1The morphology and distribution of six benthic colonial diatoms were investigated from the perspective of fractal geometry and stream ecology to test whether colonial complexity of benthic diatoms is associated with a tolerance to environmental variability, that is, if a random force, such as the unpredictability of current velocity, could be responsible for the development of a high morphological organization.
2The fractal dimension of diatom colony perimeters ranged from 1·06 to 1·54, indicating a vast morphological variation from simple geometric shapes to very complex outlines. The niche breadth of the six colonial diatoms, defined from regression models of species abundance along a current velocity gradient, also showed a substantial variation, from 0·48 to 0·79 m s−1.
3There was a strong positive relationship between diatom morphological complexity and species niche breadth, suggesting that increased morphological complexity in colonial diatoms is a possible evolutionary strategy for survival in unpredictable environments.
Diatoms are ubiquitous and are often the dominant algal group in freshwater benthos. This research focuses on common colonial diatoms growing in the benthos of running waters, and the relation between colonial morphology and habitat features. The theoretical background of this investigation lies in fractal geometry and chaos theory. Mandelbrot (1982) introduced fractals in natural sciences, and his ideas have been implemented in ecology (Sugihara & May 1990). Most natural objects do not conform to Euclidean dimensionality, and fractal geometry made possible the description of complex entities such as clouds (Lovejoy 1982) and vegetation (Morse et al. 1985). Fractal properties of organismal morphology have recently stirred the interest of a diverse group of scientists studying sponges (Kaandorp 1991); brown algae (Corbit & Garbary 1995); and vascular terrestrial plants (Alados et al. 1999; Morse et al. 1985). However, the adaptive value of fractal structures as a function of environmental gradients has not been adequately addressed (Abraham 2001). On the other hand, chaos theory entertains the transition between order and chaos, and shows how randomness creates perfectly deterministic shapes. This was ingeniously demonstrated by the chaos game (Peitgen, Jurgens & Saupe 1992), for example: following a set of simple rules a random roll of a die generates highly ordered fractal structures.
There are few studies on the evolutionary pathways and environmental constraints of plant morphological radiation. Based on their investigations on five macroalgae, Littler & Littler (1980) proposed a functional form hypothesis to explain attributes of productivity, ecology and survival on the basis of the gross morphology of marine algae. Littler (1980) showed that algal morphology and photosynthetic performance are related, which is suggestive of adaptive evolutionary strategies. Moen, Ingvarsson & Walton (1999) found that grazing increased the morphological complexity of clonal plants. Despite such findings, plant morphology is still the primary domain of taxonomic and phylogenetic studies, and structure and function remain disparate properties of organismal life history.
The colonies formed by many benthic diatoms display a whole spectrum of morphologies, which so far have been described only in qualitative terms. Aquatic ecologists attempted to uncover the adaptive value of algal morphological diversity by considering the time of species appearance during succession, which was linked to species access to light and nutrients. Thus there are some suggestions that the size of diatom colonies is related to successional stage, for example, low-profile, pioneer species vs long-bodied, late-successional colonizers (Hoagland, Roemer & Rosowski 1982; McCormick & Stevenson 1991). However, conventional approaches cannot explain why, within each successional sere, there is a wide array of growth forms with shapes ranging from simple, smooth, continuous, straight lines (e.g. Fragilaria capucina filaments) to highly complex, jagged, broken, curved lines (e.g. Fragilaria crotonensis colonies). Colonial growth form is widespread in periphyton developing in streams where current velocity is not only the major mechanical force but, by affecting the ion and nutrient transport within the benthic mat (Stevenson & Glover 1993), current also has a complex physicochemical effect on the periphyton (Stevenson 1996). A recent spatial study of stream periphyton revealed that current velocity alone accounts for 35% of the variance in diatom distribution, whereas only 13% was contributed by other factors (Passy 2001). If a freshwater species has evolved tolerance to a broad range of current regimes, it could also be adapted to a variety of chemical and nutrient availabilities, which would constitute a broad environmental niche. Hence it was appropriate to select current velocity as a collective variable to characterize the environment of a species and its ecological niche.
Conditions of existence have primary importance in plant as opposed to animal evolution (Niklas 2000), thus the most logical place to search for an explanation of diatom colonial complexity would be their characteristic environment. This study focused on environmental variability as a possible mechanism driving diatom colonial heterogeneity. My hypothesis was that random and diverse environments would select for species with complex colonial morphologies, whereas species with simple outlines would be better able to tolerate constant, uniform environments. In unpredictable environments, a species would have a better chance for survival if it maintains a complex colonial morphology. Such morphology either would secure multiple orientation planes for the constituent cells to optimize their fitness to a variety of hydrodynamic regimes differing in shear stress, microturbulence and nutrient supply rate; or it would provide large interstitial spaces between the individual cells, allowing for easier passage of nutrients and gases. Therefore a species’ environmental niche breadth – the amount of variability it can withstand – would be directly related to its colonial morphology: the larger the niche, the more complex the colony. Species with wide niches have a similar chance of establishing in slow and fast current regimes, so the temporal conditions of existence of an offspring or a vegetative clone are random and unpredictable. The opposite holds for species with narrow niches – an offspring or a clone can survive only within a few current regimes, so their environment is predictable and relatively deterministic. Emigration and immigration in situ experiments revealed that both processes account for substantial proportions of the standing crop of benthic diatoms (Stevenson & Peterson 1991), implying that adaptation to temporal heterogeneity is particularly important for diatoms. Moreover, diatoms are ideal objects to test such a hypothesis because, unlike other colonial or multicellular organisms, the members of their colonies, being held together by frustular projections or mucilage, do not have protoplasmic connections with each other. Consequently, diatoms would adapt more directly to environmental stimuli because they do not have to conform to the biomechanical and physiological constraints that govern the body plans of more complex multicellular organisms.
Materials and Methods
Field and Laboratory Techniques
The study area was an unshaded, cobble-bottom reach of White Creek (Washington County, NY). On August 27 1999, diatoms were sampled and current velocity and depth were measured at 81 locations on a regular square sampling grid (for details on the study area and diatom distribution see Passy 2001). The grid had an extent of 16 m2, a distance between neighbouring sampling points (interval) of 0·5 m, and an elementary sampling unit (grain) of 0·01 m2. Current velocity readings were taken with a flow meter (model 2000, Marsh-McBirney Inc., Frederick, MD) at approximately mid-depth of the water column. Periphyton was scraped from several stones within each 10 × 10 cm sampling unit, composited, and preserved in 4% formaldehyde. In the laboratory, samples were washed with distilled water to remove the formaldehyde, homogenized using a mixer or vigorous shaking, and mounted in Naphrax (Northern Biological Supplies Limited, Ipswich, UK). Between 450 and 1600 diatom frustules were enumerated with an oil immersion objective at magnification of 1000×.
Image Analysis and Measuring Fractal Dimension (D)
Micrographs of two to three diatom colonies were taken at the magnification that reveals the most morphological detail, traced manually, scanned and converted to 600 dpi TIFF images. The images were converted to geographic information systems raster grids. The grids were resampled to create a square grid with 1024 rows and columns. The grids were then processed using a thinning function to reduce the linear features of the colonies to a single pixel width and to remove spurious background pixels. A series of square grids with sides containing 2n pixels (n = 1–7) was superimposed over each diatom colony (Fig. 1). Powers of 2 higher than 7 were not used in the analysis because they resulted in a convex distortion of the log–log plots described below, and underestimation of the fractal dimension, D (for more details on techniques and problems with measuring D see Kenkel & Walker 1996). The number of pixels making up the colony outline was counted, log-transformed, and expressed as a linear function of the log number of grid side pixels. The slope of this regression yielded the fractal dimension of the colonies as described by Morse et al. (1985). D provides a direct measurement of shape complexity. In the case of perimeters, it takes values in the interval [1, 2], as 1 signifies a simple linear pattern and 2 an extremely complex pattern that tends to fill a plane.
Diatom colonies are three-dimensional structures, but there are enormous technical problems with measuring D of three-dimensional objects, consequently for fractal analysis two-dimensional projections of the colonies were used. As the shapes analysed were drastically different from one another, and this difference was preserved in the projections, a planar conversion was considered justified and representative of the shape complexity of the real three-dimensional objects. For example, some colonies approximated simple geometric shapes such as cylinders and prisms, both of which retained their Euclidean dimension upon planar projection, while the complex three-dimensional stalks and rosettes remained complex stalks and rosettes after collapsing onto a two-dimensional plane.
Measuring Niche Breadth
Although species niche constitutes tolerance to multiple abiotic and biotic factors, it has often been treated as a frequency distribution along a single gradient. The shape of this response curve has been the basis for various definitions of niche and measures of niche breadth (McNaughton & Wolf 1970). In this study, niche breadth was defined from diatom response curves along a current velocity gradient. The range of current velocities was divided into 10 current intervals, defined at 0·06–0·07 m s−1 increments. The cell counts of each colonial diatom were converted to a percentage relative abundance, and averaged for each regime to reduce the random noise arising from the inherent patchiness of species distribution. The average values were log-transformed and regressed against the current gradient to take advantage of a particular property of unimodal models, that is, a parabola fit to log-transformed abundances is actually a Gaussian response curve fit to the original abundance data (ter Braak & Looman 1995). A parabola can be described by a simple polynomial function of the kind:
where ŷ = expected value of the response variable, that is species percentage relative abundance, x = current velocity, and b0, b1 and b2 = parameters. Two important ecological parameters of the Gaussian response curve can be derived from the parameters of the quadratic equation: optimum (u), the value of x that gives maximum species abundance, u = −b1/(2b2), and tolerance (t), a measure of ecological amplitude, defined as a standard deviation, which has the same units as the original variable, t = 1/(−2b2)−0·5. For species with estimated negative optima, b1 was set to zero, thus conferring a value of zero to their assumed optima. Niche breadth (NB), defined only at current velocities equal to or higher than zero, was derived from t as follows: for species with balanced or right-truncated response curves, the range of distribution was calculated as two standard deviations about the optimum, or NB = 2t; for species with left-truncated curves, NB = u + t, because to the right of the optimum species distribution was defined by t, whereas to the left of the optimum it was defined only in the interval [0, u]. Note that species with u = 0 have NB = t.
Results and Discussion
A thick periphytic mat, which is characteristic of a later successional sere, covered the entire stream bottom at the time of this survey. Current velocity ranged from 0·03 to 0·66 m s−1, and depth ranged from 0·02 to 0·19 m. Partial canonical correspondence analysis was conducted on diatom data (18 species with relative abundance 1%); environmental data (current velocity and depth measurements); and spatial data from the 81 sample locations (Passy 2001), which revealed that current velocity was the most important environmental factor controlling diatom distribution in the study reach, and it was used to represent species environmental niches.
Six of the seven dominant diatom species in this study were colonial forms with diverse morphologies (Fig. 2). The only colony that consisted of a frustular and a visible mucilage component was Gomphoneis minuta. Both components were considered when fractal dimension was measured because of evidence that an allied species, Gomphoneis herculeana, responds to increased current velocities by producing more mucilage (Biggs & Hickey 1994). Therefore stalks are not inert parts of the colony, and deserve attention when colonial complexity is assessed.
The average fractal dimension of diatom colony perimeters ranged from 1·06 to 1·54, indicating a vast morphological variation from simple geometric shapes to very complex outlines. All regression models of log-diatom percentage relative abundance against current regime (Fig. 3) were significant at P < 0·05. They explained between 66 and 96% of the variation in diatom distribution. The NB of the six colonial diatoms, defined from these models, showed substantial variation, from 0·48 to 0·79 m s−1. The Pearson correlation between fractal dimension and niche breadth was high (r = 0·822) and significant (P = 0·045), demonstrating a strong linear relationship between diatom colonial complexity and habitat variability (Fig. 4).
The two species with the highest fractal dimension, Synedra ulna (D = 1·54) and F. crotonensis (D = 1·49), have been reported as early and late successional dominants, respectively (Johnson, Tuchman & Peterson 1997; Steinman & McIntire 1986). Thus almost equally complex growth forms were found in distant successional seres, indicating that colonial complexity in benthic diatoms cannot be driven by factors associated with successional time of appearance. The present study suggests colonial morphological complexity to be an adaptive evolutionary strategy for survival in unpredictable, random environments.
Other factors, such as light and grazing, can potentially influence diatom morphology. However, based on my data on the spatial distribution of colonial diatoms within a 16 m2 stream study reach, such effects are unlikely, for the following reasons. The study reach was in an unshaded, shallow, clear-water stream where substantial light attenuation due to high plankton density, turbidity or depth did not occur. Therefore wavelength or quantitative differences in light impinging on the stream margin vs the thalweg benthic mat cannot account for the distinct and predictable distributional patterns of colonial diatoms in these zones. The same argument can be extended against a grazer-driven diatom colonial complexity. At a microscale, within-cross-channel transect, Li et al. (2001) documented negligible variation in macroinvertebrate metrics, including diversity, density, and percentage of Ephemeroptera, Plecoptera and Trychoptera species. In addition, all investigated diatom colonies in White Creek fall within the same growth form category of erect species, inhabiting the same zone of the benthic mat, which is subject to indiscriminate herbivory by grazers with similar mouthparts. Grazers affect the physiognomy of benthic mats by decreasing algal abundance in the overstorey and increasing it in the understorey (Steinman 1996), but they had no effect on taxonomic diversity (Gresens & Lowe 1994), suggesting a lack of selective grazing within a benthic zone. Consequently, colonies sharing the same zone experience the same grazer pressure, which is unlikely to affect their environmental niche at the study scale or to account for their morphological variation. Moreover, in this study area all factors other than current velocity had minimal effect on diatom distribution.
This study was designed to link process and pattern, environmental causation and a phenotypic response – it recognizes tolerance to a wide range of current velocities as a possible underlying evolutionary mechanism in morphological radiation. The differential fractal geometry of diatom colonies described here offers new insights into understanding the life-history strategies and functional responses to habitat variability of periphytic species. Biggs, Stevenson & Lowe (1998) proposed C-S-R functional groups for stream periphyton, in an extension of Grime's theory on life-history strategies in plants (Grime 1977): strategies for growth in stable, nutrient-rich habitats (C-selected); stable, nutrient-poor habitats (S-selected); and disturbed habitats (R-selected). Biggs et al. (1998) hypothesized the distribution of 35 common periphytic algae within a habitat matrix, defined by a disturbance and a resource gradient. They derived their distributional model entirely from empirical knowledge. However, there are no theoretical bases or measurable traits that would allow the reliable positioning of a species in this matrix, especially if there are no empirical data on the species. The correlation between fractal dimension and niche breadth of diatom colonies, discussed here, provides both theory and trait.
The theory implicates differential colonial complexity as a response mechanism to environmental unpredictability – a trait easily measurable with fractal tools. For example, species with simple colonial morphology would be found in stable, nutrient-rich or poor environments (C- or S-selected), while species that have allocated evolutionary time and effort to developing complex colonial outlines would dominate in unpredictable, disturbed (R-selected) habitats. Diatoms with simple colonies (e.g. Melosira varians and Meridion circulare) were found in C- and S-selected habitats, respectively, whereas diatoms with much more complex morphologies (e.g. Synedra ulna, S. rumpens, Diatoma hiemale var. mesodon, Gomphoneis minuta var. cassieae) thrived in R-selected habitats (Biggs et al. 1998).
This study provides a new perspective on the pathways of morphological evolution in algae. Its implications have the potential to elucidate further the evolution of complexity in organic structures, which should be tested for other biological groups and environmental settings.
I am indebted to Doug Freehafer for conducting the GIS work. My deepest gratitude goes to Dr Pierre Legendre for his statistical advice and critical review, which greatly improved the manuscript. My sincere thanks are extended to Dr Karl Niklas for a helpful review of an early draft of this article, to Dr George Sugihara for his constructive suggestions, and to Sue Hawkins for her technical assistance.