scales of spatial patterns of distribution of intertidal invertebrates

Oecologia (1996) 107:212-224 �9 Springer-Verlag 1996

A. J. Underwood- M. G. Chapman

Scales of spatial patterns of distribution of intertidal invertebrates

Received: 25 August 1995 / Accepted: 1 February 1996

Abstract Few comparative studies of spatial patterns at different scales have examined several species in the same habitat or the same species over a range of habitats. Therefore, variability in patterns among species or among habitats has seldom been documented. This study quantifies spatial patterns of a suite of intertidal snails and a species of barnacle using a range of statistical techniques. Variability in densities was quantified from the scale of adjacent quadrats (over a distance of centimeters) to tens of kilometers. Significant differences in abundances occurred primarily at two spatial scales. Small-scale differences were found at the scales of centimeters or 1-2 m and, for many species on many shores, these accounted for most of the variability in abundances from place to place. These are likely to be determined by behavioural responses to small-scale patches of micro- habitat. Large-scale differences in abundance were also found in most species at the scale of hundreds of meters alongshore. These are likely to be due to variation in recruitment (and/or mortality) because of limited dispersal by adults of these species. There was little or no additional variation among shores, separated by tens of kilometers, than was shown among patches of shore separated by hundreds of meters, Identification of the scale(s) at which significant differences in abundance are found fo- cus attention on the processes (and the scales at which these processes operate) that influence patterns of distribution and abundance. Some of the advantages and dis- advantages of various procedures are discussed.

Key words Fractal �9 Intertidal �9 Scale �9 Spatial pattern �9 Variance

A. J. Underwood ( ~ ) �9 M. G. Chapman Institute of Marine Ecology, Marine Ecology Laboratories A 11, University of Sydney, NSW 2006, Australia

Introduction

Analysis of spatial pattern is an essential basis for under- standing scales at which organisms interact with one another or with their environment. Non-random patterns of distribution and abundance usually identify the scales of processes which influence these patterns. Some processes can only act at small scales and some only at large scales. Documentation of pattern at a range of scales therefore focuses attention on the range of potential processes that may be important to species. Many statistical procedures have been developed to identify scales of spatial pattern, including h-scatterplots, correlations, serial autocorrelation, hierarchical analyses of variance, semivariograms, indices of aggregation or crowding, variances among paired samples, correlograms and fractal geometry (Pielou 1969; Goodall 1974; Cliff and Ord 1981; Palmer 1988, 1992; Carlile et al. 1989; Wirier et al. 1991; Cullinan and Thomas 1992; Rossi et al. 1992; Leduc et al. 1994). Many of these have been applied to ecological data, including estimates of patterns of dispersion of and variation in physical variables, chlorophyll and planktonic organisms (see the review volume edited by Steele 1978), some work on spatial structure in abundances of organisms in marine sediments (Morrisey et al. 1992; Thrush et al. 1994), patchiness of subtidal assemblages at different spatial scales (Chapman et al. 1995), the cover of terrestrial plants (Carlile et al. 1989; Leduc et al. 1994), patchiness of pelagic organisms (Downing 1991), distribution of insects with respect to algal cover (Sarnelle et al. 1993), patterns of abundance of beetles and barnacles (Rossi et al. 1992) and patchiness of environmental variables (Bell et al. 1993).

It is commonly held that samples closer together in space should be more similar to each other than those farther apart because of responses of organisms to patchy habitats or other organisms (e.g. Brown 1984; Palmer 1988, 1992; Carlile et al. 1989), although Bell et al. (1993) indicated that terrestrial habitats may be very variable at small spatial scales. Similarly, samples taken at short time intervals are generally thought to have

smaller variance than those at larger intervals because of serial autocorrelation (Pielou 1974) and temporal changes in abundances (see particularly Frank 1981; Connell and Sousa 1983).

For rocky intertidal systems, there have been studies focussed on the influences of various patchy processes of disturbance (Paine and Levin 1981), recruitment (Judge et al. 1988), scales of patchiness of intertidal assemblages (Sousa 1984; De Vogelaere 1993) and on spatial scales of diversity of species (Hawkins and Hartnoll 1980). Small-scale, local heterogeneity in habitat and the distribution and abundance of animals is well-documented in marine systems, including Australian intertidal (Underwood 1976; Underwood and Chapman 1989, 1992; Chapman 1994a, b) and subtidal rocky reefs (Ken- nelly 1987; Chapman et al. 1995). There has, however, been no work to examine simultaneously a variety of spatial scales of abundances of invertebrates on rocky shores in New South Wales.

The fractal dimension, D, summarises relevant as- pects of complex spatial patterns or temporal variability (Leduc et al. 1994). D can also be used to identify the sizes and distributions of patches of organisms or habitats (Carlile et al. 1989; Palmer 1992). It is affected by the grain of the pattern relative to the size of the sampling unit and the positions and orientations of the transects (or grids) from which it is calculated (Leduc et al. 1994). If variance between samples increases as samples are placed further apart (or the interval between them is increased), the slope of the plot of the semivariance (or variance) of pairs of samples against the distance (or time lag) between these samples will be positive. Flatten- ing of this slope indicates the range over which samples close together are no more similar to each other than those farther apart, i.e. the range over which data can be considered independent. Sarnelle et al. (1993) showed that dips in this asymptote were due to outliers in the data. A negative slope would indicate more similarity between samples further apart than those closer together. Methods such as semivariograms and fractal dimensions compare the magnitude of variance between two samples allowing a test of the general hypothesis that this will increase as samples are placed farther apart.

In addition to identifying scales of spatial pattern, similar techniques can be used to identify the scales at which samples are independent. Most statistical procedures to test hypotheses about ecological phenomena as- sume independent data, but it is reasonable to expect that samples that are not well separated in space or time might exhibit spatial or temporal dependence because of localized ecological processes. Autocorrelation, D and the slope of a semivariogram can be used to identify scales at which data are independent (Cliff and Ord 1981; Rossi et al. 1992).

Although useful in identifying spatial pattern in large and complex landscapes, many methods do not specifi- cally quantify any increase in variance over and above that shown at smaller spatial scales. In contrast to methods such as semivariograms or autocorrelations which

O E C O L O G I A 107 (1996) �9 Springer-Verlag 213

examine variability as a continuous function of scale, hierarchical analyses of variance only examine variance in block sizes to the power of 2 (or more) of the original block size. This, together with the fact that variance at the larger block size is calculated from fewer replicates than at smaller block sizes, is sometimes considered a disadvantage of this methodology (Palmer 1988). Hierar- chical analyses of variance, however, quantify any increase in variance at larger spatial scales and the relative importance of different scales to the overaI1 variability (Underwood 1981a; Wirier et al. 1991; Burdick and Graybill 1992; Morrisey et al. 1992; Searle et al. 1992).

Documenting the spatial scales at which significant differences in abundances of organisms are found can fo- cus attention on the relative importance of different ecological processes (e.g. small-scale behavioural processes in species with limited adult dispersal, large-scale patterns of mortality/recruitment) which may determine these patterns. Such documentation requires evaluation of the appropriateness of various available methods. Dif- ferent ecological processes influence densities of intertidal organisms on rocky shores at different spatial scales. Rocky shores in south-east Australia also provide a range of comparable species and some with very different ecologies that are known to be influenced by processes at several scales. For most intertidal species, which disperse via a planktonic larval stage but which have limited adult mobility, variations in recruitment and mortality will lead to variations in abundances from one shore to another, i.e. at scales of kilometers (Underwood and Denley 1984). Within a single shore, mobile animals can show considerable small-scale (less than meters to tens of meters) variability in abundance which is primarily determined by behavioural responses to habitat (Un- derwood 1976; Fairweather 1988a; Underwood and Chapman 1989; Chapman and Underwood 1994). Be- haviour of mobile predators may not only determine small-scale patterns of abundance of prey, but may itself be altered by these patterns of abundance (West 1988; Fairweather 1988b). At intermediate scales of tens or hundreds of meters upshore or alongshore, patterns of abundance may be determined by behaviour (e.g. the upper boundary of macro-algae may be determined by grazing of snails, Underwood 1980), differences in recruitment (Denley and Underwood 1979; Connell 1985) or mortality (Connell 1961) and combinations of these (Menge 1976; Underwood et al. 1983; Fairweather and Underwood 1991).

The aims of this study were to investigate spatial patterns in a range of common intertidal animals on exposed rocky shores in south-east Australia over different spatial scales using different statistical procedures and to test the general hypothesis that spatial variability differs at various distances between samples. We wished to examine patterns for several species in the same habitat. More importantly, we wished to determine how consistent patterns appear when analysed in replicated stretch- es of habitat. Many previous descriptions have come from only a single site or time of sampling. Quantifying

214 OECOLOGIA 107 ([996) �9 Springer-Verlag

description of pattern precedes any attempt at ecological a explanation. Thus, we are not attempting here to account for patterns observed. Nevertheless, because some processes are known or can be inferred (see above), we can discuss general hypotheses about the relative possible importance of recruitment, mortality and behaviour at various scales.

If behaviour of adults is important in determining these patterns, there should be significant variability in abundances at scales smaller than a few meters because these species do not disperse great distances after recruitment. If recruitment/mortality is important in determining patterns, there should be significant variability in abundances at scales of tens or hundreds of meters along a shore and from one shore to another. In sessile species, recruitment/mortality may also affect spatial variability at the scale of meters within a shore. They are, however, unlikely to determine spatial patterns at this scale in spe- b cies that are mobile, do not consistently home to the same point on the shore and which are known to move in response to their environment. The methods used in this study included semivariograms and fractal geometry, variances between pairs of quadrats, hierarchical analyses of variances, correlation co-efficients and autocorrelation. Data were collected in two general protocols to cover a range of spatial scales. At the smallest spatial scale on a single shore, animals were counted in contiguous quadrats along replicate transects a few or tens of meters long. At a larger spatial scale, animals were counted in replicate quadrats spaced within an hierarchical design along transects hundreds of meters long on shores separated by up to 30 km. Transects ran alongshore to incorporate the range of habitats occupied by each species because intertidal animals occupy an essen- tially linear habitat. Vertical distributions of species on r rocky shores vary in response to factors such as wave-ex- posure, slope, height in the tidal range, etc. On each shore, transects were alongshore at a height representative of the middle (from top to bottom) of the range of distribution of each species, thereby similarly represent- ing the population of each species on each shore. It is important to make comparisons of different scales without confounding differences in abundances caused by sampling outside the habitat of a species at some scales. Choosing to sample within a habitat (regardless of the actual presence or absence of the animal within the sampled quadrats) is entirely consistent with previous comparisons of spatial scales (Kummel et al. 1987; Carlile et al. 1989; Bell et al. 1993).

Materials and methods

All species were sampled on intertidal shores around Sydney, New South Wales, Australia. Shore 1 is within the Cape Banks Scientif- ic Marine Research Area on the northern headland of Botany Bay (Underwood 1975; Underwood et al. 1983; Fairweattler and Un- derwood 1991). Shore 2 (Long Bay) lies approximately 2 km north of shore 1. Shores 3, 4 and 5 (Little Head, Barrenjoey and Whale Beach) are approximately 30 km north of shores 1 and 2.

I I I I I I I I I I I I I I - - : 1 1 I I I I I t - s _ t _ L t . . . . . . . . . . . . . . . . . . . . . . . . .

t t t t t f . . . . . . . . . . . . . . . . . . . . . t t t t t

I I I I I I I I I I I I I - : S ] ' l ' l I I I

I I I I I I I I I I I I I I - - - 1 1 1 I I I l t _ t t=_t t _ f t _ ~ t__t t _ t t _ f t _ f L _ t

I I I I I I I I I I I I I I - - - - 1 I i I I I I I t t t t L t - - t t t t t t t t t t

I I I I I I I I I I f I I - - - _ 1 1 I J I I I t t t t t t 2 t t t t t t t f t t t t

I I I I I I I I I I I t l I - - ] 1 1 I I I I I f___1' f___1' t___t' ___I' f___1'

I I I I I I I I t I I 11 I - - - _ ] I I I I I I t t t t t _ ~ t I, 1, t t t

1 1 1 1 1 1 1 1 1 1 1 1 1 5 - - _ 1 1 1 1 1 1 1 t t t t t t t t

Fig. la-c Analyses of consecutive quadrats along replicate transects on a shore, a Serial autocorrelation is calculated with increasing distance between pairs of quadrats (i.e. separations) using all possible pairs of quadrats; b Pearson's r with increasing distance between pairs of quadrats using all possible pairs of quadrats without using any quadrat twice for each separation; c Pearson's r with increasing distance between pairs of quadrats using random pairs of quadrats for each separation (n = 10 or 20, see text for details)

All shores were sampled within a period of a few weeks, but all could not be sampled on the same day. All transects (and species) on a shore were sampled at the same time. These data, therefore, do not address temporal (e.g. seasonal) changes in spatial patterns, but spatial variability in these patterns.

All shores are gently-sloping sandstone rock-platforms with an extensive midshore area inhabited by a suite of intertidal snails, encrusting algae and barnacles (as described by Underwood 1975, 1981b). The micro-algal, grazing gastropods Austrocochlea porcata [=A. constricta (Lamarck)], Nerita atramentosa Reeve and Be- mbicium nanum (Lamarck), the limpet Cellana tramoserica (Sow- erby), the predatory whelk Morula marginalba Blainville and the barnacle Tesseropora rosea (Krauss) are the most common medi- um-large animals (up to 3-4 cm maximal dimension) on these shores. They were sampled from midshore areas on shores 1-4. Littorina unifasciata, small (< 1 cm long), abundant highshore periwinkles, were sampled along transects higher on the shore on shores 1-3 and on shore 5.

Contiguous quadrats along replicate transects

To examine patterns at the smallest spatial scale, A. porcata, B. nanum, M. marginalba, N. atramentosa and C. tramoserica were counted in contiguous 0.25-m 2 quadrats along three replicate 32-m transects (i.e. each of 64 contiguous quadrats) on shore 1. L. unifasciata were counted in 128 contiguous 20-cm 2 subquadrats in each of 15 replicate transects on shore 2.

Spatial pattern was quantified within each transect to test the hypothesis that variance in abundance is large at small spatial scales because it is determined by behaviour. This part of the study examined spatial pattern at the scale of centimeters to tens of meters only. We used serial autocorrelation, Pearson's correlation co- efficient, variances in abundance between random pairs of qua& rats (Goodall 1974), semivariances, D and hierarchical analyses of variance. Serial autocorrelations were calculated for all distances between pairs of quadrats (hereafter, referred to as separations) (Fig. la). The separation between pairs of quadrats varied from 1 (adjacent quadrats) to 32 (or 64 for L. unifasciata) (i.e. half of the length of the transect). Distances greater than half of the length of the transect were not included in these analyses because they are not adequately replicated along the length of the transect (Rossi et al. 1992). The significance of each value (i.e. for each separation along the transect) was determined from 1000 randomisations of the data for each transect, with the probability level set at 5%.

Product-moment correlation co-efficient (Pearson's r) was calculated in each of two ways. For the first set of r values, all available quadrats were used for each separation without any quadrat being used more than once for each calculation of r (Fig. lb) Therefore, n was larger for some separations than for others. For the second set of r values and estimates of the mean variance between pairs of quadrats, values were calculated from 10 (for smaller transects) or 20 (L. unifasciata) random pairs of quadrats (Goodall 1974) at each of a selected set of separations, i.e. at separations of 1-4 and then at intervals of 4 from 8 to 32 for the larger snails and at separations of 1-8 and then at intervals of 8 from 16 to 64 for L. unifasciata (Fig. lc). The significance of each r value was determined using a probability level of 0.05 corrected by the Bonferroni procedure for repeated tests using the same data. At the same time, the variance between each pair of quadrats was calculated and the mean variance and standard error calculated for each separation.


Hierarchical analyses of variance were done separately on each transect for block sizes of 2 (adjacent quadrats), 4, 8, 16, 32 (smaller transects) and 64 (L. unifasciata). Significance of the F- ratios was determined for each level of the analysis and the components of variation calculated from each mean square (using the completely hierarchical random effects model, as in Winer et al. 1991; see also Underwood and Petraitis 1993). Negative components of variation occur when higher level factors have very little additional effect on the variance and the contribution of higher level factors is, by chance, underestimated (or that of a lower level is, by chance, overestimated in the analysis). In these cases, negative values were set to zero, although this can bias the estimates of variance (Scheff6 1959; Winer et al. 1991). The percentage of variation for each level of the analysis was calculated as that com- ponent of variation divided by the sum of all components of variation (after negative values were set to zero) multiplied by 100.

Hierarchical sampling design on replicate shores

To examine patterns on a single shore at a larger spatial scale, densities were measured in a series of selected sites on a single 1212 m transect on shore 1. This distance spanned a greater range of habitats and environmental conditions (i.e. amounts of wave-ex- posure, which influences patterns of distribution and abundance on these shores; Underwood 1981b) alongshore compared to the replicate transects described above. Sampling was a nested design (Table 1) with four replicate 0.25-m 2 quadrats at each site. Dis- tances between sampling sites were selected to span those at which small-scale behavioural processes may operate (2 m and 10 m) and those at which spatial pattern might be determined by differences among habitats or patterns of recruitment (hundreds of meters). The larger snails and the barnacle T. rosea were counted in each quadrat; L. unifasciata were counted in five 20-cm 2 subquadrats per quadrat.

To examine spatial patterns at scales that include variation among shores, the larger snails and T. rosea were sampled along 212-m transects (with sampling sites at similar spacing to above; see Table 1) on each of four shores. The shores were arranged in a nested design, with two shores approximately 2 km apart, in each of two areas approximately 30 km apart. L. unifasciata were counted along 1212-m transects on the two shores in one area and at similar spacing along 712-m transects on the two shores in the other area. Smaller transects than 1212 m were necessary because many shores on this coast are smaller than 1 km in length and the larger species were not found along the entire length of each shore.

To examine the model that variance among samples increases with increasing distance between samples along the length of a shore, semivariances were calculated for each species using all pairs of quadrats at increasing separations along the 1212 m transects. For these analyses, the numbers of L. unifasciata per quadrat were estimated as the mean density per subquadrat multiplied by 121 (the number of subquadrats per quadrat). All semivariances calculated from fewer than 30 pairs of quadrats and those for which there was zero variance were omitted (Rossi et al. 1992) and D was then calculated. Fractal dimensions within replicate shores and at larger spatial scales among shores were also calculated from 212-m transects (for all species except L. unifasciata) and from 712-m transects for L. unifasciata. Semivariances were calculated for each species using all pairs of quadrats at increasing separations along each transect and the data from each transect

Table 1 Sampling design for analysis of spatial variance in densities of seven species of intertidal animals; n = 4 replicate quadrats at each site; Littorina unifasciata were counted in five replicate subquadrats per quadrat (i.e. a total of 20 subquadrats in each site)

Distances(m) ofsi tesat which samples were taken along ~ansect 0 2 10 12.....100 102 110 112 ......... 200 202 210 212 ........

......... 500 502 510 512.....600 602 610 612 ............. 700 702 710 712 ..........

............ 1000 1002 1010 1012 ........... 1100 1102 1110 1112....1200 1202 1210 1212

216 OECOLOGIA 107 (1996) �9 Springer-Verlag

were combined for the calculation of D. Semivariances were also calculated for 50 random pairs of quadrats from each set of shores ,~ 60. within each area (i.e. a quadrat on one shore was randomly paired with a quadrat on the other) and these were set at a distance of ~ 40 2 kin. Finally, semivariances were calculated across the largest $ distance by pairing 100 quadrats randomly selected from one of

6 20 the shores in one area to 100 quadrats randomly selected from one z of the shores in the other area. These pairs were set at a separation of 30 km. These values were included in the calculation of D 0 which therefore estimates variances at different distances along shores (averaged over all shores) and among shores at two large spatial scales�9

The data were also analysed using hierarchical analyses of t variance�9 Each species was examined along the 1212 m transects ~ (factor 1; 500-m intervals, 3 levels; factor 2, 100-m intervals, 3 -~ 0.5. levels, nested in factor 1; factor 3, 10-m intervals, 2 levels, nested in 1 and 2; factor 4, 2-m intervals, 2 levels, nested in 1, 2 and 3; 0 n = 4 quadrats and for L. unifasciata only, factor 5, quadrats, 4 levels, nested in 1, 2, 3 and 4; n = 5 subquadrats). The significance -~ of the F-ratios and the components of variation were calculated for ~-0.5 each level in the analysis. For comparisons among shores, 212-m or 712-m transects were similarly examined within two higher lev- -1. els in the analysis. Far shores examined variance across the two areas (i.e. at a scale of approximately 30 kin) and Near shores ex-

1- amined variance across shores within each of these areas (i.e. at a scale of 2 km).

R e s u l t s

Cont iguous quadra ts a long rep l ica te t ransects

~- 0.5-

60 t3_

-0.5

10 20 30 40 50 60 64 Distance along transect

�9 O 0 0 0

00 00000 0 O0 ~ ) 0 0 ~' ~ 0 0 ,

4 0 0 0 ~ 16 20 ~ o 28 32 Oo

Separation between pairs of quadrats

Abundances were a lways pa tchy (see examples in Figs . 2a and 3a). Ser ia l au tocor re la t ion a long t ransects genera l ly gave s igni f icant pos i t ive corre la t ions at the 1 smal les t spat ia l scale(s) (Table 2a), as shown for A. por-

~. o.5 cata on t ransect 1 (Fig. 2b) and N. atramentosa on tran- -= sect 2 (Fig. 3b). S igni f icant pos i t ive cor re la t ions were o

0 found be tween ad jacent quadrats in A. porcata (3 tran- ~ sects), B. nahum (2 t ransects) , C. tramoserica (3 tran- o_

-0.5 sects), M. marginalba (2 t ransects) and N. atramentosa (3 t ransects ; summar i s ed in Table 2a). For some species -1 on some transects , s ignif icant posi t ive corre la t ions were found at more than one smal l spat ia l scale (Table 2a). L. ~ ~ 50o unifasciata gave s igni f icant pos i t ive corre la t ions at the _ ~ smal les t spat ia l scale (i.e. be tween ad jacen t quadra ts ) in .~=~ 4oo 10 of 15 t ransects , at the next larges t scale in 7 t ransects 3"6 300 and at the next largest scale in 5 t ransects . S igni f icant ~-~ 8. 200 corre la t ions at la rger scales were not common , were pos- ~ ~, i t ive or negat ive and var ied among t ransects wi th in spe- Q ~ 100 cies and among species in id iosyncra t i c ways (Table 2, ~ 0 Fig. 3b). There was no genera l t rend for pos i t ive or nega- t ive cor re la t ion at any in te rmedia te or large scale wi th in or a m o n g species .

Ca lcu la t ion o f Pea r son ' s r us ing all poss ib le pairs o f quadrats (wi thout any quadra t be ing used twice for any s ingle ca lcu la t ion of r) and for r a n d o m pairs o f quadrats (wi th n = 10 or 20 quadra ts for each ca lcula t ion o f r) y i e lded s imi lar pat terns to those shown by serial au tocor- re la t ion (Figs. 2 and 3), a l though, in these analyses , only posi t ive corre la t ions were s ignif icant (Table 2b). Few corre la t ions were , however , s igni f icant after Bonfe r ron i ad jus tment o f the p robab i l i t y levels for mul t ip le tests using the same data (Figs. 2c, d and 3c, d). S igni f icant c o r -

c

o 0 O0 0 0 0 0

0 0 0 0 ~ 0 0 o _

, O0 0 0 , UO t3

" 0 0 6 0 0 12 16 20 Oo 28 32 O

O Separation between pairs of quadrats

O

O

d

O

O 0 0

0 0

o 8 12 16 20 24 28 32

O


e

�9 + , as �9 �9 �9 .at

4 8 12 16 20 24 28 32 Separation between pairs of quadrats

Fig. 2 a Number of Austrocochlea porcata per quadrat in 64 consecutive quadrats along transect 1; b serial autocorrelation between pairs of quadrats separated by distances from 1 (adjacent quadrats) to 32 (half the length of the transect); e Pearson's r for pairs of quadrats separated by distances from 1 to 32; d Pearson's r for 10 random pairs of quadrats separated by a preselected set of distances; e mean variance (SE) between 10 random pairs of quadrats separated by a preselected set of distances (see text for details); (Q significant values, �9 non-significant values)

30-

"~ 20- o-

~ 1 0 - O Z

1"

0.5. o 8 "5 0

~-05 Q. O9

-1

10

. . . . . ~ a

20 30 40 50 60 64 Distance along transect

0 o 0 o 0 o N , 0 ^ ~

4 8 12 ~176176 32 OO


I

,.. 0.5 e)

�9 ~ 0

o_ -0.5

0 O 0

O 0

000

0 0 O0 ' ' o u ' d oOd

0 8 12 016 o o O o o o o 32 O0 O0


0.5

0

n -0.5

0 O 0

0 O O

8 12 16 20 ~_4 o 32 O

0 Separation between pairs of quadrats

~'~ 8o,

~ 40'

x~ 0 4 8 12 16 20 24


e

28 32

Fig, 3 a Number of Neri ta a tramentosa per quadrat in 64 consecutive quadrats along transect 2; h serial autocorrelation between pairs of quadrats separated by distances from 1 (adjacent quadrats) to 32 (half the length of the transect); e Pearson's r for pairs of quadrats separated by distances from 1 to 32; d Pearson's r for 10 random pairs of quadrats separated by a preselected set of distances; e mean variance (SE) between 10 random pairs of quadrats separated by a preselected set of distances (see text for details); (O significant values, �9 non-significant values)

OECOLOGIA 107 (1996) �9 Springer-Verlag 217

relations were generally only found at the smallest spatial scale(s) (Table 2b). When random pairs of quadrats were examined, there were occasional significant correlations at larger spatial scales (e.g. at a separation of 16 quadrats for N. a tramentosa on transect 2; Fig. 3d). The animals were distributed very patchily along the transects (Figs. 2a and 3a), with large peaks of density generally only spanning one or two quadrats. These significant correlations, which did not occur when all quadrats along the transect were used, were probably due to the chance inclusion of a single quadrat with very large density in the calculation for that separation.

The average variance between pairs of quadrats did not generally increase as the distance between quadrats increased. Typically, the largest variance usually occurred at an intermediate separation and was often determined by one or a few large peaks in density (as shown for A. porcata, Fig. 2e). N. a tramentosa was the only species that tended to show an increase in variance with distance along some transects (Fig. 3e), due to a large- scale pattern of abundance superimposed on small-scale patchiness. For example, densities were smallest towards the middle of this transect and greatest at either end (Fig. 3a), leading to greatest variance between pairs of quadrats when they were separated by approximately half the length of the transects and therefore likely to be located towards the middle and either end (Fig. 3e). The similarity in densities at either end of the transect, however, suggests that had the snails been sampled for another 64 consecutive quadrats, variances would have again decreased as densities became more similar at these larger scales.

Hierarchical analyses of variance showed that significant differences among blocks were more common at the smaller size of block (Table 3). From the structure of these nested analyses, it is known that this is not a prob- lem of decreased power at larger scales where there are fewer degrees of freedom. In fifteen of these 21 transects, there were significant differences in either the smallest or the next-largest size (i.e. between the means of adjacent pairs of blocks or adjacent sets of four blocks, respectively), or both. In contrast, densities were usually similar across the larger block sizes. No significant differences were found between the two halves of the transect (i.e. block-size of 32) for the larger snails and only one transect showed a significant difference in densities between the two halves (i.e. block-size 64) for L. unifasciata. Patterns were similar for all species.

The components of variation also showed greater variation at the smallest spatial scale, in this case between adjacent quadrats (i.e. between the replicates in the analyses of variance), as illustrated for N. atramentosa (Fig. 4a), B. nanum (Fig. 4b) and L. unifasci- a m (Fig. 5). In contrast, C. t ramoser ica showed considerable variability at intermediate scales on some transects (Fig. 4c). Because the spatial scales are completely hierarchical (i.e. fully nested) and therefore commensu- rable, calculation of their relative contributions to variability in densities is of some value (see the discussion in

218 OECOLOGIA 107 (1996) �9 Springer-Verlag

Table 2 Number of transects with significant correlation a determined from serial autocorrelation and b determined by product- moment correlation using independent data and the Bonferroni pro-

cedure for determination of significance between quadrats separated by different distances along transects; n = 3 (only distances for which there was at least one significant correlation are presented)

Species Direction of correlation

Distance between quadrats

1 2 3 4...12 13 14 15...18 19 20 21 22...26 27..,31

a Serial autocorrelation

Austrocochlea porcata

Bembicium nanum

Cellana tramoserica

Morula marginalba

Nerita atramentosa

positive negative

positive negative

positive

positive

positive negative

b Product-moment correlation

A. porcata positive 1 - -

C. tramoserica positive 2 1 -

34. marginalba positive 1 -

N. atramentosa positive 2 1 -

3 - 1 . . . . 1 . . . . 1 1 - 1 1 -

2 . . . . . . .

. . . . . 1 - 1

3 3 2 1 . . . . . .

2 - - - 1 . . . . .

3 1 3 2 2 . . . . . . . . . . l 1 - - -

1 . . . . . .

1 . . . .

- 1 1 -

1 - - 1

T a b l e 3 Number of transects with significant F-ratios at different block sizes (in multiples of 2) of contiguous quadrats along transects 64 or 128 (L. unifasciata) quadrats long (number of transects = 15 for L. unifasciata, 3 for all other species)

Species Block size 64 32 16 8 4 2

A. porcata - 0 0 2 0 2 B. nanum - 0 1 0 0 1 C. tramoserica - 0 2 1 2 1 M. marginalba - 0 0 0 0 1 N. atramentosa - 0 0 1 1 1 L. unifasciata 1 2 4 1 3 5

Underwood and Petraitis 1993). The proport ion of variance accounted for by variabil i ty be tween adjacent blocks of the smallest size (0.25 m 2 for large snails or 20 cm 2 for L. un i fasc ia ta) was general ly large, 2 5 - 7 1 % (A. porca ta ) , 5 2 - 8 8 % (B. nanum) , 3 0 - 4 2 % (C. t ramoser- ica), 3 4 - 8 3 % (M. marg inaIba) , 2 1 - 5 2 % (N. at- ramen tosa ) and 3 1 - 9 3 % (L. uni fasciata) . In contrast, the proport ion of variabil i ty accounted for by differences between the largest size of block (0.5 m x l 6 m for large snails or 4.5 cmx288 cm for L. un i fasc ia ta) was very small, 0 - 1 % (A. porca ta ) , 0 - 1 0 % (B. nahum) , 0 - 1 2 % (C. t ramoser ica) , 0 % (34. marg ina lba) , 0 % (IV. at- ramen tosa ) and 0 - 1 4 % (L. uni fasciata) .

Hierarchical sampling design on replicate shores

Sampl ing along 712-m and 1212-m transects gave fractal d imens ions D similar to a value of 2 for all species (Table 4a), indicat ing spatial independence of samples at all scales, i.e. at all distances apart. Densit ies varied consid-

3 O

2 0

1 0

0

-10

| �9

II �9

124 ; t'6 24

10

.g 8

tg 6 �84 >

"6 �9 4 ffl

=m 2 o im 13.

0 �9 16 2'4 i

40

20

0

-20

I

: c

�9 ~6 24 32

B l o c k - s i z e

Fig. 4 Components of variation calculated from an hierarchical analysis of variance for block-sizes of 1 (adjacent quadrats) to 32 (half the length of the transect) for a N. atramentosa, b Bembicium nahum and e CeIIana tramoserica

200

"6

O

150

100

50

, ~ I i

-50-

|

�9 . " ,i ! 10 20 30 40 50 6'0 70

Block-size

Fig. 5 Components of variation calculated from an hierarchical analysis of variance for block-sizes of 1 (adjacent quadrats) to 64 (half the length of the transect) for L. uni fasciata

erably along the transect, but were extremely patchy from site to site and there were no general trends (illustrated for A. porcata, C. tramoserica and L. unifasciata (shore 1) in Fig. 6). The value of D for N. atramentosa was greater than 2 which indicates that samples further apart are more similar than those closer together, due to a large patch with big densities towards the middle of the transect and smaller densities at either end. As expected from

OECOLOGIA 107 (1996) �9 219

Table 4 D (fractal dimensions) within a 712-m and 1212-m-long transects within single shores and b within 212-m or 712-m transects within replicate shores and across shores separated by 2 km or 30 km

Shore Length Species D of transect

a Within shores

Shore 1 1212 m A. porca ta 2.09 Shore 1 1212 m B. nahum 2.00 Shore 1 1212 m C. t ramoser ica 2.02 Shore 1 1212 m M. marginalba 2.01 Shore 1 1212 m N. a t ramentosa 2.38 Shore 1 1212 m Z Jvsea 1.97 Shore 1 1212 m L. uni fasciata 1.94 Shore 2 1212 m L. uni fasciata 2.00 Shore 3 712 m L. uni fasciata 2.00 Shore 5 712 m L. uni fasciata 2.00

b Within and among Shores

Shores 1-4 212 m A. porcata 1.97 Shores 1-4 212 m B. nahum 1.91 Shores 1-4 212 m C. t ramoser ica 1.91 Shores 1-4 212 m M. marginalba 1.90 Shores 1-4 212 m N. a t ramentosa 1.96 Shores 1-4 212 m T. rosea 1.91 Shores 1-3, 5 712 m L. uni fasciata 1.95

Fig. 6 a, c, e Mean density 6 (SE) per 0.25 m 2 quadrat a for a nested set of samples 30] 4 along a 1212 m transect (details t § of spacing between samples 20 t 4 O ~ 2 in text); b, d, f semivariograms for all distances (lags) between 0 all quadrats along the transect 11t for a, b A. porcata , c, d C. t ramoser ica and e, f L. uni- eeq . .-,~,=-,..z,. r , . .~176 ~-~?l~.~e.,~eO.;, . . . . . . -2

fa sc ia ta

b

c 8 6 l ~40t + , , .~4

' A~ �9 �9 ~ J" E J &-o �9 oeT ~' ,,....2 to ~ - e OoeOO oeeo o04~oo o

. . . . . . . . . . . . . . . . . .". . . . . . . . . . . . . . , . ! . -JO r

e 16

4000] + 12

§ 8 2ooo 1

Samples along shore (not to scale)

Log of distance between pairs of quadrats

220 O E C O L O G I A 107 (1996) �9 Springer-Verlag

Table 5 a Significance of F- ratios and b percentage contribution to the variance of each spatial scale from that of replicate quadrats (or subquadrats in L. unifasciata) to sites 500 m apart (see text for details), for seven species of intertidal animals

ns P>O.05, * P<O.05, �9 * P<O.O1, *** P<O.O01

Species Source of variation

500m 100m 10m 2 m Quadrat Subquadrat

a Significance of F-ratios

A. porcata ns *** ns ** B. nahum ns ** ns *** C. tramoserica ns ** ns ** M. marginalba ns * ns ns N. atramentosa ** ns ns *** T. rosea ns ns ns *** L. unifasciata (shore 1) ns *** ns **

(shore 2) ns ns * ns

b Percentage contribution to the variance

A. porcata 18 55 5 6 B. nahum 0 47 0 20 C. tramoserica 0 57 8 9 M. marginalba 0 16 1 0 N. atramentosa 26 0 3 33 T. rosea l0 5 21 33 L. unifasciata (shore 1) 1 16 0 12

(shore 2) 0 4 7 4

16 32 26 83 38 31

5 66 7 78

Table 6 a Significance of F-ratios and b percentage contribution to the variance of each spatial scale from that of replicate quadrats (or subquadrats in L. unifasciata) to sites 100 m apart on replicate shores and between shores 2 km (near shores) or 30 km (far shores) apart (see text for details)

* P<0.05, ** P<0.01, *** P<0.001, ns P>0.05

Species Source of variation

Far shores Near shore 500m 100m 10m 2 m Quadrat Subquadrat

a Significance of F-ratios

A. porcata ns ns - ns ns *** B. nanum ns ns - ns ** ** C. tramoserica ns ns - ns ns * M. marginalba ns ns - ns ** ns N. atramentosa ns ns - ns * ns 71. rosea ns ns - *** ns ns L. unifasciata ** ns ns *** ns *** **

b Percentage contribution to the variance

A. porcata 0 11 - 0 16 38 35 B. nanum 1 25 - 0 40 9 25 C. tramoserica 0 14 - 4 2 70 10 M. marginalba 0 0 - 36 28 3 33 IV. atramentosa l 8 0 - 20 20 7 35 T. rosea 0 5 - 51 0 8 36 L. unifasciata 12 0 0 2 6 3 5 72

the va lues o f D, the s e m i v a r i a n c e p lo ts s h o w e d no pos i - t ive s lope (Fig. 6) and the re was c o n s i d e r a b l e va r i ab i l i t y in v a r i a n c e s b e t w e e n s imi la r d i s t ances , h e n c e the l ack o f a s m o o t h s lope. Th i s is due to the s m a l l - s c a l e pa t ch ine s s in dens i t i e s a m o n g i n d i v i d u a l quadra t s , c a u s i n g l a rge o r sma l l v a r i a n c e s d e p e n d i n g on w h e t h e r quadra t s w i t h l a rge dens i t i e s w e r e i n c l u d e d in the c a l c u l a t i o n o r not.

S i m i l a r t r ends w e r e f o u n d w h e n t ransec t s w e r e c o m - pa red w i t h i n and ac ross shores s epa ra t ed by app rox i - m a t e l y 2 o r 30 k m , a l t h o u g h f rac ta l d i m e n s i o n s w e r e s l igh t ly s m a l l e r fo r m a n y spec i e s (Tab le 4b). T h e r e f o r e , the re was i n c r e a s e d va r i ab i l i t y a m o n g s a m p l e s at the l a rge r spa t ia l sca les o f k i l o m e t e r s , w h i c h i n c l u d e d var i - ab i l i ty f r o m sho re to shore , bu t th is was no t l a rge e n o u g h to a l ter g rea t ly the v a l u e o f D, i.e. the re was spat ia l i nde - p e n d e n c e w i t h i n and a m o n g shores .

H i e r a r c h i c a l ana ly se s o f v a r i a n c e o f dens i t i e s a l o n g the 1212 m t ransec t s s h o w e d s ign i f i can t d i f f e r e n c e s be- t w e e n si tes s e p a r a t e d by the sma l l e s t d i s t ance , i .e. 2 m apart , o v e r and a b o v e the v a r i a n c e a m o n g r ep l i ca t e quad -

rats, fo r al l spec ies e x c e p t M. m a r g i n a l b a and L. uni fas- c ia ta on shore 2 (Table 5a). L. un i fasc ia ta s h o w e d s ign i f - i can t d i f f e r e n c e s at the l eve l o f quad ra t s on e a c h shore . T h e ba rnac le , T. rosea, s h o w e d no l eve l s o f s i g n i f i c a n c e a b o v e this. S a m p l e s at i n c r e a s i n g d i s t ances apart , f r o m 10 m to 100 m to 500 m (on a v e r a g e o v e r all s i tes on the shore) , w e r e no m o r e d i f f e ren t f r o m e a c h o the r than sam- p les 2 m apart . O t h e r spec ies s h o w e d s ign i f i can t d i f fe r - ences a m o n g si tes e i the r 100 or 500 m apart , but at o n l y o n e o f these scales . T h e r e was no gene ra l t r end fo r s ig- n i f i c a n c e l eve l s to inc rease , i.e. for s i tes to b e c o m e m o r e d i f fe ren t , as t hey b e c a m e fu r the r apar t (Table 5a).

The percentage contribution of the components of variation showed a similar trend with large variation at even smaller scales, i.e. among replicate quadrats within each site or, in the case of L. unifasciata, among replicate subquadrats per quadrat (Table 5b). The percentage of variation accounted for by variance among replicate quadrats ranged from 83% of the variation for M. marginalba to 16% for A. porcata and subquadrats (i.e. replicate patches 20 cm 2 approximately 20-30 cm apart) provided between 66% and 78% of the variance in densities of L. unifasciata (Table 5b).

Similar results were found when variances were compared within transects, across nearby shores and across widely-separated shores and there were no significant differences in densities across shores (at either scale) for any species except L. unifasciata (Table 6). Nearby shores added between 0% (N. atramentosa, L. unifasci- am and M. marginalba) and 25% (B. nahum) to the variance; widely-spaced shores added between 0% (C. tramoserica, T. rosea and M. marginalba) and 18% (N. atramentosa) to the variance. Therefore, most variability in distribution and abundance of these species was between replicate quadrats within a shore, often at the smaller spatial scales. There was little variability among shores and greater variance among shores separated by up to 30 km away than among quadrats within a site or among sites on the same shore.

Discussion

All species in this study showed most variation in patterns of abundance at the smallest spatial scales, between contiguous quadrats or between those separated by less than 1 m along transects, or among replicate quadrats or subquadrats in a site (i.e. among adjacent patches of habitat only 0.25 m 2 or 20 cm 2 in size). Den- sities of animals in contiguous quadrats along replicate transects were generally positively correlated between adjacent quadrats, but, except for the large limpet C. tramoserica, there were no consistent patterns when distances between quadrats increased (up to distances equivalent to half of the length of the transect). Densities of C. tramoserica were positively correlated when distances between quadrats varied from zero (i.e. adjacent quadrats) to approximately 1-2 m (distances 2 to 4 quadrats apart). Similar patterns were obtained using serial autocorrelation or Pearson's r, but in the latter analyses fewer scales of spatial separation gave statistical- ly-significant results when the probability levels were adjusted for multiple tests using the same data. Signifi- cant correlations at the smallest scales were obtained because the animals were distributed in small patches, with large peaks in abundance which usually only extended over approximately 1 m (i.e. adjacent quadrats) or a few meters (C. tramoserica). These large peaks were separated by similar-sized patches of smaller abundances. N. atramentosa was the only species that showed a larger pattern of abundance superimposed on small-scale


patchiness, with densities decreasing over approximately 16 m and then increasing again.

The close relationship between local density of the whelk M. marginalba and crevices has been extensively documented (Fairweather et al. 1984; Moran 1985; Fair- weather 1988a). This species is commonly associated with particular patches of habitat (i.e. crevices and holes) which may vary in abundance at scales of tens or hundreds of meters. Similarly, patchiness in densities of A. porcata is related to availability of pools (Underwood 1976), which are scattered at spatial distances of a few to tens of meters. L. unifasciata are similarly associated with cracks, crevices and holes (Underwood and Chap- man 1989, 1992; Chapman t994a, b), which appear to vary in abundance at a scale of centimeters in some areas and many meters in others. Evidence from this study shows, however, that most spatial variability in abundances is at the smallest spatial scale(s), i.e. at centimeters to meters. This may be explained by a haphazard scattering of suitable microhabitats across a shore and, therefore, the associated densities being uncorrelated at all except the smallest spatial scales, which are within these microhabitats. Variance in spatial pattern of such topographic features has not yet been quantified, but we predict that it will show no patterns at relatively large scales. The distribution of N. atramentosa suggests that they respond to features of habitat varying at scales of tens of meters alongshore.

Other analyses showed that, except for N. atramentosa, variance between pairs of quadrats separated by different distances along replicate transects did not increase with increasing distance between quadrats as has been proposed when abundance of organisms is determined by environmental variables (Brown 1984; Palmer 1988, 1992; Bell et at. 1993). If densities were similar along the transect, it may be argued that the scale over which these animals were sampled was not large enough to encompass different habitats or patches and therefore one would not necessarily expect such an increase. The large amount of small-scale variability in densities along the transects, however, suggests that the opposite is the case. Environmental cues that govern abundances of these species are extremely small-scale and locally variable. As such, they are more likely to alter spatial variation in abundance via behavioural processes than via processes of recruitment and/or mortality.

These intertidal snails move around on a daily basis, thereby regularly changing patterns of distribution. These changes occur at a relatively limited scale because most of these species move less than a metre and often only a few centimeters during most high tides (Under- wood 1976, 1977; Underwood and Chapman 1989; Chapman 1986, Chapman and Underwood 1994). Pat- terns of distribution during low tide reflect activity during previous high tides. Because of their limited dispersal as adults, active animals encounter the range of environmental conditions found at small scales. Differences in abundance between adjacent quadrats or samples taken at distances of two or ten meters are therefore likely

222 O E C O L O G I A 107 (1996) �9 Springer-Verlag

to be influenced by the behaviour of the animals distrib- uting themselves among patches of habitat during or after a period of activity. Foraging movements of predatory whelks, such as M. marginalba, can similarly alter patterns of distribution of their sessile prey (Fairweather et al. 1984; Moran 1985; Fairweather 1988a). Small-scale patterns of abundance of T. rosea may therefore also reflect patterns of behaviour of M. marginalba (Fairweath- er and Underwood 1991). If behaviour (rather than mortality or recruitment) determine these patterns of dispersion, we predict considerable variation in patterns at short time-scales consistent with tidal movements rather than seasonal or annual patterns of recruitment or mortality. Experimental tests of these proposals are planned. Note that Bell et al. (1993) stated that terrestrial habitats (e.g. forests or cultivated fields) could be extremely variable at the scale of a few meters, but they examined variances at the scale of kilometers and hundreds of kilometers to examine variances among samples. Any small- scale variability was ignored and fused together to obtain a representative sample from a site. The small-scale patchiness in their habitats may therefore have been great, but it was not measured.

Analysis of spatial patterns at the scales of tens to hundreds of meters alongshore and between shores separated by approximately 2 or 30 km showed large-scale spatial patterns that are likely to be caused by differences in recruitment and/or mortality. Along a single shore, all species except T. rosea and L. unifasciata (on shore 2) showed significant variation in densities at scales of hundreds of meters. Because of no or limited dispersal by adults of these species, it is unlikely that such patterns could be explained by behavioural responses of adults to microhabitats. Differences may, however, be caused by larval behaviour, reflected by variation in recruitment or by mortality after recruitment. Except for differences in densities of L. unifasciata among shores 30 km apart, all other species showed similar densities among different shores, whether these were separated by 2 or 30 km. Variability in abundance was nearly all contained within shores. Much of it was accounted for by variability among replicate (sub)quadrats or sites 2 m apart, again probably reflecting behavioural processes. Abundances within shores were as variable (and similar to) those among shores, suggesting that variation in recruitment/mortality is determined by processes that vary along a shore, causing patchiness in densities across a shore as great as that among shores. These shores were, however, selected to represent typical open-coast shores; recruitment, small-scale patterns of dispersion and behaviour do vary between open and extremely sheltered shores (Underwood 1996).

These data, therefore, suggest that in this suite of intertidal animals, patterns of abundance are determined by many different processes. Hypotheses about the relevant processes can be proposed once the patterns have identi- fied the appropriate spatial scales. Behavioural interac- tions among animals or between them and small-scale

environmental variables (Underwood 1976; Chapman 1994a, b; Chapman and Underwood 1994) are likely to govern pattern at scales smaller than a few meters. This is very important and accounts for much of the variability in pattern within shores in those species in which adults can disperse and respond to their habitat. Sessile species may, however, be affected by small-scale environmental variability directly causing mortality (Connell 1961; Dayton 1971) or by localized behaviour of more mobile species (Fairweather 1988b). Differences in densities along shores at the scale of hundreds of meters are probably due to differences in recruitment among patches of shore, although differential mortality is also possible (Dayton 1971; Underwood et al. 1983; Menge et al. 1985; Fairweather and Underwood 1991). As long as shores are selected to represent similar habitats, there is very little difference in density from shore to shore. Sim- ilar (or comparable) processes are likely to account for spatial patterns in other species that disperse widely via propagules, but which have little or no adult dispersal, e.g. most plants.

This study was not designed to provide a comparison of the statistical properties of the various methods used. That topic has been done thoroughly by previous reviews (e.g. Cliff and Ord 1981; Cullinan and Thomas 1992; Rossi et al. 1992). It is, however, worth reiterating some points. First, the techniques cannot all be compared to determine which is "best". They are appropriate for different tasks. As Rossi et al. (1992) pointed out, they are probably best incorporated into a study with (and, per- haps, best of all after) the usual array of descriptive and inferential statistical analyses of data have been used. Thus, serial autocorrelation is a technique well-suited to analyses of patterns in patchy habitats where there are clear cyclic trends in abundances across the area. Of the three varieties of correlations used here, serial autocorrelation had the greatest capacity (power) to detect significant small-scale patterns - largely because it used the most data. It also uses all of the data non-independently and seems most likely to be affected by any small-scale anomalies in patterns of clumping of animals. Using independent (Pearson) correlations at each spacing of quadrats allows completely independent tests at any spacing. Picking the same number of data points for each spacing at random from those available solves the prob- lem of greater size of sample at some scales.

Using serial autocorrelations or fractals allows precise definition of scales at which quadrats (or anY other sampling units) are spatially independent. This is useful for planning ecological experiments (see also Underwood 1994). There seems to have been little discussion of how to test hypotheses about values of fractals (D) - probably because most studies have a single estimate based on one transect of data. Where replicated transects are sampled, replicate estimates of D are available and any of the clas- sical inferential procedures can be used. For example, to test the null hypothesis that data are distributed with "white noise" variances and no pattern at different spa-

OECOLOGIA 107 (1996) �9 Springer-Verlag 223

tial scales, the null hypothesis that D = 2 could be tested by a t-test using the mean and standard error of D from replicate transects.

Nested analyses and calculation of variances at different spatial scales provide a different assessment of pattern. These methods are uniquely capable of providing independent estimation of variance at each spatial scale uncluttered by confounding with variation at smaller scales. Their overwhelming advantage over such techniques as the more widely-used block procedures of Greig-Smith (1983) is that data are taken independently at each scale allowing straightforward statistical testing in the hierarchical analysis of variance. The spatial scales at which processes cause variations in abundance are then easily detected and the magnitides of variances estimated. Tests of hypotheses about or confidence limits for these estimates are available (Burdick and Graybill 1992; Searle et al. 1992), Where replicated estimates are available, hypotheses about differences between habitats are straightforward (Underwood 1996).

The major difference between hierarchical analyses of variance and "continuous" procedures, such as analyses using fractals or autocorrelation, is that there are fewer problems with imposing arbitrary scales onto the study, as is inevitably necessary for sampling for nested de- signs. There are fewer problems, but the choice of size of sampling unit, length of transect and where it starts will all have potentially large influence on the outcome. The major advantage of nested analyses over the other procedures is that much larger spatial scales can be sampled because the data do not have to be collected continuously over the entire range of the study.

These analyses indicate that samples are independent if the distance between samples is greater than 50 cm (1 quadrat) or 5 cm (1 subquadrat) for most species (and greater than 2 m for C. tramoserica). They validate commonly-used methodology of sampling intertidal assemblages on shores in New South Wales and elsewhere, where the distance between replicate quadrats within a site is generally greater than 1 m and the distance between replicate subquadrats within a quadrat is approximately 20-30 cm (or the length of six subquadrats) (see also Underwood 1996). They also suggest that for most species an area of approximately 16 m 2 can adequately represent a site (Chapman 1994b; Underwood 1996) because most variation in density is found within an area of those dimensions. Replicate sites are then necessary to represent adequately a shore (Underwood 1981a; Hurl- bert 1984).

Acknowledgements We thank the Australian Research Council (for a Special Investigator's Award to A.J.U.) and the Institute of Marine Ecology for financial support. We thank one referee of that grant for stating that correlative analyses would be more useful than nested analyses - prompting this convincing rebuttal. We thank K. Astles, E Gibson, T. Glasby, J. Harris, G. Housefield, V. Mathews and S. McCune for assistance in the field. Anonymous referees and C.H. Peterson provided helpful improvements to the manuscript.

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