relatively large-scale patterns, which are probably stable over periods of perhaps days and may reflect population dynamic responses to resource levels, is a fine-scale heterogeneity which is probably very
Heterogeneity in Ciliate Distribution
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degree of blocking Fig. 4. The apparent correlation between pairs of taxa as a function of the number of samples combined or blocked together. A The increasing correlations between ciliates and crustacean zooplankton in transect 1 (broken line), between ciliates and rotifers in transect 2 (upper solid line), and between F. acuminata and a hypotrich in transect 2 (lower solid line). B The decreasing correlations between S. gyrans and H. grandinella in transect I (solidline) and transect 3 (broken line).
transient and may reflect behavioral aggregation in response to discrete food sources. Behavioral aggregation is suggested by the tendency of the autocorrelation functions to fluctuate around zero rather than remain positive, reflecting that areas of high ciliate density tend to be adjacent to areas of low ciliate density. Almost all of this variation mentioned above could be considered ephemeral spatial variation [7] since within site and within time variation are great in this pond [ 12]. Spatial variation at scales less than 1 m has been noted for marine plankton [4, 5]. The apparent association between species frequently becomes more positive or negative as samples are combined, reflecting that species are more independently distributed at the spatial scales at which behavioral aggregation is thought to occur. Independent behavioral aggregation suggests a way in which either filtering or grazing animals may utilize different resources that does require a more proximate mechanism of selective feeding. The ciliate species pairs used as examples in Fig. 4, F. acuminata and the unidentified hypotrich (probably Oxytricha sp.) and H. grandineUa and S. gyrans, are likely to occur in the surface film and the water column, respectively. Their relative independence at a fine scale is noteworthy as these species would be expected to have overlapping diets. Although the occurrence of ciliates in small patches is not an unexpected feature of the data, the uniform spacing of these patches in certain cases (particularly transect 3, which contained mostly Stentor polymorphus), is difficult to explain. It is possible that a mechanical process, e.g., the action of waves on the surface film, rather than a purely behavioral process may be involved in patch formation in some instances. It should be noted, however, that small-scale heterogeneity arises even on homogeneous artificial substrates [3, 9]. Irrespective of the mechanism of patch formation, the way in which species cope with or exploit this ephemeral spatial heterogeneity probably underlies the
34
W.D. Taylor and J. Berger
observed variation among ciliates in a constellation of attributes related to feeding, dispersal, and population growth [I 1]. Acknowledgments. This work was supported by NSERCC operating grant A-3473 to J. Berger. Financial assistance was also obtained from an Ontario Graduate Scholarship to W. D. Taylor. Mr. Stephen Taylor kindly constructed the sampler.
References I. Box, G. E. P., and J. M. Jenkins: Time Series Analysis-Forecasting and Control, Rev. ed. Holden-Day, San Francisco (1976) 2. Cairns, J., Jr., J, A. Ruthven, and R. L. Kaesler: Distribution of protozoa in a small stream. Am. Midl. Nat. 92,406-414 (1974) 3. Cairns, J., Jr., and W. H. Yongue, Jr.: The distribution of protozoa on a relatively homogeneous substrate. Hydrobiologia 31, 65-72 (1968) 4. Cassie, R. M.: Microdistribution of the plankton. Oceanogr. Mar. Biol. 1,223-252 (1963) 5. Hammer, W. M., and J. H. Carlton: Copepod swarms: attributes and role in coral reef ecosystems. Limnol. Oceanogr. 24, 1-14 (1979) 6. lwao, S., and E. Kuno: An approach to the analysis of aggregation pattern in biological populations. In G. P. Patil, E. C. Pielou, and W. E. Waters (eds.): Spatial Patterns and Statistical Distributions. Pennsylvania State University Press, University Park, Pa. (1971) 7. Lewis, W. M., Jr.: Comparison of temporal and spatial variation in the zooplankton of a lake by means of variance components. Ecology 59,666-671 (1978) 8. Lloyd, M.: "Mean crowding". J. Anim. Ecol. 36, 1-30 (1967) 9. Maguire, B., Jr.: The passive dispersal of small aquatic organisms and their colonization of isolated bodies of water. Ecol. Monogr. 38, 161-185 (1963) 10. Pielou, E. C.: Mathematical Ecology. John Wiley and Sons, New York (1977) I 1. Taylor, W. D.: Maximum growth rate, size and commonness in a community of bactivorous ciliates. Oecologia (Bed.) 36,263-272 (1978) 12. Taylor, W. D.: Sampling data on the bactivorous ciliates of a small pond compared to neutral models of community structure. Ecology 60 (in press)
Df[~I~[[.
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M i c r o s p a t i a l H e t e r o g e n e i t y in the D i s t r i b u t i o n o f C i l i a t e s in a S m a l l P o n d William D. Taylor* and Jacques Berger Depa~mentof Zoology,Universityof Toronto,Toronto,Ontario,CanadaM5S IA I
Abstract. Five transects of contiguous samples from the surface of a small pond and one transect from its bottom were collected in order to quantify microspatial heterogeneity in the distribution of c iliated protozoa. Examination of the frequencyabundance relations for these transects suggests that they can be approximated by negative binomial distributions with a common k of 1.87. Contagiousness or crowding increases with population density. Mean patch size and mean interpatch distance were measured for 4 transects as 1.5 to 2 cm and 3 to 4 cm, respectively. This heterogeneity is suggested to arise from behavioral aggregation about discrete food sources and be very ephemeral. Blocking of adjacent contiguous samples was used to investigate the effect of sample size on the apparent correlation between the numbers of pairs of taxa. In all cases examined, taxa were relatively independent in their distribution at small sample sizes and became more negatively or positively associated as samples were combined. This may reflect that the small scale patches are essentially monospecific. Introduction Spatial heterogeneity in the distribution of aquatic microbes is easily observed by placing a small drop of pond water on a slide and examining it under a microscope. Clouds of bacteria surround dead algae or animal material. Feeding on these aggregations may be various ciliates, flagellates, and rotifers. Similarly, examination of the walls of an aquarium containing enriched natural waters may reveal clonal patches of sessile ciliates expanding about their founding members. In field studies, this spatial heterogeneity results in observations that samples collected close together in space may be quite dissimilar in their microfauna [2, ! 2]. It may also explain the paradox that numerical response curves generated for microscopic * Presentaddress: Departmentof Biology,Universityof Waterloo,Waterloo,Ontario, Canada, N2L 3GI. 0095-3628/80/0006-0027501.60 9 1980 Springer-Verlag New York Inc.
28
w.D. Taylorand J. Berger
predators in the laboratory generally suggest that required prey densities are rather high relative to what one would commonly find in a field sample. The purpose of this report is to describe microspatial heterogeneity in the distribution of ciliates in a small pond in terms of the frequency-abundance relationship, patch size, and interpatch distance and to note some resultant effects of scale on the measurement of species associations.
Materials and Methods The small pond used in this study has been described elsewhere [I 1, 12]. All of the samples described here were taken in the morning (9 to 11 a . m . E . D . T . ) in 1975. Counting was performed by placing the contents of the samples into a hemispherical watchglass or small petri dish and removing the live animals singly with a micropipet while viewing a stero dissecting microscope (6.4 to 40• magnification). Counting proceeded sequentially along the transects and was completed within 4 h of collection. Two sampling methods were employed. The first used the apparatus illustrated in Fig. 1, which holds 64 glass tubes with 5 mm I.D. protruding 31.6 mm below the frame of the apparatus. When lowered into the water until the frame just touches the surface film, it encloses 64 samples, 1 ml each, along a transect 0.45 m in length. It can be closed by screwing down the upper bar, which has a gasket of dried silicone sealant greased with petroleum jelly. When the sampler is removed and inverted, the samples remain at the open end of the tubes and the sampler can be carded back to a field station. The samples were removed from the sampler tubes with a Pasteur pipet. This method was used to collect samples of surface water near the pond's margin. The second method was used to collect samples of bottom sediment in a shallow (15 cm) area of the pond. A 30 cm length of the same 5 mm I.D. tubing was used to collect a transect of 20 " c o r e " samples, I ml each, at 2.5 cm intervals to a depth of approximately 3 cm into the benthos. The cores were removed while the upper opening was covered by an index finger and the sediment "pipetted" into small screw-capped vials. Since some mixing of sediment and water column occurred, we excluded the aerobic taxa Stentor, Strobilidium, Stokesia, and Lembadion from the counts, although these comprised relatively few individuals.
Results
Faunistic Description of the Transects Five transects were collected with the apparatus illustrated in Fig. 1. The first was collected on August 19 and contained principally Strobilidium gyrans (31% of the total) and Halteria grandinella (21%). It also contained many rotifers, mostly Keratella sp. The second transect was taken on August 20 and contained an abundance of an unidentified hypotrich (possibly Oxytricha sp.), which accounted for 30% of the total fauna as well as Ophryoglena sp. (21%) and Frontonia acuminata (17%). The hypotrich and F. acuminata probably were living on the surface film. Transect 3 was obtained on September 21 and was dominated by Stentorpolymorphus (60%). H. grandinella (5%)
Heterogeneity in Ciliate Distribution Fig. 1. The sampling apparatus used to collect contiguous samples from the surface of the pond. See text for description and dimensions.
29
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and S. gyrans (3%) were again present in this sample. The fourth transect was taken on October 11 and contained small numbers of S. gyrans (78%) and Stokesia vernalis (22%). The fifth transect was also collected on October ! ! and contained mostly the same hypotrich as transect 2 (88%) and the usually benthic Spirostomum teres (I 2%). The benthic transect was collected on November 22. It was dominated by Dexiotricha colpidiopsis (75%) but also contained significant numbers of Metopus spp. (15%).
Relationship Between Densi~ and Degree of Clumping The mean number of ciliates per sample varied between 0.34 and 9.98 for the surface transects and was 13.35 for the benthic transect. To compare the heterogeneity of these transects, the mean crowdmg (m) was calculated for each as N
r * m=
Xi(X i - 1)
i=1 N
i=1
where N is the number of samples and Xi is the number o f ciliates in the ith sample [8]. The index m has several useful properties as an index of contagiousness [6, 10]. When m*"ts equal to the variance and the mean (x). For the the X i follow a Potsson . . dmtnbutlon, . . six transects, r~ is linearly related (r z -- 0.995) to k-with a slope greater than one, suggesting that these transects follow negative binomial distributions with a common k parameter (Fig. 2). The slope (b = 1.53) furnishes an estimate o f k = l/(b - 1) = 1.87 [81. The intercept of the regression of ~ on m, called the "index of basic contagion" (a), provides an estimate o f the mean number of individuals per non-empty sample at low densities. The zero-truncated mean equals a + i. That the regression fits approximately through the origin (n~ = 1.53 .'7 - 0.11) indicates that there is no clumping of ciliates at very low densities. Put another way, the model that ciliates always occur in patches o f a certain size distribution, and therefore that density is determined by the frequency o f patches, is contradicted by the fit of the regression of r~ on ~- through the origin. Patchiness increases with density. To evaluate the regression of m on x as a method for fitting k, X 2 goodness of fit tests were performed for the transects with enough classes and samples (transects I, 2, 3, and 5). Satisfactory fits (0.25 < P < 0.65) to k = 1.87 were obtained.
Patch Size and lnterpatch Distance The patch size and interpatch distance of a transect, i.e., the " s c a l e " of spatial heterogeneity, can be made more easily discernible by calculating the autocorrelation
b/(
30 22 20" 18. 16-
W. D. Taylor and J. Berger
|4-
SJ ~
12-
m
S/'/'f
I08-
t
6-
s~J~s$ Fig. 9..The relationshipbetweenmeancrowding(r'n) and mean numberof ciliates per samplein the 5 surface transectsand the benthic transect (b). The broken line indicatesthe expectedrelationshipfor random distributions.
420
function or correlogram for that transect. This is simply the correlation (product moment correlation coefficient) between the numbers ofciliates in samples as a function of the distance between the samples or lag (K). N-K
Z
i=1 N
Z
i=l
Thus the correlation between the number of ciliates in adjacent samples is rl, in samples separated by one sample it is 1"2,etc. If patch size is large relative to the diameter of a sample, then adjacent samples will tend to have similar numbers of ciliates, and rl will be positive. As K increases past the mean patch size, rr will decrease. At a distance of half the interpatch distance, rK will be minimal, as sample pairs K units apart will tend to fall "in and out of patch." At a value of K equal to the mean interpatch distance, rr will increase again. The autocorrelation function should fluctuate about zero with a periodicity equal to the interpatch distance as it dampens. Two problems can eomplicate interpretation of the autocorrelation function. The first is when patch size is small relative to the sample size. If the patch size is less than or equal to the sample size, the autocorrelation function will be negative at K = 1, as adjacent samples will often be in and out of a patch. When a patch is about 2 sampling units wide, the autocorrelation function may be weakly positive at K = !. The second difficulty that may arise is a trend across the transect or low-frequency oscillations. These may result in uniformly high correlations at small values of K and a failure of the autocorrelation function to dampen. These trends may be eliminated by
3i
Heterogeneity in Ciliate Distribution
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Fig. ;3. Histograms indicating the number ofciliates in samples from transects I, 2.3. and 5 (top to bouom). Adjacentto the histograms are their corresponding autocorrelation functions (correlograms)before (solid lines) and after (broken lines) differencing for K -- I to 16.
h.ln.,_ ,. n, ! .I,._g_lL L =
L 9
t7 l
repeating the analysis replacing the actual number of ciliates in each sample with the difference in numbers between adjacent samples. (For example, the sequence l, 4, 7, 6, 3 would become 3, 3, - l, - 3.) This does not change the periodicity of the transect, but reduces low-frequency fluctuations in the running mean. Differencing affects the apparent size o f the patches, as the autocorrelation function becomes negative sooner. If the patch size is 2 units and the undifferenced function is positive at rl, it will become negative. This reflects that samples at the "shoulders" of a patch, which have similar ciliate numbers, will become opposite in sign after differencing. For further discussion o f these techniques the reader may consult [ ! ]. The total numbers ofciliates in the samples of transects 1,2, 3, and 5, along with their aut0correlatidn functions before and after differencing, are shown in Fig. 3. For transect l, r~, r 2 , and ra are positive before differencing and r~ is positive after differencing, indicating a patch size of about 3 sampling units or 2 era. Peaks in autocorrelation at K = 4, 10, and 16 indicate an interpatch distance of about 5 or 6 sampling units or about 4 cm.
32
W.D. Taylor and J. Berger
The autocorrelation function for transect 2 is positive at K = ! before differencing and negative after differencing, indicating a mean patch size of about 2 units or 1.5 era. Inspection of the transect reveals that although there are some larger patches of 3 or 4 units, some patches are single"spikes." Peaks at K = 6 and 12 indicate a periodicity of 6 sampling units or about 4 cm. Transect 3 contains a coarse patch which causes the undifferenced autocorrelation function to be positive until high values of K are reached. The initially negative differenced autocorrelation function and the drop in the undifferenced autocorrelation function between K --- 1 and 2 suggest a patch size of about 2 units or 1.5 cm superimposed on the coarser trends. These small patches can be seen to have a pronounced periodicity of about 4 units or 3 cm, which is easily discerned even without examination of the autocorrelation functions. Transect 5 again has a patch size of about 2 units (1.5 cm) with a periodicity of about 6 units (4 cm). In summary, fine scale patches are frequently 1.5-2.0 cm in diameter and on average are about 3 or4 cm apart. The failure of the autocorrelation functions to damp reflects the presence of larger-scale trends in mean and variance within the transects. That the autocorrelation functions fluctuate around zero, rather than staying positive, indicates that areas of high ciliate density tend to be adjacent to areas of low ciliate density.
Effect of Spatial Heterogeneity on the Measurement of Species Association Patchiness in species' distributions may cause scale-dependent changes in their apparent spatial relationship. These scale-dependent changes can be examined by repeatedly combining or "blocking" adjacent samples frorrl the transects and recalculating similarity measures on the smaller set of larger samples. Some examples of spatial relationships (measured by linear cross-correlation coefficients) between taxa from the transects are given in Fig. 4. Figure 4A contains three examples of associations that become increasingly positive with blocking. The crustacea are primarily Cladocera and copepod nauplii while the rotifers are mostly Keratella sp. Figure 4B illustrates an opposite effect of blocking on the apparent correlation between numbers of Halteria grandinella and Strobilidium gyrans from 2 transects. In all cases, correlations between the abundance of taxa are weaker at smaller sample sizes. This observation is consistent with the fine-scale microfaunal patches being essentially monospecific, but independently distributed and overlapping. Repulsed monospecific patches would give rise to negative associations which would become less so with blocking. Contagious monospecific patches (i,e., mixed patches) would lead to strong positive associations at fine scales.
Discussion Visual inspection of the transects presented in Fig. 3 reveals that there are large differences among them in the abundance of ciliates. Within some of the transects there are coarse trends as well. Superimposed on these relatively large-scale patterns, which are probably stable over periods of perhaps days and may reflect population dynamic responses to resource levels, is a fine-scale heterogeneity which is probably very
Heterogeneity in Ciliate Distribution
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degree of blocking Fig. 4. The apparent correlation between pairs of taxa as a function of the number of samples combined or blocked together. A The increasing correlations between ciliates and crustacean zooplankton in transect 1 (broken line), between ciliates and rotifers in transect 2 (upper solid line), and between F. acuminata and a hypotrich in transect 2 (lower solid line). B The decreasing correlations between S. gyrans and H. grandinella in transect I (solidline) and transect 3 (broken line).
transient and may reflect behavioral aggregation in response to discrete food sources. Behavioral aggregation is suggested by the tendency of the autocorrelation functions to fluctuate around zero rather than remain positive, reflecting that areas of high ciliate density tend to be adjacent to areas of low ciliate density. Almost all of this variation mentioned above could be considered ephemeral spatial variation [7] since within site and within time variation are great in this pond [ 12]. Spatial variation at scales less than 1 m has been noted for marine plankton [4, 5]. The apparent association between species frequently becomes more positive or negative as samples are combined, reflecting that species are more independently distributed at the spatial scales at which behavioral aggregation is thought to occur. Independent behavioral aggregation suggests a way in which either filtering or grazing animals may utilize different resources that does require a more proximate mechanism of selective feeding. The ciliate species pairs used as examples in Fig. 4, F. acuminata and the unidentified hypotrich (probably Oxytricha sp.) and H. grandineUa and S. gyrans, are likely to occur in the surface film and the water column, respectively. Their relative independence at a fine scale is noteworthy as these species would be expected to have overlapping diets. Although the occurrence of ciliates in small patches is not an unexpected feature of the data, the uniform spacing of these patches in certain cases (particularly transect 3, which contained mostly Stentor polymorphus), is difficult to explain. It is possible that a mechanical process, e.g., the action of waves on the surface film, rather than a purely behavioral process may be involved in patch formation in some instances. It should be noted, however, that small-scale heterogeneity arises even on homogeneous artificial substrates [3, 9]. Irrespective of the mechanism of patch formation, the way in which species cope with or exploit this ephemeral spatial heterogeneity probably underlies the
34
W.D. Taylor and J. Berger
observed variation among ciliates in a constellation of attributes related to feeding, dispersal, and population growth [I 1]. Acknowledgments. This work was supported by NSERCC operating grant A-3473 to J. Berger. Financial assistance was also obtained from an Ontario Graduate Scholarship to W. D. Taylor. Mr. Stephen Taylor kindly constructed the sampler.
References I. Box, G. E. P., and J. M. Jenkins: Time Series Analysis-Forecasting and Control, Rev. ed. Holden-Day, San Francisco (1976) 2. Cairns, J., Jr., J, A. Ruthven, and R. L. Kaesler: Distribution of protozoa in a small stream. Am. Midl. Nat. 92,406-414 (1974) 3. Cairns, J., Jr., and W. H. Yongue, Jr.: The distribution of protozoa on a relatively homogeneous substrate. Hydrobiologia 31, 65-72 (1968) 4. Cassie, R. M.: Microdistribution of the plankton. Oceanogr. Mar. Biol. 1,223-252 (1963) 5. Hammer, W. M., and J. H. Carlton: Copepod swarms: attributes and role in coral reef ecosystems. Limnol. Oceanogr. 24, 1-14 (1979) 6. lwao, S., and E. Kuno: An approach to the analysis of aggregation pattern in biological populations. In G. P. Patil, E. C. Pielou, and W. E. Waters (eds.): Spatial Patterns and Statistical Distributions. Pennsylvania State University Press, University Park, Pa. (1971) 7. Lewis, W. M., Jr.: Comparison of temporal and spatial variation in the zooplankton of a lake by means of variance components. Ecology 59,666-671 (1978) 8. Lloyd, M.: "Mean crowding". J. Anim. Ecol. 36, 1-30 (1967) 9. Maguire, B., Jr.: The passive dispersal of small aquatic organisms and their colonization of isolated bodies of water. Ecol. Monogr. 38, 161-185 (1963) 10. Pielou, E. C.: Mathematical Ecology. John Wiley and Sons, New York (1977) I 1. Taylor, W. D.: Maximum growth rate, size and commonness in a community of bactivorous ciliates. Oecologia (Bed.) 36,263-272 (1978) 12. Taylor, W. D.: Sampling data on the bactivorous ciliates of a small pond compared to neutral models of community structure. Ecology 60 (in press)
