A spatially explicit approach to trophic interactions and landscape formation: patchiness in small-scale variability of grazing effects along an intertidal stress gradient

Summary

1. It is well known that grazing contributes to spatial and temporal patterns of algal cover on rocky shores, but this effect has traditionally been studied through grazer exclusion experiments using randomly positioned treatments at particular levels on the shore. Additionally, the effects of grazing on algal composition and biomass are expected to vary across gradients of physical stress and according to grazer size classes.

2. We examine two possible sources of spatial variability on rocky shores: (i) across-shore variability and (ii) size class of grazers. We combined this approach with an across-shore experiment, with experimental blocks running continuously from low to high shore, to examine the spatial structure of the effect strength of grazing for different size classes of grazers.

3. The results indicate that grazing effects vary among zones, habitats and grazer size classes. Micrograzers played a weak role in structuring the algal community and composition. Both macrograzers and mesograzers were important structuring agents on the upper low shore to the mid shore, but only mesograzers were important in tidal pools. Patterns across the shore of grazing effects were dynamic and patchy, acting simultaneously at different scales. The spatial pattern of grazing effects across the shore was also variable in time and was explained by the interactions among physical and biotic factors, often at the longer (10-m scale) spatial intervals (or lags); mesograzers influenced almost the whole range of lags.

4. We conclude, based on cross-semivariograms, that abiotic factors set variability at large scales, while the effects of biotic factors (in this case grazing) operate simultaneously at scales ranging from small to large.

5.Synthesis. Combining zonation and across-shore experiments indicates that grazing effects do not follow a continuous gradient, but instead have a patchy distribution. This approach provides information about spatial variability that is not available using only the traditional approach, contributing to our understanding of zonation models.

Introduction

The formation of landscapes is a dynamic and hierarchical process involving the interaction of physical factors and biotic components (Levin 1976; Collins 1992; Dale 2000; Turner, Gardner & O’Neill 2001). Understanding not just the temporal, but also the spatial variation in the interaction of biology, environment and disturbance which shapes landscapes is one of the central challenges in ecology and requires that spatial complexity be estimated. Using indices of spatial heterogeneity, it is possible to describe the complexity of different levels of organization within an ecosystem (from the level of an individual organism to that of a community), and also of the factors influencing the spatial patterns observed, such as disturbance (Veen et al. 2008). Spatial heterogeneity is defined as the degree of spatial dependence between the variance of a variable and some spatial dimension (Palmer 1988; Dungan et al. 2002). Grazing is one of the fundamental trophic interactions that modulate landscapes by creating spatial patterns in the vegetation in both terrestrial (Belsky 1983; Burns, Collins & Smith 2009) and marine systems (Underwood & Jernakoff 1984; Coleman et al. 2006), and has traditionally been examined using grazer exclusion experiments. Here we use grazing effects on a rocky shore as a case study to analyse how different physical and biological effects interact to shape the landscape of a marine rocky shore across a gradient of desiccation stress. We focus on marine benthic systems, but note parallels in the development of our understanding of grazer–plant interactions in terrestrial systems.

State of the Art

Grazing in intertidal landscapes

The biology of rocky shores exhibits complex spatial configurations at small scales because of the continuously changing balance between marine and terrestrial conditions. For simplicity these landscapes are traditionally divided into three major regions or zones, which vary in distance and height from the mean height of low water spring tides (MLWS): low, mid and high shore (Hawkins & Hartnoll 1983; Menge & Branch 2001). These regions differ in the diversity, strength of trophic interactions and spatial heterogeneity of the organisms they support because they represent regions along a gradient of stress that marine organisms suffer when exposed to increasingly terrestrial conditions (Hawkins & Hartnoll 1983; Foster 1992; Menge & Branch 2001).

From the 1960s to the 1970s, considerable effort was expended in identifying the proximal causes of zonation. The overall conclusion was that intertidal landscapes are shaped by physical factors represented by two gradients of stress: that of emersion (desiccation and heat, or freezing in cold latitudes) when the tide retreats (this gradient increases upshore (Southward 1975)) and that of wave action, which increases downshore and towards high tide. Wave action simultaneously causes disturbance through dislodgement of organisms and delivers propagules. Parallel to the search for the role of physical factors in causing zonation, other studies examined the role of biotic factors such as grazing and predation. These latter studies included the use of predator exclusion approaches, such as predator removal from some areas and the use of exclusion cages (Connell 1961; Kitching & Ebling 1961; Paine 1966; Dayton 1971). From the 1970s to the 1980s, grazing and predation were studied at different levels on the shore, focusing on how the interplay between abiotic and biotic factors drives zonation (Lubchenco 1978; Sousa 1979; Underwood 1980; Branch 1981; Jara & Moreno 1984; Underwood & Jernakoff 1984). Since the late 1990s two divergent lines of approach have developed. Some studies have examined changes in community structure at large spatial scales of hundreds of kilometres (bioregional and continental scales) using grazing exclusions (Bustamante, Branch & Eekhout 1995a; Bustamante et al. 1995b; Menge & Branch 2001; Coleman et al. 2006). These studies showed that there is high variability induced by the regional conditions in which a system is embedded. In these studies, patchiness within zones at small scales was almost always observed. This was usually reported but not quantified, and sometimes considered as ‘residual variability’ or variability not explained by the trophic interaction analysed in both terrestrial (Belsky 1983) and marine systems (Benedetti-Cecchi 2000). However, species interactions occur on much smaller spatial scales that depend on the physical size and mobility of the organisms and at the same time other studies focused on the meaning of such small-scale patchiness, considering it as emanating from the inequality in distribution of benign and harsh conditions for each species. Abundances of species vary accordingly, as does the strength of their interactions. For example in the case of rocky shores, small-scale topographic complexity can create humid depressions where conditions are benign for seaweeds and grazers, weakening the effects of grazers on algae, because grazers also received benefits through an increase of food availability (Williams 1993, 1994; Benedetti-Cecchi & Cinelli 1995; Williams, Davies & Nagarkar 2000). The interactive effects of grazing and disturbance were also studied in terrestrial systems in the late 1990s (Milchunas & Lauenroth 1989; Collins 1990, 2000; Knapp et al. 1999; Collins & Smith 2006) and, as with marine systems (Atalah, Anderson & Costello 2007), inequality in the distribution of disturbance and grazers was found to influence plant patchiness (Adler, Raff & Lauenroth 2001; Veen et al. 2008). At the same time, others investigated the small-scale effects of grazers in relation to variations in primary productivity and the consequences for overall algal or plant assemblages (Bakker, de Leeuw & van Wieren 1983; Belsky 1983; Branch et al. 1992; McQuaid & Froneman 1993).

All these past efforts seemed to be framed in a context of spatial reductive determinism with an unstated assumption that spatial patterns in landscapes as a whole can be predictable if it is possible to calculate each factor exactly. Finally, towards the 2000s, intertidal studies started to re-focus on predicting certain types of spatial and temporal configurations, for example random versus non-random spatial arrangements or temporal cycles of abundance and recruitment of species (Schaffer & Kot 1985; Johnson et al. 1997; Burrows & Hawkins 1998; Johnson, Burrows & Hawkins 1998; Menge et al. 2005). Spatial statistics have started to play a strong role in the identification of non-random patterns and in estimating the complexity of systems (Dale et al. 2002; Denny et al. 2004), while other studies have concentrated on explaining spatial variability of resources in trophic interactions without taking into account either the spatial structure of the resources or the spatial structure of the trophic interaction (Berlow 1999; Benedetti-Cecchi 2000, 2003). Previous studies have aimed at understanding the scales at which ecological processes occur in the intertidal, using several geostatistical tools (Denny et al. 2004; Erlandsson & McQuaid 2004). However, in the intertidal, the across-shore gradient from low-shore marine to high-shore terrestrial conditions forms a spectacularly intense gradient of physiological stress and these studies have mainly examined processes along the shore at the same tidal height, i.e. at the same point along the marine to terrestrial gradient. Here, we analyse the spatial structure in the variability of a trophic interaction across this gradient, expecting to find a gradual decay in the variance of this interaction as the severity of abiotic conditions (as perceived by marine species) increases across the landscape.

Grazer size classes

A further source of complexity is the mode of feeding and the size of grazers. Algal spatial patterns can be extremely complex when different types and sizes classes of grazers converge to inhabit the same parts of the shore simultaneously. Grazers can affect algae at two ontogenetic stages: by consuming (i) adult plants or (ii) algal sporelings and propagules (Hawkins & Hartnoll 1983; McQuaid 1996; Johnson et al. 1997; Burrows & Hawkins 1998). We categorized grazers according to body size as macrograzers, mesograzers and micrograzers, as size closely correlates with both mode of feeding and diet, and we were able to exclude different size classes in our experimental treatments. These types of grazers often coexist within zones so that their effects are interactive (McQuaid 1982), but they show broad trends of differential vertical distribution (Hawkins & Hartnoll 1983; Branch et al. 1992; Foster 1992; Menge & Branch 2001). We predicted that the strength of grazing effects on the algal community will depend partly on the balance of the size classes of the grazers present.

Grazing strength across the shore

Models of the intensity of grazing effects as a function of distance up the shore describe impact as increasing with elevation up to the mid shore, after which the importance of grazing diminishes towards the high shore (Hawkins & Hartnoll 1983; Foster 1992). While this scheme has been supported many times (e.g. Menge et al. 1986; Kaehler & Williams 1997, 1998) using traditional experimental designs, it does not consider the effects of grazer size or the existence of smaller scale variability and spatial structure in grazing effects. For example, topographic variability will alter grazing effects, influencing their spatial structure (i.e. the existence of patchiness, gradients or random patterns in grazing effects). Because traditional experimental designs involve random distribution of experimental units, they cannot provide information on the spatial structure of a variable. Here we used an alternative approach involving geostatistical tools (Dale 2000; Turner, Gardner & O’Neill 2001) to examine the relationship of grazing effects with topographic complexity and grazer size classes.

Comparison of results between the traditional approach which only considers the effects of grazing on the biomass of algae (classical zonation design) and a geostatistical approach that considers and describes numerically the spatial patterns of grazing effects on different algae was the main objective of this study. This objective was achieved by examining the following hypotheses:

• 1
   Grazing affects algal biomass and species composition at all levels on the shore and the results will be in agreement with the zonation schemes of Hawkins & Hartnoll (1983) and Foster (1992).
• 2
   Micro-, meso- and macrograzers influence the algal community differently. Consequently, the effect of grazing will change according to the abundances of different size classes of grazers among different heights and habitats on the shore.
• 3
   The effect strength of grazing exhibits spatial structure across the shore driven by the interaction of biotic and abiotic factors.
• 4
   The relationship between the spatial structure of grazing effects and these factors changes in time as the balance among these factors shifts.

Materials and methods

Study Site and Organisms

Two experiments were conducted at Old Woman’s River (33°45′ S, 27°15′ E) on the south coast of South Africa. The shore was chosen as it is a relatively flat sandstone platform (minimizing topographic complexity) and is moderately exposed, to conform with the scheme of Hawkins & Hartnoll (1983) and Foster (1992). We tested grazing effects on three functional groups of algae: (i) green foliose algae represented by Ulva rigida, (ii) red foliose algae represented by Porphyra capensis, and (iii) red algal turfs. We also assessed effects on the entire assemblage of micro- and macroalgae, represented by chlorophyll a concentration. Additionally, in another experiment we assessed the spatial patterns of grazing strength per se across the shore using the metric log-response ratio (LRR) (Osenberg, Sarnelle & Cooper 1997).

Zonation Experiment – Effect of Grazer Size Class

A randomized block design was used to examine the effects of different size classes of grazers at three heights across the shore (low, mid, high shore) as used in earlier studies (Underwood & Jernakoff 1984; Coleman et al. 2006) and in high-shore tidal pools.

In South Africa, the most prominent low-shore macrograzers are large (>3 cm), well adapted to resist strong wave action and undertake short foraging movements. These include the gardening limpets Scutellastra cochlear on the low shore, (Branch et al. 1992) and S. longicosta living higher on the low shore (McQuaid & Froneman 1993). Such gardening limpets can exhibit extremely high densities (>200 m², Bustamante, Branch & Eekhout 1995a). Large macrograzers on the mid shore belong to the limpet genus Cymbula. Smaller mesograzers (1.5–2 cm) live across the shore and feed on epilithic algae (microalgae and macroalgal sporelings) and soft foliose algae. Mesograzers include the juveniles of some macrograzers, adult pulmonate limpets (Siphonaria spp), and gastropods such as Oxystele spp (Whittington-Jones 1997; Hodgson 1999) and are particularly abundant on the mid shore where grazing effects are often reported to be strong (Jara & Moreno 1984; Williams 1993, 1994; Benedetti-Cecchi 2000; Benedetti-Cecchi, Bulleri & Cinelli 2000; Nielsen & Navarrete 2004; Coleman et al. 2006). Finally, very small micrograzers are abundant on the upper mid and high shore. These are mainly small epilithic grazers (littorinids <1 cm) feeding on a microalgal community of cyanobacteria, lichens and macroalgal spores (Cubit 1984; McQuaid 1996; Mak & Williams 1999; Kaehler & Froneman 2002).

There were four treatments: total exclusion of grazers (ET); exclusion treatment (T) excluding only meso- and macrograzers; procedural control (Pc) to detect artefacts; and control (C) areas with free access to all grazers. The total exclusion (ET) consisted of fenced areas of 0.25 × 0.25 m, surrounded by an antifouling paint (Blakes Cruising, Southampton, UK) strip (5-cm wide) outside a fence to prevent micrograzers reaching the fence. Previous studies report no artefacts of this paint (Dye 1993; Kaehler & Froneman 2002). The exclusion treatment (T fence without paint) allowed access only to micrograzers. The procedural control involved two partial fences (plus paint) in opposite corners of an incomplete square, limiting access to grazers, but not excluding them. Controls (C) had four screws to mark a square with free access to grazers. Ten blocks (each with all four treatments) were randomly distributed in each zone, with one block in each of the nine shallow tidal pools on the high shore (average area 2 m² and 5-cm deep).

All plots were scraped clear and burned with a butane-propane torch to remove the existing algal community. For pools, this required initial draining. Treatments within blocks were c. 15 cm apart, blocks within zones were between 1 and 10 m apart.

Height and distance upshore were measured from a fixed point identified as MLWS, zones were identified by species composition.

The experiment ran for 13 months (February 2005–March 2006). Epilithic chlorophyll a concentration and cover of macroalgae (calculated from digital photographs using Image tool 3.0; Department of Dental Diagnostic Science at The University of Texas Health Science Centre, San Antonio, Texas, USA) were measured (initially monthly, later at 6-week intervals) for each experimental unit. Chlorophyll a was measured using three randomly positioned 1-cm² rock chips collected from each plot with a chisel (468 chips per sample per date). Plots in low and mid-shore exclusion treatments were covered by macroalgae after a few weeks and so the chlorophyll a extracted from rock chips came from both microalgae and macroalgae. On the high shore, macroalgae occurred only episodically and most chips supported no macroalgae. Chlorophyll a concentration was estimated following Bustamante et al. (1995b) and Jenkins et al. (2001) using a SHIMADZU UV-1201 spectrophotometer.

The following were estimated for each block: aspect of each block from MLWS (the elevation from MLWS divided by distance from MLWS), horizontal distance and elevation (measured using a surveying level) from MLWS, and relative water movement. The latter was estimated during three spring tides from weight loss of cement balls because of erosion by water movement. The balls were cast in moulds and fixed to the rock by a screw that was embedded during construction. Balls were attached to a pre-drilled hole in the substratum and positioned to avoid contact with surrounding objects. The balls were dried at 60 °C for 12 h and weighed before and after deployment on the shore for 48 h. These devices give a numerical estimation of how much water movement has occurred around each block (McQuaid & Mostert 2010), but not an estimation of wave forces. Cement ball erosion is expected to differ across the shore, from low to high shore, due to period of emersion and these differences are specific for each shore. Densities of grazers in each zone were estimated using two quadrats of 1 m² set next to each block.

Transect Experiment: Spatial Structure of Grazing Strength Across the Shore

A 54-m transect of experimental blocks, from the bottom of the shore at MLWS to the supralittoral zone and not passing through tidal pools, was used to detect grazing effects across the shore. Each block comprised the treatments used in Experiment 1 (see above) except the simple exclusion treatment (T), which lacked antifouling paint, with a total of 54 blocks separated by 1 m between the centres of blocks. The grazer densities, aspect of the shore, elevation, distance from MLWS and water movement were recorded for every block as above. The experiment ran from 1 July 2005–15 May 2006. During this period, four measurements of algal cover and physical factors were made.

Statistical Analyses

Experiment 1: zonation experiment – effect of grazer size class

Abiotic and biotic factors were individually compared among levels on the shore using one-way anova or t-tests. Two-way repeated measures (RM) anova was used to test the effects of grazers on the whole algal assemblage (chlorophyll a concentration) with the fixed factors zone (four levels: low, mid, high shore and high tidal pools), treatment (four levels) and within effect ‘Time’ (eight levels). Grazing effects on algal groups were analysed using one-way RM-anova for each group in each zone with Bonferroni correction where necessary. The sphericity assumption was checked using Mauchly’s test, and when this assumption was violated, Greenhouse–Geisser correction of the P-values was performed. In the few cases where necessary, the data were Arsin(sqrt(x + 1))-transformed (Underwood 1997). Significant effects were explored using SNK tests.

Experiment 2: grazing effects across the shore using a transect

The experimental design was based on the use of geostatistical tools (semivariograms and cross-semivariograms), which estimate how the variance of a measured variable depends on the distance intervals (or the lag) between samples. This allows the determination of spatial patterns in the data (Fortin & Dale 2005).

Grazing strength at each block was estimated for each algal species or group using LRRs, which were calculated following Osenberg, Sarnelle & Cooper (1997) as:

• (eqn 1)

Positive values of LRR indicate that grazers promote the abundance of the algae through fertilization (Taylor & Rees 1998) or by releasing them from competitors (McQuaid & Froneman 1993), while negative values indicate reduction of the algal abundance by consumption. Zero values indicate no grazing effects.

The log-response ratios were analysed in three ways: (i) LRR was used as a dependent variable to study the spatial pattern of variability in grazing strength across the shore using semivariogram analyses; (ii) for descriptive purposes, LRR was regressed against MLWS to analyse the zonation of grazing strength across the shore; and (iii) the relationships between LRR and independent physical (aspect, elevation, water movement) and biological (densities of grazer size classes) predictor variables across the shore were studied using cross-semivariogram analyses. Average density of grazers in each block was estimated using two 1-m² quadrats set next to each block on each of two dates (n = 4). We estimated the observation error of these quadrats (standard deviation) and calculated confidence intervals for each block. Then we simulated values 10 times within these confidence intervals and the fractal dimension was calculated to determine if the spatial patterns corresponded to those estimated using only the average value.

1 Spatial patterns in grazing strength were examined using semivariogram analysis. Here, semivariograms represent the relationship between the variability of the LRR and spatial scale or lag (Dale 2000; Turner, Gardner & O’Neill 2001), i.e. how variability changes with the lag. Semivariance was calculated for different lags across the shore using the formula:

• (eqn 2)

where N_(h) is the number of pairs of data points separated by the lag h and (Z_i+h−Z_i) are the values of the studied variable at lags i and i+h. Twenty-seven lags were included in the transect, therefore the variation in the number of pairs of lags varied from 53 pairs at lag 1 m to 27 at lag 27 m. The spatial heterogeneity, defined as the change in the value of variance across lags, was estimated using the fractal dimension ‘D’ (Turner, Gardner & O’Neill 2001), calculated as:

• (eqn 3)

where D represents degree of partitioning into self-similar pieces (as spatial periodicity) of the variance of the variable of interest (Mandelbrot 1977). The value of D varies from 1 to 2, where values from 1 to 1.5 indicate ‘gradient behaviour’ of the variability in relation to the lag; values around 1.5 indicate a cut-off between a gradient pattern and the existence of large periodic patches across lags, which tend to become smaller and less periodic as D approaches 1.97. Finally, the range of values between 1.97 and 2.00 indicates the presence of a random pattern, i.e. the existence of small patches at small lags and lack of periodicity across lags, and consequently a lack of spatial heterogeneity, i.e. no relationship between variance and scale.

The term ‘m’ represents the slope in the regression between the natural logarithm (ln) of the semivariance and the ‘ln’ of the lags. This relationship can nest one or more subrelationships with different slopes, these are known as ‘scaling regions’. Scaling regions were detected using the three-step procedure described in Erlandsson & McQuaid (2004).

2 Zonation of grazing strength was analysed using polynomial regression analyses. The Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (BIC) were used to find the best adjustment for the relationship of LRR with distance from MLWS as the predictor variable. The AIC and BIC operate by rewarding goodness-of-fit, but include penalties for overfitting if the model has too many predictor parameters (Akaike 1974; Quinn & Keough 2003). The AICc formula involves a correction for deviations when the ratio n/K is lower than 40, as in our case:

• (eqn 4)

where ln = natural logarithm, n = number of observations, RSS = residual sum of squares and K is the number of parameters. To select the best-fitting model, we estimated ‘W_i’, which represents the probability of a model being the best among competing models. We accepted as the best fit, the model with the highest value of W_i. This involved first calculating (Δ_i), which is: AIC_i−AICc minimum. W_i was then calculated as:

• (eqn 5)

Additionally, in order to double-check our findings, we calculated the Schwarz Bayesian Criterion (BIC) (Quinn & Keough 2003), which it is more restrictive than the AICc. We used the following formula:

• (eqn 6)

The competing model with the lowest value for BIC represents the best adjustment (Quinn & Keough 2003).

3 The strength of grazing and a physical factor may exhibit positive spatial co-variance at some lags, while at others the relationship may be neutral or negative. The relationship between the strength of grazing effects, expressed as the LRR, and every predictor variable (abiotic and biotic) was analysed using cross-semivariance analysis to examine the spatial co-variability of both variables at specific lags. There was some collinearity among predictor variables, but this was never above r² = 0.75, which is low (Sokal & Rohlf 1995), and the absence of collinearity is not an assumption for cross-semivariogram analyses (unlike multi-regression tests).

The cross-semivariance was calculated as:

• (eqn 7)

where N is the total number of data points; N_(h) is the number of pairs of data points separated by the distance or lag h; X_i and X_i+h, and Z_i and Z_i+h are the values of LRR and the values of one of the physical factors, respectively at two different lags i and i+h. Significant differences of cross-semivariance values from zero were tested using the sampled randomized test (Sokal & Rohlf 1995).

Results

Zonation Experiment – Effect of Grazer Size Class

Variability of abiotic and biotic factors among levels on the shore

The physical factors ‘distance from MLWS’, ‘elevation’ and ‘water movement’ differed significantly among zones (low, mid and high shore). Aspect ratio of the level of shore showed low variation; only the low shore had a greater aspect ratio than the other zones (Table 1). Macrograzers were present only on the low and mid shore where they exhibited similar densities (Table 1), although species composition differed. The limpets Scutellastra cochlear, S. barbara, S. tabularis and very few Cymbula oculus were observed on the low shore, with only C. oculus on the mid shore. Mesograzers were equally abundant on the low and mid shore, but densities were significantly greater in tidal pools, where micrograzers (littorinids plus juveniles of mesograzers and mesograzers) were also present. Only littorinid micrograzers were observed on the high shore (Table 1).

Table 1.   Mean ± SD of physical factors in different zones from experiment 1. < or > indicates the direction of significant Student–Newman–Keuls results

Factor	Zones				One-way anova or t-test
	Low	Mid	High	Tidal pools
**P < 0.01, ***P < 0.001 and NS non-significant. 0 indicates organism not present
Distance from MLWS (m)	6.3 ± 2.2	<28.3 ± 2.8	<50.9 ± 1.3	<56.1 ± 2.1	F3,34 = 1051.5***
Aspect	0.08 ± 0.01	>0.03 ± 0.002	=0.02 ± 0.003	=0.03 ± 0.002	F3,34 = 172.66***
Elevation above chart datum (m)	0.5 ± 0.2	<0.8 ± 0.1	<1.7 ± 0.2	>0.9 ± 0.54	F3,34 = 89.07***
Water movement (g)	10.4 ± 0.6	>6.6 ± 0.6	=6.2 ± 0.9	=5.7 ± 1.2	F3,34 = 62.2***
Number of macrograzers m^−2	3.6 ± 1.3	=2.2 ± 3.2	0	0	t17 = 1.2 NS
Number of mesograzers m^−2	0.7 ± 0.6	<12.4 ± 10.3	0	<45.8 ± 51.0	F2,25 = 5.7**
Number of micrograzers m^−2	0	0	173.6 ± 105.9	>45.9 ± 48.7	t17 = −3.3**

Grazing effects on total algal biomass (chlorophyll a)

We never observed grazers inside simple or full grazer exclusion treatments. Two-way RM-anova showed that most effects on chlorophyll a, including interactions, were significant. The interaction ‘Level of the shore × Treatment’ was significant (F_9,136 = 2.7, P = 0.007), indicating that there was a significant grazing effect only on the low shore and in rock pools (SNK: ET = T > Pc = C). The ‘Time × Level of the shore’ interaction was also significant (F_21,952 = 4.35, P < 0.00001); broadly there was more chlorophyll a from autumn to spring on the low shore and in tidal pools and during the winter months for the mid shore, with no-variability on the high shore. Of the remaining interactions, ‘Treatment × Time’ was not significant (F_21,952 = 0.89, P = 0.58), while ‘Level of the shore × Treatment × Time’ (F_63,952 = 1.63, P = 0.004) was significant, but showed non-logical groupings. The highest order term ‘Level of the shore’ was significant (F_3,136 = 384.04, P < 0.00001, SNK: low = mid shore > rock pools > high shore), while the term ‘Treatment’ indicated significant reduction of algal biomass by grazers (F_3,136 = 10.97, P < 0.00001, SNK: total exclusion (TE) = exclusion (T) > procedural control (Pc) = control (C)). The term ‘Time’ indicated that March 2005 had the lowest concentration of biomass, April 2005 (early autumn) to November 2005 (spring) showed consistent, high chlorophyll a concentrations that decreased in January (summer) and March of 2006 (late summer) (F_7,952 = 36.6, P < 0.00001) (see Fig. S1, in Supporting Information).

Grazing Effects on Algal Functional Groups

Low shore

The green foliose alga Ulva rigida was affected by grazers (one-way RM-anova, ‘Treatment’ effect: F_3,32 = 6.9, P = 0.001, total exclusion = exclusion > procedural control = control), with no differences among the effects of macro-, meso- and micrograzers on the low shore (i.e. no differences between total exclusion and exclusion treatments). The interaction ‘Time × Treatment’ was not significant (F_24,256 = 1.37, P = 0.18). There was significant temporal variation in the abundance of U. rigida, with greater cover during the early than the later months (F_8,256 = 30.9, P < 0.0001, March 05 = April 05 = May 05 > March 06 > June 05 = August 05 = September 05 = November 05 = January 06). Red turfs were not affected by grazers (F_3,32 = 0.83 P = 0.49). Their abundance increased with time (F_7,224 = 27.54 P = 0.0001), the last sampling dates (January and March 2006) exhibiting greater cover. See Fig. S2.

Mid shore

Ulva rigida was the only algal species observed and was not affected by grazing (Treatment: F_3,36 = 2.12, P = 0.11), with minimal temporal variability in abundance (F_8,288 = 5.32, P = 0.001, SNK test indicated lowest abundance was at the beginning of the experiment in March 2005 (late summer). See Fig. S2.

High shore and tidal pools on the high shore

On the high shore, no macroalgae recruited into any of the experimental treatments, nor was cyanobacteria cover quantifiable from photographs. Ulva rigida was the dominant species in tidal pools on the high shore. The macroalgae, Endarachne sp. and Colpomenia sinuosa, were sporadically observed in tidal pools, but disappeared rapidly (within 2 weeks) and their cover was always <5%.

Ulva rigida in tidal pools was affected by grazers (Treatment: F_3,32 = 3.66, P = 0.022). In addition, there was slight temporal variation in its cover after settlement. Cover in March 2005 (late summer) was lower than on the other sampling dates (Time: F_8,256 = 12.22, P < 0.00001).

Another conspicuous algal group in tidal pools was a black film comprising cyanobacteria species including Gleocapsa spp., Aphanocapsa spp., Chroococus spp. and other blue green groups that could not be identified. This functional group was not affected by grazers (Treatment: F_3,32 = 1.51, P = 0.23) and exhibited a peak in abundance in April 2005 (early autumn) (Time: F_8,256 = 13.14, P < 0.00001). See Fig. S2.

Transect Experiment: Spatial Structure of Grazing Strength Across the Shore

Relationships among factors across the shore

Three different functional groups of algae were recognized along the transect: red turf on the lower part of the transect (elevation <0–0.51 m above chart datum (C.D.), water movement 10.7 ± 1.1 g day⁻¹ and distance from MLWS: <0–5 m); foliose green algae, represented by Ulva rigida, (<0–1.21 m above C.D., entire range of water movement and <0–43 m from MLWS); foliose red algae, represented by Porphyra capensis, (0.63–1.21 m above C.D., water movement of 93 ± 75.5 g day⁻¹, and 24–43 m from MLWS). Macrograzers were found ranging <0–0.84 m above C.D., coinciding with the ranges of U. rigida and red turfs. Mesograzers overlapped with U. rigida and P. capensis, ranging 0–1.43 m above C.D. and 0–50 m from MLWS, with highest abundances at 43 m from MLWS, and an average of 1.04 m ± 0.2 above C.D. Micrograzers were found 44–54 m from MLWS in a part of the shore where macroalgae were absent (Fig. 1).

Figure 1.  First column represents the spatial distribution of the factors: aspect ratio, elevation above chart datum water movement, density of macro-, meso- and micrograzers. Values are shown against distance from Mean Low Water Spring Tide. The second column shows the corresponding spatial analyses using semivariograms, plotting semivariance values against the natural log of the lag values. Regression lines indicate significant scaling regions.

Most abiotic and biotic factors were highly significantly correlated (Spearman analysis). These included the anticipated positive relationships between distance from the sea and both elevation (r² = 0.74, t₅₃ = 12.3, P < 0.0001) and micrograzers (r² = 0.37, t₅₃ = 5.5, P < 0.0001). Distance from the sea was negatively correlated with water movement (r² = 0.59, t₅₃ = −8.8, P < 0.0001) and macrograzers (r² = 0.53, t₅₃ = −7.6, P < 0.0001). Aspect ratio and elevation were not significantly correlated (r² = 0.01, t₅₂ = 1, P = 0.32), while aspect ratio and distance from MLWS were highly correlated (r² = 0.74, t₅₂ = 12.8, P < 0.0001). Mesograzers were not correlated with any physical factor (P > 0.05 and r² < 0.1 in all cases), but were negatively correlated with both macrograzers (r² = 0.13, t₅₃ = −2.8, P < 0.01) and micrograzers (r² = 0.10, t₅₃ = −2.37, P < 0.05). Likewise, macro- and micrograzers were negatively correlated (r² = 0.08, t₅₃ = −2.2, P < 0.05).

Across-shore spatial patterns of macroalgal functional groups

Grazing effects represented by LRR on red turfs, Ulva rigida and Porphyra capensis were analysed using semivariograms to determine their spatial structure. (i) Grazing effect strength across the shore for red turfs exhibited patchiness during spring and summer (October 2005 (spring) and January 2006 (summer)), after which these effects exhibited no structure because of the loss of algal biomass resulting in random patterns (Table 2). (ii) The spatial structure of grazing strength on U. rigida exhibited patchiness at small scales represented as one scaling region, in September 2005 (early spring) and October 2005 (spring), two scaling regions in January 2006 (summer) and random patterns in May 2005 (late autumn) (Table 2, Fig. 2). Most scaling regions exhibited fractal dimensions that suggest patchy distribution (1.5 < D < 1.97) across the shore. (iii) Finally, grazing effects across the shore for P. capensis were patchy during September 2005 (early spring), after that they were randomly distributed.

Table 2.   Spatial analysis for the detection of spatial patterns and fractal dimension (D) for the different physical (aspect ratio, elevation, water movement), and biotic factors (density of macro-, meso-, micrograzers), and the effect of grazing represented by the log-response ratio (LRR) for red turfs, Ulva rigida and Porphyra capensis on different sampling dates. The right-hand-side column provides an interpretation of the analysis (Part 1) and of D (Part 2), respectively

Transect	lag (m)	Slope	SE	R^2	t (d.f. = 25)	D	Spatial pattern
*P < 0.05; **P < 0.01; ***P < 0.001; NS, not significant †Non-significant but still there is spatial heterogeneity, because there is one scaling region positive and the next one is negative (Erlandsson & McQuaid 2004)
Part 1: detecting dependence between variable and lag using regression and estimation of fractal dimension D for
Abiotic factors
Aspect	1.00–27.0	0.46	0.04	0.81	10.44***	1.77	Spatial heterogeneity, multiple scaling region Part 2a
Elevation	1.00–27.0	0.65	0.05	0.88	14.06***	1.67	Spatial heterogeneity, multiple scaling region Part 2b
Water movement	1.00–27.0	0.59	0.04	0.89	13.95***	1.74	Spatial heterogeneity, multiple scaling region Part 2c
Biotic factors
Density macrograzers	1.00–27.0	0.44	0.06	0.73	7.8***	1.78	Spatial heterogeneity, 1 scaling region
Density mesograzers	1.00–27.0	0.52	0.03	0.92	16.89***	1.74	Spatial heterogeneity, 1 scaling region
Density micrograzers	1.00–27.0	0.53	0.04	0.88	13.81***	1.74	Spatial heterogeneity, 1 scaling region
LRRs on Algal species
LRR Red turf September 2005	1.00–27.00	0.08	0.04	0.1	1.98 NS	1.97	Non-significant heterogeneity, random pattern
LRR Red turf October 2005	1.00–27.00	0.17	0.05	0.3	3.4**	1.91	Spatial heterogeneity, 1 scaling region
LRR Red turf January 2006	1.00–27.00	0.2	0.04	0.49	4.9***	1.89	Spatial heterogeneity, 1 scaling region
LRR Red turf May 2006	1.00–27.00	−0.08	0.05	0.01	−1.58 NS	1.97	Non-significant, random pattern
LRR Ulva September 2005	1.00–27.0	0.22	0.03	0.67	7.23***	1.89	Spatial heterogeneity, 1 scaling region
LRR Ulva October 2005	1.00–27.0	0.26	0.04	0.74	5.6***	1.87	Spatial heterogeneity, 1 scaling region
LRR Ulva January 2006	1.00–27.0	0.01	0.06	0.00	0.22 NS	1.98†	Spatial heterogeneity, multi-scaling regions Part 2d
LRR Ulva May 2006	1.00–27.0	−0.00	0.03	0.00	−0.019 NS	1.99	Non-significant, random pattern
LRR Porphyra September 2005	1.00–27.0	0.48	0.07	0.97	6.26*	1.93	Spatial heterogeneity, 1 scaling region
LRR Porphyra October 2005	1.00–27.0	−0.01	0.04	0.00	−0.5 NS	1.99	Non-significant, random pattern
LRR Porphyra January 2006	1.00–27.0	−0.05	0.04	0.09	−1.58 NS	1.97	Non-significant, random pattern
LRR Porphyra May 2006	1.00–27.0	−0.03	0.04	0.02	−0.74 NS	1.98	Non-significant, random pattern
Part 2: detection of significant multiple scaling regions
(a) Aspect	1.00–4.00	1.12	0.04	0.99	31.46 (2)***	1.43	Trend
	5.00–20.0	0.20	0.06	0.47	3.5 (14)**	1.89	Patchy
	21.0–27.0	1.83	0.20	0.94	8.9 (5)***	1.01	Trend
(b) Elevation	1.00–17.0	0.49	0.03	0.93	15.34 (15)***	1.75	Patchy
	18.0–23.0	2.49	0.09	0.99	20.4 (4)***	1.01	Trend
	24.0–27.0	0.84	0.17	0.98	10.4 (2)***	1.57	Patchy
(c) Water movement	1.00–8.00	0.39	0.04	0.87	10.3(15)**	1.80	Patchy
	9.00–27.0	1.08	0.16	0.83	6.83 (8)***	1.45	Trend
(d) LRR Ulva January 2006	1.00–10.0	0.4	0.04	0.93	10.7 (8)***	1.79	Patchy
	11.0–27.0	−0.75	0.13	0.69	−5.83 (15)***	1.63	Patchy

Figure 2.  Distribution of log-response ratios for red turf, Ulva rigida and Porphyra capensis on four sampling occasions. First column represents the distribution of the variable in space from mean low water spring tide. The second column shows the corresponding spatial analysis (or semivariogram), plotting semivariance values against the natural log of the lag values. The regression lines indicate significant scaling regions.

Data obtained by the regression of LRR on U. rigida against distance across the shore produced inverse quadratic functions, with low grazing effects (around zero) at the bottom and the top of the shore during September 2005 (early spring) to January 2006 (summer), and stronger grazing effects (more negative values) around 20–28 m from MLWS (Fig. 3a–c). The relationship changed to linear in May 2006 (late autumn), with the strongest grazing effects at the bottom on the shore (Fig. 3d), however, the coefficient of determination for this sampling date was extremely low (r² = 0.09). Note also that negative LRR values indicate consumption of algae. The criteria for selecting the best regression adjustment are shown in the Table S1.

Figure 3.  Polynomial regressions between log-response ratios for Ulva rigida and distance for the transect data. Lines on the graphs represent the best regression adjustment. (a) Quadratic adjustment during September 2005 (early spring); distance F_1,51 = 14.9, P = 0.0003, dist²F_1,51 = 19.3, P = 0.0005. (b) Quadratic adjustment during October 2005 (spring); distance F_1,51 = 28.71, P = 0.000002 and dist²F_1,51 = 31.9, P = 0.000001; (c) Quadratic adjustment for January 2006 (summer); distance F_1,51 = 3.04, P = 0.08 and dist²F_1,51 = 4.62, P = 0.036. (d) Linear adjustment for May 2006 (late autumn); distance F_1,52 = 5.73, P = 0.02.

Spatial Patterns of Physical and Biotic Factors Along the Transect

Elevation and aspect ratio had high heterogeneity; each had three positive scaling regions. For both factors, one scaling region had a trend-like pattern at short lags and two had patchy patterns at longer lags (D = 1.01–1.89; Table 2, Part, 2a,b; Fig. 1). Water movement had two positive scaling regions: one patchy at shorter lags (D = 1.80) and one trend-like at longer lags (D = 1.45; Table 2, Part 2; Fig. 1). Each grazer class exhibited a single positive scaling region, with a fractal dimension indicating patchy distribution across lags. For macrograzer, D = 1.78, and for both meso- and micrograzers D = 1.74 (Table 2, Fig. 1). These D values were in the range of error expected (based on simulations) of: 1.77–1.90 for macrograzers, 1.67–1.96 for mesograzers and 1.70–1.87 for micrograzers.

Patterns of spatial variability in LRR varied among grazer size classes depending on algal group, date and the spatial scale considered. The biomass of red turfs was not reduced by macrograzers, but their spatial variability at large scales (19–27 m) was reduced in spring and later enhanced during summer by this grazer size class (Table 3A). Mesograzers produced the opposite effect on these turfs, increasing their spatial variance during spring and reducing it during summer at the largest scales (19–27 m), while micrograzers did not affect red turf spatial variance. For P. capensis, macrograzers affected spatial variance on the largest scales, as did micrograzers, but mesograzers reduced spatial variability across all scales (0–27 m) (Table 3B).

Table 3.   Results of cross-semivariogram analyses reporting the number of lags (out of a possible 27) at which each log-response ratio (LRR) for a specific alga showed a significant relationship with the corresponding predictor variable (abiotic or biotic). –ve and+ve indicate negative and positive relationships with LRR, respectively. ‘0’ indicates no significant lag found. The lags were pooled into three groups: 0–9 m, 10–18 m and 19–27 m. (A) LRR on red turfs, (B) LRR on Ulva rigida and (C) LRR on Porphyra capensis

Red turf	September 2005 (early spring), lags between			October 2005 (spring), lags between			January 2006 (summer), lags between			May 2006 (late autumn), lags between			Dates pooled, Total
Factor	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m
(A)
Aspect	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Elevation	0	0	3+ve	0	0	4+ve	0	0	6−ve	0	0	0	0	0	7+ve, 6−ve
Water movement	0	0	0	0	0	3−ve	0	0	6+ve	0	0	0	0	0	6+ve, 3−ve
Macrograzers	0	0	7−ve	0	0	4−ve	0	0	6+ve	0	0	0	0	0	6+ve, 11−ve
Mesograzers	0	0	1+ve	0	0	2+ve	0	0	6−ve	0	0	0	0	0	3+ve, 6−ve
Micrograzers	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Porphyra capensis	September 2005 (early spring), lags between			October 2005 (spring), lags between			January 2006 (summer), lags between			May 2006 (late autumn), lags between			Dates pooled, Total
Factor	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m
(B)
Aspect	0	0	5+ve	0	0	0	0	0	0	0	0	0	0	0	5+ve
Elevation	0	0	1−ve	0	0	0	0	0	0	0	0	0	0	0	1−ve
Water movement	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Macrograzers	0	0	2+ve	0	0	0	0	0	0	0	0	0	0	0	2+
Mesograzers	5−ve	8−ve	8−ve	5−ve	3−ve	1−ve	4−ve	3−ve	0	0	0	0	14−ve	14−ve	9−ve
Micrograzers	0	2+ve	1+ve	0	0	0	0	0	0	0	0	0	0	2+ve	1+ve

Ulva rigida	September 2005 (early spring), lags between			October 2005 (spring), lags between			January 2006 (summer), lags between			May 2006 (late autumn), lags between			Dates pooled, Total
Factor	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m	0–9 m	10–18 m	19–27 m
(C)
Aspect	0	0	0	0	0	3+ve	0	0	0	0	0	0	0	0	3+ve
Elevation	0	0	3+ve	0	0	0	0	0	0	0	0	0	0	0	3+ve
Water movement	0	0	0	0	0	5+ve	0	0	0	0	0	0	0	0	5+ve
Macrograzers	0	0	0	0	0	4+ve	0	0	0	0	0	4−ve	0	0	4+ve, 4−ve
Mesograzers	0	0	7−ve	5−ve	7−ve	9−ve	3−ve	2−ve	0	0	0	0	8−ve	9−ve	9−ve
Micrograzers	0	0	0	0	7+ve	9+ve	0	3+ve	0	0	0	0	0	10+ve	9+ve

Finally, in the case of U. rigida (Table 3C), which showed no zonation, mesograzers tended to reduce spatial variability across the whole range of scales (0–27 m), while macrograzers enhanced or decreased the spatial variability at different times, although only at the largest scales. Micrograzers acted weakly reducing the algal abundance of U. rigida but they increased its variability at mesoscales and the largest scales (10–27 m).

Discussion

Traditional experiments assessing the effects of grazing usually concentrate on the overall reduction of vegetation biomass and, while geostatistical tools have been used successfully in terrestrial (Dale et al. 2002; Cousens et al. 2006) and marine systems (Johnson et al. 1997; Denny et al. 2004; Erlandsson & McQuaid 2004) to examine the formation of spatial patterns, the two approaches have never been combined. Still less frequently have such tools been used to characterize trophic spatial structure. Here, we have used an approach combining the traditional block design with geostatistical analysis to estimate the spatial structure of grazing effects across a gradient of stress on a rocky shore. The first of our hypotheses were that: (i) grazing affects algal biomass and species composition at all levels on the shore and that the results would be in agreement with the zonation schemes of Hawkins & Hartnoll (1983) and Foster (1992), and (ii) different size classes of grazers affect algal communities differently. The first hypothesis was rejected by the zonation experiment and supported by the transect experiment. This dichotomy is superficial but provides a better understanding of the system. The second hypothesis was supported by two different experimental designs and by different types of analysis. The subsequent hypotheses were: (i) the effect strength of grazing exhibits spatial structure or heterogeneity across the shore that is driven by the interaction of biotic and abiotic factors, and (ii) the relationship between the spatial heterogeneity of grazing effects and these factors changes in time as the balance among these factors shifts. These hypotheses were supported, but, critically, could only have been addressed using this combined approach.

Comparison with Earlier Models

The two experiments gave complementary information about grazing effects and overall, both indicated that grazing was important in determining algal biomass. The ‘zonation experiment’ indicated that grazing effects followed a pattern different from that predicted by the earlier zonation models of Hawkins & Hartnoll (1983) and Foster (1992), in which grazing is most important on the mid shore. In our study, grazers reduced biomass of U. rigida and chlorophyll a on the low shore and in tidal pools, but did not affect red turfs or P. capensis. The transect experiment supported the scheme of Hawkins & Hartnoll (1983) on all dates but more strongly on the first three sampling dates (early spring to summer), with regressions identifying the strongest grazing effects being on the mid shore (Fig. 3), and only superficially in late autumn and winter, when primary production seems to have overridden grazing intensity, increasing LRR values across the shore (to more positive values). This is despite the fact that, in contrast to the north-east and west Atlantic, or the north-east Pacific, grazing pressure in South Africa does not appear to diminish in winter, presumably because minimum temperatures are not particularly low. Additionally, the transect allowed us to assess variability in grazing effects across the shore as represented by log-response ratios.

The discrepancy between the experiments reflects their natures. First, the blocks of the zonation experiment started higher on the shore (5 m above MLWS) than the transect (0 m), missing a part of the shore where the transect identified no grazing effects. The zonation experiment found no grazing effects on the mid shore because most experimental blocks did not coincide with the peaks of strong grazing effects detected by the transect, while regression analyses of the transects smooth the data, masking the considerable residual variability (residual = 1−R², Fig. 3) because of small-scale differences in grazing effects between blocks. Second, the zonation experiment was based on parametric statistics, which focus on categorical differences and are not sensitive to gradients.

The regressions and semivariograms are complementary and can be used to describe how spatial patterns in grazing effects across the shore change in time. The semivariograms can be understood as a translation of the polynomial regressions into a description of changes in the variability of LRR across lags. Inverse quadratic functions between LRR and distance were found to apply from September 2005 (early spring) to January 2006 (summer). The quadratic function between LRR on U. rigida and distance denoted a large patch in the middle of the transect. This patch was about 30-m long in September (early spring), enlarging to 35–40 m in January (summer).

Viewed in terms of semivariogram analysis, the presence of this large patch implies that there were small differences in LRR between short lags (blocks close to one another showed similar grazing effects), with the differences increasing at longer lags. In May 2006 (late autumn), the regression between LRR and distance showed a weak but significant positive linear trend in the upshore direction (Fig. 3d).

The spatial analysis did not detect any periodicity or patchiness in LRR across the shore, indicating spatial randomness (D = 1.99) in the distribution of grazing effects. These changes in the position of peaks in grazing effects probably reflect seasonal changes in algal productivity. Primary productivity in this region of South Africa peaks in winter (Bustamante et al. 1995b). This reduces the relative effects of grazing by increasing the cover of algae in control treatments, resulting in positive and neutral values of LRR. This explains the short-term change in the across-shore pattern of LRR in early autumn (May 2006). During spring to summer, desiccation increases towards the mid and high shore, reducing the growth of filamentous algae and increasing the effects of grazing.

Zonation of two out of three macroalgae was evident in the absence of grazing in both experiments, with red turfs and P. capensis being restricted to the low and mid shore, respectively. Algal biomass reduction through grazing was non-significant in these two species and the across-shore experiment indicated that these algae exhibited spatial heterogeneity, often at large scales (long lags). This spatial heterogeneity was due to the occurrence of each alga at certain levels on the shore, represented by a single positive scaling region, indicating that variability (differences between lags) increases as one moves away from the main patch. Therefore, grazers induced the largest spatial variability at the longest lags (27 m). The conclusion from both experimental approaches is that grazers do not control the abundance of red turfs or P. capensis, but that grazing strongly enhances their spatial variability, with this spatial structure varying in time. In contrast, U. rigida did not exhibit zonation. Grazing effects on U. rigida resulted in the reduction of its biomass, although this was weak on the low shore and stronger (grazing effects more negative) and patchy towards the upper mid shore. Across this range (0–43 m from MLWS), grazing effects exhibited high spatial variability, indicating the existence of patches rather than a gradient or a random pattern (fractal dimension = 1.63–1.98, during September (early spring) to January (summer), but D = 1.99 in May 2006). This type of patchiness occurred across all scales, from small to large (Table 2, Fig. 3). All three algal groups studied showed random patterns at the end of the experiment in May 2006 (late autumn). Random patterns represent spatial homogeneity either because of the absence of algal biomass on the landscape (red turfs and P. capensis, which disappeared through successional effects) or because of small-scale variability across the transect (U. rigida, which showed more homogeneity in abundance at small scales), implying independence between variability of the alga and spatial interval (lag). Independence of a variable in space creates uncertainty or unpredictability, denoted by values of D > 1.97. This description of spatial patterns in grazing effects on early successional stages, described using LRRs across the shore and through time, represents a refinement of the models of Hawkins & Hartnoll (1983) and Foster (1992).

The semivariograms provide insights about the lags (scales) at which grazing effects operate by describing the dispersion of patches of LRR through the relationship between variance and lag. For example, a positive relationship (slope) between LRR and lag (in the semivariogram analysis) indicates the presence of small patches dispersed homogenously at small lags (so that variance between the lags is small) but not at longer lags (where the variance is larger). In contrast, the semivariogram for January 2006 (Fig. 2) had two scaling regions (slopes), indicating regular small-scale patchiness (as described above) up to a certain lag, after which there was a negative relationship, implying the presence of bigger patches that became more regular as the lag increased. Therefore, grazing effects operate simultaneously at multiple scales and on different species generating complexity in algal mosaics. How grazing contributes to the formation of spatial structure in algal landscape cannot be assessed using only traditional experiments.

Effects of Grazer Size

Different size classes of grazers showed clear patterns of abundance across the shore, with macrograzers on the low and mid shore and micrograzers only on the high shore. Mesograzers showed similar distribution to U. rigida and were present across the shore. The effects of each size class were evident in both experiments: the total exclusion and exclusion treatments never differed significantly, but both differed significantly from the controls in terms of both chlorophyll a and percentage cover of algae. This suggests that micrograzers do not play an important role in determining the abundances of algal communities, which contrasts with the earlier findings of Kaehler & Froneman (2002) for the high shore of the same site.

From the cross-semivariogram analysis in Experiment 2, we can see that the interaction between the abundance of grazer size classes and grazing strength helps to shape the algal landscape across the shore by affecting spatial variability in the algal community.

Spatial Patterns of Grazing Effects

There are countless potential predictor variables that can modulate grazing effects and their spatial variability. Some predictor variables can be redundant, meaning they can be replaced or omitted with little effect on the intensity or spatial variance of grazing effects. This was the case for the abiotic predictor variables: aspect of the shore, elevation and water movement. These three variables were redundant in the context of spatial variability in grazing effects on U. rigida, while they affected grazing effects on red turfs differently, switching between positive and negative at different sampling times. The variability in the aspect of each block and in water movement do not seem to contribute to the variability in grazing effects on red turf and P. capensis, respectively.

Temporal and Spatial Variability

Our results indicate that the influence of factors regulating the spatial variability in grazing effects changes with time. Not only can their effects alter with time, they can also differ with spatial scale at a given time. However, overall it was clear that abiotic factors influenced the spatial variability of grazing effects at larger scales, while the biotic factor ‘grazers’, especially mesograzers, reduced spatial variability across the whole range of scales studied (see Table 3, dates pooled). This implies that abiotic factors set variability at large scales (19–27 m), while biotic factors operated simultaneously at small, intermediate and larger scales (0–27 m).

Finally, our study revealed that grazing effects on the shore were due only to macrograzers and mesograzers, but we can not discard a weak micrograzer influence on algal assemblages. More importantly, geostatistical analysis indicated that grazing effects for specific algal groups were highly variable and occurred only at particular scales. We conclude that traditional zonation experiments are useful in determining the intensity of grazing effects, but that descriptions and predictions of the variability inherent in grazing effects can be detected only using geo-referenced experimental designs. We suggest that the approach we have taken can usefully be applied to identify the drivers of small-scale variability across environmental gradients in other ecosystems.

Predicting grazing effects in any ecosystem, and how they will shape landscapes, is a complex task because it implies an understanding of the spatial structure of the interaction between vegetation and grazers. This complexity increases when the environmental conditions are highly variable in time and space. These sources of complexity can produce different types of landscapes: fully unpredictable ‘random’ or predictable, but ‘patchy’, landscapes. Our contribution to understanding grazing effects lies in showing that that the components of grazing strength exhibit a certain order. Two seminal papers (Berlow 1999; Benedetti-Cecchi 2000) report that weak trophic interactions have consequences that enhance spatial variability of the prey. The nature of this variability has not been categorized and can be random or non-random. In our study we came to similar conclusions: grazing effects can be non-significant in terms of reduction of vegetation biomass, while creating spatial patterns that vary over time from patchy to random, or from predictable to unpredictable. This approach can also be used to categorize the effects of other disturbances or interactions on the production of spatial patterns (Collins 1992, 2000; Veen et al. 2008). Perhaps more importantly, it can be used to determine whether these patterns are stable in time.

Acknowledgements

This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and the National Research Foundation. We are particularly grateful for the patience and insights of two anonymous referees.