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1Conceptual models of ecosystem development commonly predict a phase of initial colonization characterized by the nucleation, growth and coalescence of discrete patches of pioneer plants. Spatiotemporal dynamics during subsequent development may follow one of three different models: the classical model, in which initially discrete patches of competitive dominant (secondary) colonists coalesce to form a homogeneous cover; the patch dynamics model, in which renewal mechanisms such as disturbance create a shifting mosaic of patches at different stages; and the geoecological model, in which the vegetation gradually differentiates along edaphic gradients related to the underlying physical template.
2These models of spatiotemporal dynamics were tested using vegetation and soil data from an 850-year chronosequence, comprised of seven lava flows on Mt Hekla, Iceland. The scale and intensity of spatial pattern were quantified on each flow using spatial analyses (mean-variance ratios, quadrat variance techniques and indices of autocorrelation). Changes in spatial pattern with increasing terrain age were compared with predicted trajectories, in order to identify which of the models of spatiotemporal dynamics was most consistent with the observations.
3The early stages of ecosystem development were characterized by colonization of the pioneer species, especially Racomitrium mosses, in discrete patches (‘Pioneer colonization stage’, < 20 years), which then grew laterally and coalesced to form a continuous, homogeneous carpet (‘Pioneer expansion stage’, 20–100 years). Later in the sequence, higher plants established in discrete patches within this pioneer matrix (‘Higher plant colonization stage’, 100–600 years). Over time, heterogeneity re-emerged at a larger spatial scale as the vegetation differentiated according to topographic variations in the underlying substrate (‘Differentiation stage’, > 600 years).
4Synthesis. The spatiotemporal dynamics observed in the early stages of this succession were consistent with a model of pioneer nucleation in micro-scale safe sites, followed by growth, coalescence and eventual fragmentation of pioneer patches. The spatial patterns which emerged later in development support the geoecological model, with spatial differentiation of vegetation related to meso-scale substrate topography. The findings provide insight on how vegetation patterns emerge at different stages of ecosystem development in response to differing scales of heterogeneity in the underlying physical environment.
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Ecosystem development involves long-term (decades to centuries) directional changes in ecosystem properties such as biomass, productivity, species diversity and nutrient cycling. An understanding of the mechanics of ecosystem development is crucial to the successful management and restoration of ecosystems (Robinson & Handel 2000; Walker & del Moral 2003), as well as to the prediction of ecosystem response to future environmental change. Considerable research effort, both theoretical and empirical, has focussed on temporal changes in global (non-spatial) ecosystem variables; however, the spatial component of ecosystem development has received less attention (Perry 2002). Research on contemporary ecosystems provides strong evidence that spatial structure mediates species interactions (e.g. Bertness & Callaway 1994) and diversity (e.g. He & Legendre 2002). Understanding how the spatial structure of an ecosystem develops is therefore central to understanding and predicting its long-term dynamics. The overall aim of this study was to document changes in spatial structure across an 850-year chronosequence of ecosystem development, thereby providing data to test three alternative models of spatiotemporal dynamics.
Most ecosystems exhibit spatial structure, i.e. a distribution of constituent parts that differs significantly from complete spatial randomness (Greig-Smith 1979). Complete spatial randomness is a neutral condition often thought to reflect the dominance of external, stochastic processes, for example disturbance, in ecosystem development. Spatial structure is considered the result of deterministic, internal processes (Cale et al. 1989) or differential biotic responses to environmental heterogeneity. Spatial structure has two key components – scale and pattern intensity (Dale & Blundon 1991). If a single variate is considered (e.g. the occurrence of a plant species in a sample unit), spatial scale may be defined as the mean sizes of regions of high density (patches) and low density (gaps). In the following analysis, pattern intensity is taken as the ‘contrast’ between patch and gap phases (Kotliar & Wiens 1990). Spatially heterogeneous ecosystems exhibit high intensity variations in system attributes; in contrast, spatially homogeneous systems exhibit uniformity in appearance and the distribution of constituents (Kotliar & Wiens 1990). Structured distributions may be either aggregated (patchy or clumped) or segregated (regular). In plant assemblages, aggregated distributions are linked to positive interactions (e.g. facilitation) that ameliorate environmental constraints on plant colonization, growth and reproduction within a localized area (Yarranton & Morrison 1974). In contrast, segregated distributions are linked to negative interactions (e.g. competition) that lead to competitive exclusion and spatial segregation (Getzin et al. 2006). Ecosystem development involves systematic changes in the biota (e.g. biomass and productivity of vegetation) and physical environment (e.g. depth and fertility of soils), which might be expected to shift the balance of negative and positive interactions over time. Hence, systematic changes in spatial structure should also be expected over the course of ecosystem development.
Based on previous research, three alternative models of the spatiotemporal dynamics of ecosystem development can be formulated. Hereafter, these are termed the classical, patch dynamics and geoecological models. All three predict a similar sequence in the early stages of development, i.e. colonization and establishment (‘nucleation’) of pioneers in randomly distributed safe microsites, followed by internally-driven growth and the coalescence of patches (Yarranton & Morrison 1974). In the early stages of primary succession (i.e. on newly-formed sites with no biological legacy), plant cover is low and growth conditions are stressful, in part due to the weakness of biotic reaction on the physical environment (Matthews & Whittaker 1987; Matthews 1992; Whittaker 1993). Spatial variability is high (Christensen & Peet 1984), reflecting local variations in the physical environment and stochastic processes of recruitment (del Moral 1998, 1999; Dlugosch & Del Moral 1999) and disturbance (Matthews 1992). Positive interactions between neighbours that enhance survival and growth of at least one of the species involved (i.e. facilitation) are generally more important than negative interactions such as competition (Bertness & Callaway 1994; Tirado & Pugnaire 2005). In such situations, the primary mechanism for colonization and establishment of pioneers may be patch nucleation in scarce, ‘safe’ microsites, followed by gradual patch growth and coalescence (Yarranton & Morrison 1974). Patchiness in the structure of the vegetation is likely to lead to a corresponding patchiness in soils, as clumps of pioneer plants add organic matter to the mineral sediment, stabilise loose substrates and trap wind-blown particles. Combined with short-range seed dispersal or clonal growth, the localized amelioration of environmental constraints leads to gradual expansion of pioneer patches, and hence an increase in the scale of pattern. Over time, the intensity of spatial structure increases as patches develop, and then decreases as they coalesce (Yarranton & Morrison 1974).
The three models differ in the mechanisms driving changes in later stages of ecosystem development. In the classical model, internal processes continue to dominate as intermediate and mature-stage species expand their populations through patch growth and coalescence (Yarranton & Morrison 1974). Progressive increases in biomass ameliorate the physical environment, removing environmental constraints on colonization and permitting more vigorous growth. Over time, competition for resources increases due to density effects (Holdaway & Sparrow 2006). The net effect of patch coalescence, the removal of environmental barriers to growth and the exclusion of less competitive species is a decrease in the spatial heterogeneity of the vegetation, which should also be associated with decreased heterogeneity in soils (e.g. Lane & BassiriRad 2005). Spatial heterogeneity reaches a minimum when the vegetation attains a ‘climax condition with no pattern or association’ (Kershaw 1959: 49).
In the patch dynamics model (Watt 1947; Holling 1992; Wu & Loucks 1995), internal (life history, biotic interactions) or external (disturbance) renewal mechanisms create gaps in the vegetation which subsequently revert to the pioneer stage. In general, mature stages are less resilient to renewal mechanisms, owing to high levels of internal connectivity and interdependence (‘over-connectedness’: Holling 1992). In a temperate forest for example, older trees are more susceptible to disease and uprooting by windthrow, both of which create gaps in the canopy. If the scale of the renewal mechanism is smaller than the ecosystem, then the landscape becomes a shifting mosaic of patches at different stages of ecosystem development (Watt 1947; Wu & Loucks 1995). In this model, all patches undergo succession at the same rate, but the timing of renewal is asynchronous and hence patches differ in the length of time over which they have undergone (secondary) succession.
The geoecological model (Matthews 1992) places special emphasis on the interaction of physical and biological processes during ecosystem development. As in the patch dynamics model, the vegetation differentiates into a mosaic of patches at differing stages of development, but in this case the time for (primary) succession is the same across all patches. Spatial differences in developmental stage emerge because different patches undergo (primary) succession at different rates, owing to spatial variability in edaphic factors and ecological processes (e.g. plant productivity, soil development). Spatial variability in the physical environment– as well as the positive (biotic) interactions which ameliorate environmental constraints (Bertness & Callaway 1994; Brooker & Callaway 1998; Tirado & Pugnaire 2005) – may assume greater importance in structuring vegetation in harsh or stressful environments than in more favourable environments. Even in later stages of development, physical factors may interact with biological processes to influence ecosystem spatial structure, particularly in harsh climates. In glacier forelands, for example, underlying substrate topography (and hence different levels of exposure, snow lie and geomorphological activity) interacts with pioneer expansion to create gradients of favourability for mature stage species (Matthews & Whittaker 1987; Matthews 1992; Whittaker 1993).
The three models can be distinguished empirically based on systematic changes in spatial structure (Table 1). In early stages of ecosystem development, all three models predict progressive increases in scale as pioneer patches establish, expand and coalesce (Dale & Blundon 1990). With coalescence, increases in spatial scale are accompanied by decreases in pattern intensity, leading to an overall decline in spatial heterogeneity. An increase in spatial scale also occurs with the nucleation and growth of patches of secondary colonists. However, the predictions of the models differ in later stages of development. For the classical model, pattern intensity declines with terrain age, as distribution of the competitive dominant changes from discrete patches on young sites to regular arrangements of plants or homogeneous cover on older sites. Spatial structure in the soil follows this trend of increasing homogenisation as a result of biotic reaction. In the patch dynamics model, renewal mechanisms re-set the development of mature patches, with the result that pioneer patches are created continually in a shifting, random distribution. Owing to the patchy structure, pattern intensity remains high. In the geoecological model, mature and pioneer patches also co-occur, but in a distribution pattern that is structured by substrate topography. Sediment accumulates preferentially in hollows, so that the spatial structure of the soil is also related to substrate topography.
Table 1. Models of the spatiotemporal dynamics of ecosystem development, with their predicted spatial patterns. See text for further explanation
Stage and explanation
Predicted spatial pattern
1. Pioneer colonization: random colonization of safe microsites (patch nucleation) by pioneers
1. Random distribution of pioneers relative to distribution of ‘safe’ microsites
2. Pioneer expansion: growth and coalescence of pioneer patches, leading to rapid increase in vegetation cover and soil development
2. Scale of pioneer patches increases monotonically while pattern intensity increases then decreases; bare substrate decreases in cover and depth of soil increases
3. Secondary colonization: nucleation of patches of secondary colonists amongst pioneers
3. Positive association between pioneers and secondary colonists at short lags; scale of pioneer patches decreases
1–3. (as in ‘initial colonization’ model, above)
4a. Homogenisation: growth and coalescence of patches of secondary colonists (competitive dominants); levelling of landscape as hollows are in-filled with sediment
4a. Scale of secondary colonist patches increases and pattern intensity increases then decreases; negative association between soil depth and substrate elevation at short lags
1–3. (as in ‘initial colonization’ model, above)
4b. Renewal: patches of secondary colonists revert to pioneer stage in response to random disturbance events
4b. Intensity of pattern remains high for both pioneers and secondary colonists; spatial distribution of pioneer and secondary colonists is unrelated to substrate topography
1–3. (as in ‘initial colonization’ model, above)
4c. Differentiation: secondary environmental gradients emerge as a result of coupled physical and ecological processes; expansion of secondary colonists occurs only in favourable sites
4c. Intensity of pattern remains high for both pioneers and secondary colonists; spatial distribution of pioneers and secondary colonists is associated with substrate topography; scale of vegetation patches is similar to that of substrate topography
Here, the three models of spatiotemporal dynamics were tested using detailed spatial analyses of vegetation on seven lava flows in southern Iceland, which together form an 850-year chronosequence. In the chronosequence approach, sites of different ages are compared at the same point in time in order to gain a spatial representation of a temporal sequence (Pickett 1987). The selection of suitable sites is critical because one of the primary assumptions of the approach is that factors other than time have been constant or have varied ineffectively (Stevens & Walker 1970); a well-constrained chronology is also of prime importance. We inferred changes in spatial structure through time by calculating a common set of spatial statistics for vegetation and soils on each of the seven flows in the chronosequence, and examining changes in the statistics with terrain age. We then compared the results with the predictions in Table 1, in order to provide insight on the mechanics of ecosystem development at the study site.
the study area
Iceland is a ‘model system’ (sensu Vitousek 2002) for studying ecosystem development. The biota is relatively simple due to Iceland's oceanic location, high latitude and history of glaciation (Steindorsson 1962; Sadler 1999). Human impact on Icelandic ecosystems has been of relatively short duration and is well-constrained by detailed historical records (Simpson et al. 2001). In addition, there are many well-dated lava flows that may be used in the assembly of chronosequences. Lava fields provide an ideal substrate for inferring long-term ecosystem development because they form discrete regions of new terrain that are effectively sterile when they are emplaced. The sites selected for this study are clustered around Mount Hekla (altitude: 1490 m), an active volcano in southern Iceland (64°00′ N, 19°40′ W). The region has a cool, temperate climate moderated by its maritime location: over the period for which detailed monthly records are available (1961–2005) the mean July and January temperatures were 11.0 °C and –1.7 °C, respectively (Icelandic Meteorological Office 2006). Precipitation and humidity in southern Iceland are generally high; the region around Mt Hekla received a mean annual rainfall of a little over 1200 mm in the same period (Icelandic Meteorological Office 2006).
Hekla is the second most active volcanic system in Iceland (Thordarson & Larsen 2007): there have been 18 eruptions from the summit fissure in the historical era (post-Tenth Century ad) and the area adjacent to the volcano is a mosaic of lava flows (Fig. 1). The ages of the historical flows are well-constrained; the older flows have been dated by tephrochronology and by studying contemporary accounts (Thorarinsson 1967). All of the historical flows from Mount Hekla are composed of blocky a’a lava and are characterized by loose, uneven surfaces. The geochemistry of the lava emitted from Hekla during the historical period has been more-or-less uniform; the flows studied are all andesitic in composition (Thordarson & Larsen 2007). The surfaces of the lava flows are dissected by shallow gullies (typically 2–6 m deep and 10–20 m wide), producing a terrain of hollows and low hillocks. The soils that form on the lava tend to be free-draining andosols derived mainly from the deposition of aeolian sediment and volcanic ash (tephra). They are characteristically fine with low cohesion, rendering them susceptible to erosion (Arnalds 2004). The vegetation on all but the youngest and oldest flows is dominated by thick carpets of the moss, Racomitrium lanuginosum. Surfaces less than a century old lack vascular plants and the flora is dominated by bryophytes and lichens (Bjarnason 1991). The older flows are characterized by the incidence of graminoids, woody shrubs (in particular Salix spp.) and, in some cases, birch scrub (Betula pubescens).
Direct human impact on the flows surveyed has been minimal: there is no history of cultivation or commercial exploitation (Thorarinsson 1967; Bjarnason 1991). All of the flows surveyed showed evidence of grazing by sheep; however, it is likely that grazing is light, particularly on the young, highly unstable flows (Bjarnason 1991). Climate change has occurred in Iceland over the last 850 years, most notably cooling during the little ice age (LIA, from 16th to 18th Century), but modelling exercises suggest that this event was unlikely to have driven significant ecological change below an altitude of 300 m in southern Iceland (Casely & Dugmore 2007). Potentially, disturbance by the deposition of tephra is a major mechanism of ecosystem renewal in the Mt Hekla area. However, tephrochronological studies suggest that none of the sites surveyed has experienced catastrophic tephra deposition in the historical era (Thorarinsson 1967).
Data were gathered from seven historical lava flows in the vicinity of Mount Hekla. The flows dated from 1980, 1947, 1845, 1554, 1389, 1300 and 1158 ad, giving a temporal range of almost 850 years. Hereafter the flows are referred to by their emplacement date (in years ad). Transect surveys were carried out in July 2005. A single transect was located on each flow. The chronosequence approach is premised on the assumption that growth conditions have remained similar for each of the sites composing the sequence (Stevens & Walker 1970). The transect sites were therefore selected to minimise inter-flow variations in environmental conditions. With the exception of the 1980 flow, the altitudes of the sites were kept within a narrow range of 253–273 m a.s.l.. The lava flows from the 1980 eruption are limited in extent, and only occur at higher altitudes; consequently, the survey site for this flow was located at an elevation of 447 m a.s.l. All of the sites were located in excess of 100 m from the margins of the flow to limit the effects of adjacent flows on species composition. Following these criteria, undulating sites that encompassed the range of topographic variation were selected by visual inspection.
At each survey site, a 40 m long transect was laid out perpendicular to metre-scale variations in topography. The transect length was selected for the scale of topographic variation, that is, the transects covered at least two hillock-hollow cycles. Plant species composition was recorded along the full length of the transect, using 400 contiguous 10 × 10 cm quadrats. This size of quadrat was chosen to reflect the small-scale nature of much of the vegetation present on the lava fields (e.g. tufts of moss and patches of crustose lichens) and a contiguous sampling regime was selected to encompass small-scale variation; in wave-structured environments such as lava flows, systematic sampling is recommended over random or aggregated sampling (Legendre et al. 2002). Frequency of occurrence of plant species and inorganic surfaces (including bare rock, soil and tephra) was recorded in 16 subdivisions (each 2.5 × 2.5 cm) of each quadrat. Taxonomy was done according to Kristinsson (2005) for vascular plants, Smith (1996) for liverworts, Smith (2004) for mosses and Purvis et al. (1994) for lichens. The depth from the moss or ground surface to the solid substrate (i.e. the original surface of the lava flow) was also measured at 10 cm intervals along each transect using a 60 cm-long stainless-steel probe. In cases where depth to solid substrate (DSS) exceeded the length of the probe, depth was recorded as 70 cm, in line with estimates for maximum soil depth provided by Bjarnason (1991).
In addition to recording soil depth along the transects, pits were opened up close to the survey sites on the 1947, 1845 and 1158 flows. The 1947 flow was chosen because it is the youngest surface to have significant vegetation cover, the 1845 flow because it is the youngest flow with evidence of soil development and the 1158 flow because it is the oldest surface and provides an end-member to the sequence. The pits measured 30 × 30 cm in plan and were cut vertically through the moss carpet and down to the lava substrate beneath. Pits were dug at three hillock-hollow locations on each flow, giving six pits per flow and 18 pits in total. In each case, the thickness of the moss carpet and the thickness/composition of each sediment or tephra horizon were recorded.
The vegetation around Mt Hekla is uneven and dominated by a small number of species (Bjarnason 1991). This analysis focussed on five of the most common species: two mosses (R. lanuginosum and Hylocomium splendens), a fruticose lichen (Stereocaulon vesuvianum) and two woody shrubs (Empetrum nigrum and Betula pubescens). All of these species were abundant enough to generate meaningful results in analyses of spatial structure. With the exception of B. pubescens, they also occurred on a number of flows, allowing an assessment of temporal changes in spatial structure. Racomitrium lanuginosum and S. vesuvianum are pioneer species that rapidly colonize newly-formed lava surfaces around Mt Hekla. Whilst R. lanuginosum was dominant on all of the sites surveyed, the occurrence of S. vesuvianum declined with increasing terrain age: it was very common on the 1980 flow but rare on flows older than c. 150 years (where it was restricted to the steep faces of outcropping boulders). Empetrum nigrum was found on all but the two youngest sites. It is amongst the first shrubby species to colonize the flows around Mt Hekla. Birch (Betula pubescens) woodland is considered the mature vegetation type in southern Iceland (Ólafsdóttir et al. 2001). This species occurred as isolated individuals on flows as young as c. 150-years-old, but was only abundant on the oldest flow, where it formed dense thickets. H. splendens was similarly found on young substrates, but was most common on the oldest flows, where it formed large patches.
The analysis of frequency data from these species was carried out in five stages:
1Indices of dispersion were calculated for each of the species as a global, first order indicator of the presence of spatial structure, and as a gauge of pattern intensity where spatial structure was indicated;
2Patch/gap size was investigated using the two-term version of new local variance analysis (NLV);
3Moran's I, an index of autocorrelation (patchiness), was calculated at different distance classes (lags) where the dispersion indices suggested the presence of spatial structure;
4The spatial relationships between pairs of species (primarily co-occurrence or segregation) were investigated by calculating cross-correlograms.
Indices of dispersion were calculated for four of the five species on each of the seven flows (B. pubescens was omitted as this species was recorded by presence-absence rather than frequency data). The index of dispersion, ID, is a simple, global statistic that expresses the ratio of the variance, σ2, to the mean, x̄ (Dale 1999):
( eqn 1)
If the sampling units are randomly distributed, the observations follow a Poisson distribution; in this case, the mean is equal to the variance and ID approximates unity. If the objects have a clumped (under-dispersed) pattern, the variance is high and ID is greater than unity. Conversely, in a regular (over-dispersed) arrangement, the variance is lower than the mean and the value of ID is less than unity. In this way, the index of dispersion may be used to detect the presence of spatial structure. Pattern intensity is a measure of ‘contrast’ between patch and gap phases (Kotliar & Wiens 1990): variance-mean ratios such as the index of dispersion may therefore also be used to gauge pattern intensity (Hill 1973; Zalucki et al. 1981). Dispersion indices were calculated using the PASSAGE statistical software package (Version 1.0: Rosenberg 2001); a chi-squared test of significance was calculated for each species on each flow.
Patch/gap size was described for four of the species (refer to note regarding B. pubescens, above) using the two-term version of NLV analysis. In this case, a ‘patch’ was defined as a region of the vegetation containing the species under consideration; a ‘gap’ was defined as a region in which the species was absent (this region may still have been vegetated). This form of analysis identifies the mean size of the smallest phase in a pattern, whether that is the patch phase or the gap phase (Dale 1999). The technique is closely related to other quadrat variance techniques such as two-term local quadrat variance. The variance, V, for a given block size, b, was calculated using the following equation (Dale 1999):
( eqn 2)
The maximum block size was set at half the transect length, that is 20 m. The variance was plotted against block size and the peaks were interpreted as characteristic scales of the patch/gap phase. The significance of the peaks was evaluated by comparing the observed variance values with mean variances derived by running 999 iterations on randomised data. All calculations were carried out using the PASSAGE statistical software package (Rosenberg 2001).
Moran's I, an index of autocorrelation, was calculated at different distance classes (lags) where the dispersion indices suggested the presence of spatial structure (Legendre & Legendre 1998). Moran's I is related to Pearson's correlation coefficient: calculated values usually vary between 1 (perfect positive correlation) and −1 (perfect negative correlation). Values around zero indicate an absence of autocorrelation. Moran's I was calculated for a given lag distance, h, using the following equation (Cliff & Ord 1981):
( eqn 3)
where W is a binary weighting factor (set at 1 if the separation between the points lies within the distance class being calculated, and 0 if it does not), yh and yi are the values of the variable at sampling locations h and i, ȳ is the mean value of the variable and n is the number of points in the distance class. Lag distances that approach the transect length only compare a few points at the ends of the transect; the maximum lag was therefore set at half the transect length (20 m). I was calculated for 10 distance classes, following Sturge's rule that is number of classes = 1 + 3.3 log10(m), where m is the number of sampling units (Legendre & Legendre 1998). The interpretation of correlograms is primarily based on their shape (Legendre & Fortin 1989). If the variate in question is randomly distributed, the calculated values will approximate zero at all distances. If the variate has an aggregated distribution, the calculated values of I will be relatively high at small distance intervals and will decline with increasing separation. At intervals larger than the average patch size, the value of I becomes negative as patches are compared with gaps. The significance of individual autocorrelation coefficients was determined from their moments (Cliff & Ord 1981) after using a progressive Bonferroni correction to account for multiple testing. All calculations were carried out using the PASSAGE statistical software package (Rosenberg 2001). The shortest lag at which I decreased from positive values to zero was used as an indicator of the scale of spatial structure, whereas the amplitude of I was used as a secondary indicator of pattern intensity.
In addition to univariate analysis, correlograms may also be plotted for bivariate data. The resulting plots, known as cross-correlograms, indicate the correlation between two variables at different separation distances. Cross-correlograms were plotted for R. lanuginosum vs. S.vesuvianum to assess the spatial interaction of these two pioneer species in the earliest stages of vegetation development. Cross-correlograms of R. lanuginosum vs. E. nigrum, H. splendens and B. pubescens were plotted to investigate patch development in secondary colonists establishing in the moss carpet. A cross-correlogram was also plotted for B. pubescens vs. H. splendens to establish if the incidence of these two species on the oldest flow was correlated. If the two species tend to co-occur, high positive correlations are expected at small separation distances. Conversely, if the species are spatially segregated, negative values are expected at small lags. The cross-correlation statistic, r, for variables u and v at a given lag, h, is calculated by dividing the cross-covariance, Cuv, at lag h by the product of the standard deviations of the two variates, thus:
( eqn 4)
Cross-correlograms are asymmetrical about h = 0, that is, the direction of the offset is important and ruv (h) does not necessarily equal ruv (–h). In this analysis, the values of ruvwere averaged over the two opposite directions so that the values on the abscissa (|h|) are always positive. The active lag distance (that is, the maximum separation distance used) was again set at 20 m as cross-correlograms tend to decompose at high lags as the number of pairs per lag class decreases rapidly. A t statistic was calculated for the autocorrelation coefficient in each distance class, using the following equation (Hewitt et al. 1997):
( eqn 5)
The test statistic was again modified using a progressive Bonferroni correction to account for multiple testing. These analyses were used to indicate whether close-range interactions between particular species were positive or negative.
Cross-correlograms of abundance data (for R. lanuginosum, E. nigrum and H. splendens) vs. DSS were plotted to examine the relationship between vegetation patterning and soil depth. Correlograms of Moran's I for surface elevation were used to investigate surface levelling. Cross-correlograms of DSS vs. substrate elevation were also plotted to investigate the infilling of hollows over time. The correlograms were calculated as above (eqns 3–5).
In summary, the presence of spatial structure was investigated through indices of dispersion; this metric was also used to gauge pattern intensity. The scale of any structure present was analysed using NLV techniques and Moran's I correlograms.
The mean frequencies per quadrat of four of the species studied and of inorganic surfaces (exposed rock and bare soil) are shown in Fig. 2. Racomitrium lanuginosum occurred in almost all quadrats on flows younger than c. 500 years, but its dominance declined thereafter with increasing terrain age. The frequency of S. vesuvianum declined rapidly on flows older than c. 25 years. Empetrum nigrum and H. splendens were present from c. 150 to 600 years, respectively, and both showed marked increases in frequency on the oldest flow. Betula pubescens was recorded only on the oldest flow (58 of 400 quadrats). The incidence of inorganic surfaces was relatively high on the youngest flows, but very low on flows older than 150 years.
The indices of dispersion for R. lanuginosum indicated a patchy distribution (ID > 1) on two of the older flows (the 1389 and 1158 flows), whereas the values for other species indicated patchy distributions for all occurrences (Table 2). The value of ID (and hence pattern intensity) for R. lanuginosum was low on all but the oldest site, indicating low variance in frequency on the younger flows. The values of ID calculated for S. vesuvianum increased monotonically with increasing terrain age. Clear trends in intensity for E. nigrum and H. splendens were not apparent.
Table 2. Indices of dispersion
Flow emplacement date (years ad)
Values around 1 indicate a random distribution, values < 1 indicate a regular distribution and values > 1 indicate a clumped distribution. *Indicates values significant at P < 0.01 (χ2-test).
All of the peaks returned by the NLV analysis exceeded the mean variance derived from 999 iterations of randomised data. Interpretation of the results returned by the two-term NLV analysis (Table 3) depends upon the continuity of cover exhibited by the species in question. Racomitrium lanuginosum formed an almost continuous carpet with small gaps on the 1389 flow, but fragmented into a pattern of large patches on the oldest (1158) flow. Similarly, the pioneer species S. vesuvianum had very high levels of cover and relatively small gap size on the 1980 flow, but its cover became more fragmented to give small patches later in the chronosequence (1947 and 1845 flows). In contrast, the secondary colonist H. splendens formed small- to medium-sized patches when it first colonized (1389 and 1300 flows), but expanded to more continuous cover (with gaps) on the 1158 flow. Patches of E. nigrum generally expanded in size with increasing terrain age, and B. pubescens also formed patches on the oldest flow. These results demonstrate that spatial structure in pioneer species (R. lanuginosum, S. vesuvianum) emerged from fragmentation of large patches (particularly in S. vesuvianum, where the ‘patch’ became the small phase). In contrast, patches of secondary colonists expanded (and, in the case of H. splendens, coalesced) over time.
Table 3. Mean patch/gap size (in metres) in patchy distributions, calculated using two-term NLV analysis
Flow emplacement date (years ad)
All of the vegetation correlograms plotted exhibited significant (P < 0.05) autocorrelation at a range of scales. Representative correlograms are presented in Fig. 3. Correlograms were plotted for the flows on which each species was most abundant. Where the species concerned was abundant on more than three flows (e.g. R. lanuginosum and E. nigrum), correlograms encompassing a wide temporal range were selected to illustrate broad trends in spatial structure. The scales at which autocorrelation was observed varied with species and terrain age, although some broad patterns emerged. In all cases, I was positive at small distance intervals and tended to decrease with increasing separation distance, generally becoming negative at high lags. The clearest patterns were found in the data from the 1158 flow, where R. lanuginosum, E. nigrum, H. splendens and B. pubescens all showed high positive autocorrelation at short lags and negative values at greater distances (Fig. 3c,f,l and m). Except in the case of S. vesuvianum, both the lag at which I decreased to zero and the range of I (both positive and negative) tended to increase with terrain age, with the correlograms becoming less erratic. These trends were particularly clear in the correlograms for R. lanuginosum (Fig. 3a–c). These results indicate that, for all species except S. vesuvianum, both the scale and intensity of spatial structure tended to increase with terrain age.
Cross-correlograms for the species studied are presented in Fig. 4. The plots presented were selected using criteria similar to those used for the correlograms (Fig. 3). The cross-correlograms for R. lanuginosum vs. E. nigrum were positively correlated at short distance lags on younger sites (1845, 1554; Fig. 4a), but negatively correlated on older sites (1389, 1300 and 1158; Fig. 4b and c); the range and magnitude of negative correlation increased with terrain age. The cross-correlograms for R. lanuginosum vs. S. vesuvianum (Fig. 4d–f) indicated significant negative association at short distance lags, regardless of terrain age. On the 1158 flow, B. pubescens showed short-range positive correlation with H. splendens (Fig. 4g), and negative correlation with R. lanuginosum (Fig. 4h). Racomitrium lanuginosum and H. splendens were negatively correlated over short and intermediate lags on this flow (Fig. 4i); no strong relationship between these mosses was identified on younger flows. These results indicate that R. lanuginosum was always spatially segregated from the other pioneer, S. vesuvianum, whereas patch nucleation of the secondary colonists, E. nigrum and H. splendens, occurred within the R. lanuginosum matrix. With increasing terrain age, both E. nigrum and H. splendens became spatially segregated from R. lanuginosum.
Significant relationships were found between species abundance and DSS on the older sites. For example, on the 1158 flow, R. lanuginosum was negatively associated with DSS over short distance lags (Fig. 5a) indicating that the highest frequencies of this species were correlated with the thinnest soils. In contrast, H. splendens and E. nigrum were positively correlated with DSS over short lags (Fig. 5b and c). These relationships were either much weaker or non-existent on the younger flows (not shown).
The median DSS increased with terrain age (Fig. 6, inset). All of the sections from the 1947 flow comprised a layer of the moss, R. lanuginosum, growing directly on the surface of the lava (Fig. 6). Five of the six sections had a thin (< 1 mm) layer of silt at the base of the moss stems. The 1845 sections had moss layers of a similar depth. In addition to a surface layer of living vegetation, two of the sections also had an O-horizon composed of dead and partially decomposed moss stems. All of the 1845 sections had a layer of orange-brown silt (5–15 cm thick) at their base. The sections from ‘low’ sites were characterized by multiple bands of a fine, dark tephra in the silt. The 1158 sections were similar but markedly deeper (up to 90 cm in the hollows). The sections from the hollows were deeper than those from the hillock locations and were characterized by a large number of tephra layers: 10 distinct layers were observed in one section.
Spatial analyses of soil depth and topography are presented in Fig. 7 for selected flows (the 1980, 1845 and 1300 flows) to illustrate key points in development of the lava flow ecosystem. The 1980 flow was the youngest surface, and lies at the start of the chronosequence; the 1845 flow had a thick moss layer, the first sign of vascular plant life and the first significant accumulations of sediment; the 1300 flow is representative of mature vegetation, and the beginnings of a differentiation between the vegetation on hillock and hollow sites. The plots exhibited positive correlations at short lags and negative correlations at intermediate and longer lags (Fig. 7a–f). The spatial scale of positive correlation increased with terrain age; the amplitude of variation also increased, with high positive and negative correlations on the older flows. All of the cross-correlograms of DSS vs. substrate elevation (Fig. 7g–i) exhibited negative cross-correlation at short lags and the spatial scale of negative correlation increased with terrain age. In common with the correlograms, the range of variation of the cross-correlation statistic also tended to increase with terrain age. These results indicate that, over time, sediment tended to accumulate preferentially in hollows.
inferred developmental sequence
The long-term development of vegetation on the lava fields of Mt Hekla occurs in four stages (Fig. 8). During the first stage (‘pioneer colonization’, < 20 years; Fig. 8: Stage 1), a limited number of moss and lichen species establish on the newly-emplaced lava, forming patches in small surface irregularities (< 10−2 m in scale; N.A. Cutler et al., unpubl. data) that function as ‘safe sites’ (Harper 1977). During the second stage (‘pioneer expansion’, 20–100 years; Fig. 8: Stage 2), these incipient moss patches (in particular of R. lanuginosum) expand, coalesce and thicken to form a spatially homogeneous ‘carpet’ and the proportion of bare substrate declines rapidly. As the moss carpet develops, other pioneer species, most notably S. vesuvianum, decline in abundance and patch size. During the third stage (‘higher plant colonization’, 100–600 years; Fig. 8: Stage 3), small, isolated patches of dwarf shrubs (such as Empetrum nigrum and, eventually, B. pubescens) establish within the moss carpet, often in association with scattered forbs and graminoids. During the fourth stage (‘differentiation’, > 600 years; Fig. 8: Stage 4), the moss carpet becomes fragmented as the dwarf shrubs and their associated ground layer (e.g. H. splendens in thickets of B. pubescens) expand. Expansion of the secondary colonists is constrained by meso-scale (101 m) variations in topography: hillocks remain covered by the Racomitrium carpet whereas hollows develop patchy distributions of dwarf shrubs and, in some cases, a more continuous layer of shade-tolerant mosses (H. splendens). Other secondary colonists, including graminoids (notably Agrostis vinealis and Festuca vivipara), forbs and lichens (e.g. Peltigera membranacea), also cluster in the hollows with the shrubs, but remain rare in hillock locations. Throughout all four stages, wind-blown sediment accumulates preferentially in topographic lows, leading to an incomplete levelling of the landscape.
This inferred developmental sequence suggests that the initial stages of ecosystem development (< 600 years) at Mt Hekla are consistent with the ‘initial colonization’ model (Table 1, stages 1–3). Previous work on lava flows 6- and 15-years-old (Cutler et al., unpubl. data) showed that pioneer mosses colonize a spatially random selection of available safe sites (Table 1: Stage 1, Predicted spatial pattern 1) and that, within two decades, these incipient patches expand laterally and coalesce to form a thin, almost contiguous cover. In the present study, spatial analyses of these pioneer patches indicate that their scale had already reached a maximum (and their pattern intensity a minimum) by 26 years (1980 flow); also in this stage, the proportion of bare substrate declined sharply and soils thickened rapidly (Table 1: Stage 2, Predicted spatial pattern 2). The secondary colonist E. nigrum was initially positively associated with the dominant pioneer (R. lanuginosum) at short spatial lags; the scale of pioneer pattern subsequently decreased as secondary colonist patches expanded (Table 1: Stage 3, Predicted spatial pattern 3). Overall, changes in the scale and intensity of pattern over the first 600 years since lava emplacement are consistent with Yarranton & Morrison's (1974) model of a cyclical series of nucleation, growth and coalescence of pioneer and secondary colonist patches.
In the period > 600 years after lava emplacement, ecosystem development at Mt Hekla is most consistent with the ‘geoecological’ model (Table 1, stage 4c). The limited expansion of secondary colonist patches and the incomplete levelling of the landscape by infilling of hollows are partially consistent with predictions for the ‘classical’ model (Table 1: Stage 4a, Predicted spatial pattern 4a), but these processes did not lead to homogenisation of vegetation and soils within the period covered by the study. On the contrary, vegetation development was accompanied by an increase in pattern intensity as the spatial distribution of secondary colonist patches became structured according to substrate topography at a scale of 1–10 m (Table 1: Stage 4c, Predicted spatial pattern 4c: refer to the increased amplitude of the correlograms in Fig. 3, and the positive relationships between species density and elevation in Fig. 5). There was little evidence for a shift from positive (facilitative) to negative (competitive) interactions across the chronosequence. The cross-correlograms suggested one example of positive interaction on the 1980 flow (E. nigrum and R. lanuginosum: Fig. 4d). However, positive interactions were just as likely to be found on the oldest flow (e.g. the relationship between H. splendens and B. pubescens, Fig. 4i). Generally, the cross-correlograms suggested that short range negative interactions predominated on flows of all ages. Additionally, tephra falls occurred repeatedly over the 850 years, and although these disturbance events might have been expected to act as renewal mechanisms (Table 1, stage 4b), they did not re-set secondary colonist patches to the pioneer stage. On the contrary, landforms receiving the highest frequency and depth of tephra fall (hollows) progressed to a more mature stage than landforms showing a lighter frequency and intensity of disturbance (hillocks), and the scale of vegetation patches approached that of the substrate meso-topography (Table 1: Stage 4c, Predicted spatial pattern 4c). Hence, the spatiotemporal dynamics on Mt Hekla are consistent with the geoecological model of ecosystem development formulated for glacier forelands (Matthews & Whittaker 1987; Matthews 1992; Whittaker 1993).
the mechanics of spatiotemporal change
The mechanisms of patch nucleation and expansion were related to plant growth and vegetative reproduction, both for the dwarf shrubs and the cryptogams. The dwarf shrub species observed are capable of establishing on young substrates: small specimens of B. pubescens, Salix lanata and S. phylicifolia were all observed on the margins of the 1845 flow, for example. These occurrences were invariably isolated individuals and probably resulted from rare, long-distance dispersal events. On the oldest flows, individual shrubs are larger and extensive patches are observed. The expansion of the shrub patches is probably largely due to vegetative reproduction by the original colonists: most of the shrub species commonly observed on the older flows have vegetative modes of reproduction, including rhizomes (Salix herbacea and Vaccinium uliginosum), rooted stems (E. nigrum and Arcostaphylos uva-ursi) or adventitious rooting of layered branches (B. pubescens) (Koop 1987). Vegetative regeneration is particularly common in stressful environments, where the chances of propagation by seed are slim (Grime 2001), and similar phases of vegetative patch expansion have been described on glacial forelands (Whittaker 1993; Stöcklin & Bäumer 1996). Vegetative patch formation is not restricted to stressful habitats: there are, for example, well-documented instances of this phenomenon from upland areas in temperate latitudes (Kershaw 1959; Anderson 1961a, b). However, the predominance of vegetative reproduction accentuates the intensity of spatial structure, as daughter plants are clustered around the parent plant and are more likely to survive than seedlings (Grime 2001). Similar factors apply to lateral expansion of the cryptogams studied: R. lanuginosum and H. splendens are prostrate, branching species that may regenerate by branch growth and fragmentation; S. vesuvianum has a fruticose growth form with abundant, easily fragmented pseudopodetia.
Differentiation on a landscape scale probably involved interactions between environmental and ecological processes that amplified pre-existing spatial heterogeneity to create a gradient in edaphic conditions between hillock and hollow locations. Some obvious levelling of the landscape occurred with increasing terrain age as sediment accumulated preferentially in hollows. Complete de-coupling of substrate and surface heights did not occur, however, probably because the amount of sediment accumulated (a maximum of around 1 m in 850 years) was much lower than the amplitude of topographic variation (2–6 m, typically). Whilst de-coupling may occur over much longer timescales, or in areas with higher sedimentation rates, the legacy of substrate topography and its consequences for differential sediment accumulation and soil development remain influential on a multi-century timescale in the Hekla area. Topographically mediated variation in edaphic factors such as soil organic matter, moisture and pH have been demonstrated to be important in the emergence and persistence of structure in vegetation (e.g. Anderson 1961b; Zedler & Zedler 1969). Around Mt Hekla, such structure can only emerge on the older sites, as very young locations have no soils. This may partly explain the spatial homogeneity of the vegetation in these locations.
Positive feedback loops could accelerate differentiation if a gradient in the biotic reaction occurs as a result of preferential accumulation of sediments in sheltered hollows. For example, slightly higher levels of cover in the hollows due to the accumulation of a proto-soil would result in the stabilisation of the substrate and the retention of more wind-blown sediment. Persson (1964), for example, noted the effectiveness of the Racomitrium layer in trapping fine sand and vegetated hollows are likely to trap and retain wind-blown propagules (Tsuyuzaki et al. 1997). Positive feedback loops may also be related to differences in microclimate between hollow and hillock locations. Air humidity is higher in hollows and temperature fluctuations are less pronounced (Bjarnason 1991). The differential development of vegetation and soils would tend to accentuate these differences: Racomitrium spp. mosses, for example, increase moisture retention as well as SOM concentrations and soil microbial activity on glacial moraines (Persson 1964; Bardgett & Walker 2004). Racomitrium lanuginosum favours conditions of high humidity (Tallis 1959) and increased moisture retention resulting from increased biomass could therefore lead to further growth, an ecological ‘switch’ similar to that described by Wilson and Agnew (1992). Canopy development also has knock-on effects for ground-layer vegetation: in this case, the formation of dense thickets of B. pubescens was associated with emergence of a ground layer dominated by H. splendens rather than R. lanuginosum, which cannot tolerate shaded conditions (van der Wal et al. 2005). Factors such as the length of snow-lie and the supply of moisture from melting snow patches may also be important (e.g. Matthews & Whittaker 1987). For example, at high latitudes R. lanuginosum occurs preferentially in areas where the snow cover melts early in the spring (Tallis 1958). This may contribute to the patchy distribution of this species on the older flows, as snow would tend to lie longer in shaded hollows. Positive feedback loops have the potential to play a major role in ecosystem development, as they provide a general mechanism by which stable mosaic situations may emerge and persist (Wilson & Agnew 1992). They are likely to be particularly important in marginal habitats, where even small improvements in growing conditions can be significant biologically.
The 850-year chronosequence analysed here suggests a switch in process dominance from patch nucleation and coalescence to edaphic and ecological differentiation, with a corresponding increase in the scale of environmental variation from micro- (safe site) to meso- (topographic landform) scale. Over a longer time frame (> 1000 years), transition to either the classical or patch dynamics regime remains a possibility. On the one hand, homogenisation of the vegetation consistent with the classical model could occur if the patches of Betula continue to expand. The fact that this has not occurred over a period of 850 years may be due to the deforestation that accompanied settlement of Iceland from the Ninth Century onwards (Arnalds 1987). Prior to settlement, large expanses of continuous tree cover would have created a sub-canopy microclimate suitable for seedling establishment in what is otherwise a marginal environment for woodland development. A loss of self-regenerating tree cover (exacerbated by increased grazing pressure) may have led to reduced recruitment and, ultimately, a decline in propagule supply to adjacent areas of primary terrain, for example newly-emplaced lava flows. On the other hand, asynchronous renewal of vegetation patches consistent with the patch dynamics model could occur if the influence of the physical template diminishes over time. As the surface topography becomes more even and soils on hillocks develop further, mature stage vegetation may expand in spatial scale. Smaller-scale renewal mechanisms (e.g. windthrow) may become relatively more important to vegetation structure, leading to a hybrid geoecological/patch dynamics regime. Ultimately, the influence of underlying substrate topography may become insignificant, allowing renewal processes to dominate. Transition to the classical or patch dynamics models of spatiotemporal development may be evident only on longer chronosequences than the one studied here, or in more favourable habitats where succession proceeds more rapidly.
When placed in the context of studies in other ecosystem types, the results of this study suggest widespread applicability for a spatial model of initial colonization based on random establishment, growth and coalescence of pioneer patches (provided development is not dominated by disturbance). Similar patterns have been observed during the initial stages of ecosystem development in a diverse range of habitats, including china clay residues (Barnes & Stanbury 1951), sand dunes (Yarranton & Morrison 1974; Franks 2003) and glacial forelands (Dale & Blundon 1990). The theory of patch nucleation and coalescence is well-established in the physical sciences literature (e.g. Pardoen & Hutchinson 2000; Suemitsu et al. 2003) and the application of a simple analytical approximation based on this theory suggests that it may be useful in describing complex ecological dynamics (Korniss & Caraco 2005). In addition to providing a theoretical context for addressing fundamental questions on the relationships between local ecological processes and global dynamics, this theory could find practical application in control of species invasions and ecological restoration, both of which involve nucleation. For example, invasive species often radiate from foci and spread contagiously by patch initiation, growth and coalescence (Moody & Mack 1988). In a similar fashion, artificial habitat islands can act as foci for initiating re-vegetation in degraded ecosystems (Robinson & Handel 2000). Hence, the theory of patch nucleation and coalescence could provide a relatively simple basis for modelling the spread of invasive plants and the development of restored ecosystems.
The applicability of the geoecological differentiation model – observed on glacial forelands (Matthews & Whittaker 1987) and late in the developmental sequence at Mt Hekla (this study) – may be contingent on spatial scale. At the scale of the stand, for example, forests tend to become more homogeneous over time, even though pattern intensity at a fine scale may increase (Aldrich et al. 2003; Harper et al. 2006). Experimentation with a spatially-explicit model suggests that coherent vegetation patterns will emerge only if the scale of environmental variation exceeds that of the plant's local neighbourhood (Feagin et al. 2005). If the scale of environmental variation is too small, the plants’ individualistic responses to the local environment dominate and spatial structure is unpredictable (Feagin et al. 2005). In the context of primary succession, the plant's local neighbourhood should increase in scale to some maximum as pioneer and secondary colonist patches grow. Vegetation pattern may emerge late in ecosystem development only if the scale of environmental variation is sufficiently large to transcend the maximum range of the plant's local neighbourhood.
We are grateful for the insightful comments of two anonymous referees. We are also grateful to Gregor Sutherland and Dr Kate Smith for field assistance and Dr Brian Coppins for assistance with lichen identification. Permission to access sites was granted by The Icelandic Research Council. This research was funded by a NERC studentship to NAC (NER/S/A/2004/12729). L.R.B. was supported by a NERC Advanced Fellowship (NER/J/S/2001/00799).