, Volume 705, Issue 1, pp 1–8 | Cite as

Fractal analysis of the egg shell ornamentation in anostracans cysts: a quantitative approach to the morphological variations in Chirocephalus ruffoi

  • Emiliano Bruner
  • David Costantini
  • Graziella Mura
Primary Research Paper


The external ornamentations of the cysts in anostracans are often characterized by crests and ridges. However, their variation cannot be properly quantified by traditional morphometrics. We propose a fractal-based analysis through box-counting to evaluate and compare differences between groups. Box-counting provides a value (fractal dimension, FD) which is proportional to the coverage and space-filling property of a geometrical pattern. Therefore, it is useful to quantify features associated with the spatial organization of the crests. Crests height is moderately correlated with cyst body diameter at individual (R = 0.27; P < 0.0001) and population (R = 0.58; P = 0.05) level. The geometric pattern of the crests is not related to the cyst body size, suggesting that allometric components influencing the spatial distribution of the crests are absent or negligible. There is a faint correlation between crests geometry and height (R = 0.20; P = 0.003). Interestingly, the distribution of the FDs is bimodal, revealing two distinct morphotypes that may be associated with structural constraints, genetics, or environmental components. Taking into account the limited information on the factors shaping the external crests of the cysts, this approach can be useful in evaluating phylogenetic and ecological influences on the final phenotype of the cysts.


Chirocephalus Fractal dimension Box-counting Cyst morphology 


Understanding the causes underlying morphological variation within and between taxa is of major importance to evolutionary ecology, biogeography, developmental biology and anatomy. In order to quantify such variation, traditional metrics and landmark-based approaches are generally used when the anatomical elements can be represented through geometrically correspondent references. In contrast, the morphological variation of irregular structures is more difficult to assess, and information associated with complex anatomical elements are generally less accessible to morphometric analyses. In general, anatomical points are defined by virtue of biological homology, spatial position, or relative to other external references (Bookstein, 1991). When such references are missing and the anatomical structures are void of recognizable characters, it is difficult to provide a shared framework in which data can be standardized and compared properly. Sliding landmarks (Gunz et al., 2005), eigenshape analysis (MacLeod, 1999) and Fourier decomposition (Lestrel, 1997) are methods employed for continuous curves. Nonetheless, these methods still require some recognizable anatomical references to generate the following shape variables. When anatomy becomes more difficult to represent (e.g. complex geometrical patterns and repetitive morphological modules), quantification of similarities and differences is more tricky to achieve. In these cases one of the most used approaches is fractal analysis (e.g. Slice, 1993; Lopes & Betrouni, 2009). Formally introduced by Mandelbrot (1977), fractals are geometrical elements with peculiar properties as their modules exhibit scale-independence and self-similarity. Fractal analysis is therefore generally used to quantify patterns of reticulation, geometrical network, and complex outline, like blood vessels (Zamir, 2001; Bruner et al., 2005; Di Ieva et al., 2008), sutures (Schiwy-Bochat, 2001; Lynnerup & Jacobsen, 2003; Zollikofer & Weismann, 2011), neuronal connections (Zhang et al., 2006), animal space use (Gautestad & Mysterud, 2012), or habitat complexity (Tannier et al., 2012). In nature, although a theoretical fractal organization cannot be generally assumed, many structures present a pseudo-fractal geometry, allowing the application of the numerical tools generally used for fractal analysis. Fractal-based methods can quantify the degree of self-similarity of a network, or the space-filling properties of a geometrical figure, providing a quantitative method to compare complex morphological patterns.

Cysts of fairy shrimps (Anostraca) represent a notable example of biological structures whose morphology is difficult to quantify. Their external morphology is characterized by ornamentations (sometimes with crests and ridges) that hamper the application of traditional morphometric methods to compare and quantify differences within and between groups. Cysts (improperly also called resting eggs) are encysted gastrulae laid during the reproductive season (Nourisson, 1964). In adult females, fully mature oocytes produced by the ovaries accumulate in the oviducts, and are then poured into the uterus within the brood pouch of the female after mating. There they undergo fertilization and the embryo develops up until the stage of gastrula. The innermost layer covering the gastrula, a blastodermic cuticle produced by the embryo itself (Garreau de Loubresse, 1974), is surrounded by a complex tertiary envelope (Morris & Afzelius, 1967; Anderson et al., 1970) of lipoproteic nature, produced by the secretion of the uterine shell glands. This thick shell is a double-layered structure consisting of an inner alveolar layer and an outer cortex (Morris & Afzelius, 1967; Gilchrist, 1978). The latter is likely to have some protective function (Gilchrist, 1978), although much discussion still stands about its significance (see for example Dumont et al., 2002). Factors shaping the shell morphology are largely unknown (Mura, 2001; Mura et al., 2002),

The appearance of the outermost surface of this shell gives the egg a typical pattern, which can differ both at species and at genus level. Since the 1970s many studies focused on the external morphology of the cysts in anostracans. Earlier studies suggested that the pattern of the egg shell could represent an additional taxonomic character, because of the differences observed among genera and species (see review in Mura & Rossetti, 2010). However, a number of recent observations revealed a very contrasting scenario: occasionally interspecific differences were found to be much more marked than those observed between genera, whereas in other genera interspecific differences were not so evident (Mura, 1992, 2001). Moreover, the increase of the number of samples examined revealed the existence of a marked intraspecific variability (Mura & Rossetti, 2010). Accordingly, it was concluded that egg morphology should not be considered a reliable character to classify anostracans to species level.

Morphological differences are evident not only at the inter-population level, but also at the individual level (see review in Mura & Rossetti, 2010). The analysis of such variation requires the integration of morphology, genetics, and ecology, as well as methods enabling quantitative evaluation of the differences observed.

In this study, we propose a fractal approach to quantify the pattern and degree of variation of the cyst ridges, investigating basic proportions and relationships with egg size. We use the Italian endemic fairy shrimp Chirocephalus ruffoi (Cottarelli & Mura, 1984) as a model species. Unlike in other species, within this taxon the cysts are characterized by a ‘spiny’ appearance, due to the presence of thin and curved flanges ending in several single, bifurcate, or trifurcate spines (Cottarelli & Mura, 1984; Mura & Rossetti, 2010).

Materials and methods

The fairy shrimp C. ruffoi was originally collected in 1953 in Southern Italy, and classified as Chirocephalus diaphanus, the most common Chirocephalid. Following observations on the morphology of the cysts, a distinct morphological pattern was revealed. This lead to the recognition of a new species dedicated to its discoverer (Cottarelli & Mura, 1984). This species was subsequently also found in several temporary pools of the Central and Northern Apennines, showing a rather fragmentary and disjunctive distribution (Rebecchi et al., 1990; Mura & Rossetti, 2002).

The sample used in this study was collected during summer, between 2003 and 2006, in 12 different localities (see Table 1 in Mura & Rossetti, 2010). Individuals were collected with a plankton net (15 cm diameter, 125 μm mesh size). An average of 20 gravid females per site were isolated individually in falcon tubes, brought to the laboratory and kept in culture until deposition. A sample of 100 cysts per population per year of sampling, from randomly collected clutches of freshly deposited cysts, was examined. The cysts were rinsed clean in demineralized water and checked for quality under a stereomicroscope. The cysts were then mounted on stubs and gold coated for SEM morphology (see Mura, 1992) and photographed using an EVO LEO 040 electron microscope. All SEM observations were performed under the same light conditions to avoid undesired distortions on the images. Deformed or damaged specimens were not included in the sample.

Figure 1 shows the image processing steps. Digital images of cysts were taken and saved in tagged image file format (.tiff). The resolution of each image was 1,023 × 767 pixels. Images were then processed using ImageJ 1.38x (Rasband, 1997; Schneider et al., 2012). The scale of each picture was set using a scale bar. The main diameter of the body and the height of the crests were measured for each image. To quantify the morphological pattern of the crests, a central and most homogenous area of the cyst (square of 200 × 200 pixels) was selected and cropped. This selection limits the bias of capturing the lateral perspective of the crests, limiting the information to an approximation of the orthogonal view. Brightness and contrast were adjusted to further enhance the geometrical pattern. The resulting image was transformed into a binary image, in order to delineate the raw geometry of the crest and to separate the background. The resulting pattern was analyzed through Box-counting. Box-counting is a widespread fractal method which is able to quantify the degree of coverage of a geometrical pattern (e.g. Foroutan-pour et al., 1999; Li et al., 2009). On a square grid, the number of squares covered by the image is counted. This count is repeated iteratively by increasing or decreasing the square size (Fig. 2). The slope of the logarithmic correlation between square size and number of covered squares is termed ‘fractal dimension’ (FD), and it is proportional to the degree of coverage of the geometrical pattern, ranging from 1 (line) to 2 (surface). Diameters were collected on 445 specimens. FD was computed only on those images providing a clear geometrical pattern, thus excluding those images with graphic artefacts associated with the scan process. The final sample for the FD analysis was of 221 specimens.
Fig. 1

The cysts of Chirocephalus ruffoi (Cottarelli & Mura, 1984) are characterized by a ‘spiny’ pattern (above). Different cysts morphotypes can be found in the same species, and the factors shaping the ornaments are not currently known. The pattern of the crests can be evidenced by image processing and contrast enhancement (below). The image is transformed into binary black-and-white data, to be analyzed through fractal-based morphometrics

Fig. 2

Box-counting is based on an iterative count of the squares occupied by the image on a square grid, as the square size increase/decrease. The number of squares is log-regressed onto the square size. The resulting slope value, called fractal dimension, is proportional to the degree of coverage of the underlying geometry


Imaging and metrics were performed by the same person (DC), to avoid inter-observer differences. Repeatability of the metrics involved in this article was then tested by intra-observer error. Body size and crests heights were resampled five times in seven specimens, showing an average discrepancy of 1.0%. FD was resampled three times on 15 specimens, showing an average discrepancy of 1.3%. To test the effect of image elaboration, FD from contrasted images was also regressed on images without contrast, or on images with automatic contrast. The correlation of the values obtained from these different approaches was very high. In a preliminary analysis, values from images obtained with manual threshold and with automatic threshold showed a correlation coefficient of R = 0.96. In general, slightly different image processing procedures give similar results. It is worth noting that FD is not an absolute value, and it must be used and compared strictly within the same analytical context. Images can also be ‘skeletonized’, which involves eroding the geometrical binary pattern by quitting iteratively pixels from the outlines until only one pixel is left in contact with the neighbouring ones. This algorithm is often used to delineate the basic geometrical structure of an image. Nonetheless, the analyses after skeletonization show similar results, and they will not be therefore discussed here.

Table 1 provides the descriptive statistics for the diameter of the body and for the crests height. Figure 3 shows the distribution and correlation between these two variables. The diameter of the body shows a normal distribution (Shapiro–Wilk’s test, P = 0.55), while the crests height distribution is skewed towards larger values (Shapiro–Wilk’s test, P < 0.0001). Analyzing the whole sample, the correlation between body diameter and crests height is significant and positive, but very small (R = 0.27; P < 0.0001). However, considering the populations separately there is no clear trend between these two variables (data not shown). By using population averages, the correlation is larger but still moderate (R = 0.58; P = 0.05).
Table 1

Descriptive statistics (μm) for body diameter and crests heights (N = 445)























Fig. 3

The body diameter of the cyst displays a normal distribution, while crests height values are skewed towards higher figures. Among populations, the correlation between these two variables is significant but moderate

FD shows a bimodal pattern as opposed to a normal distribution (Shapiro–Wilk’s test, P < 0.0001) (Fig. 4). Two modes are displayed around FD = 1.55 and FD = 1.75, with a gap around FD = 1.65. The morphotype associated with the first mode is far more represented than the second one. Both morphotypes are represented in all the geographic groups.
Fig. 4

The fractal dimension, representing the degree of complexity of the crests morphological pattern, shows a bimodal distribution. Two frequent morphotypes (a, c) are separated by a morphological gap (b). The morphotype with the lowest FD (a) is the most frequent

There is no correlation between FD and body diameter (P = 0.29). The correlation between FD and crests height is statistically significant (R = 0.20; P = 0.003). However, this minor association is not really due to a linear correlation between the two variables, but due to a different distribution of the variances: specimens with low crests tend to have more variable crest morphology, widening the range towards lower FD values. On the other hand, specimens with high crests show a more homogeneous morphology, never displaying simple patterns of crest complexity. The plot contrasting these variables is characterized by the morphological gap associated with FD distribution, evidencing the lack of correlation between the presence of this gap and the cyst dimensions (Fig. 5).
Fig. 5

There is no correlation between body diameter of the cyst and fractal dimension. The correlation between crests height and fractal dimension is statistically significant, but a real linear correlation between the two variables is lacking


Since the formal introduction of the fractal geometry by Mandelbrot (1977), fractal analyses have been progressively more applied throughout all research fields. The real anatomical structures are pseudo-fractal approximations of the theoretical principle determining the fractal geometry. This means that, while in a theoretical fractal geometry the fractal parameters are intrinsic and actual properties of the spatial system, in real cases (e.g. blood vessels, neuronal networks, cell organizations, animal space use, habitat complexity) the fractal parameters provide an approximation of the natural properties of the geometrical systems. Therefore, given values are not absolute figures and are strictly dependent upon the methodological settings. This prevents the use of such tools in comparative frameworks that use heterogeneous sources of information, such as meta-analyses based on published values or analyses based on mixed samples. Nonetheless, within a homogeneous methodological context fractal-based morphometrics supplies the possibility to compare and to quantify complex geometrical components for which traditional methods are not informative.

The tertiary shell of the anostracans cysts is characterized by a complex pattern of crests. The large variation among genera, species, and populations, suggests that both genetic and environmental factors are involved in shaping such structures (see discussion in Mura & Rossetti, 2010). In the species considered in this article many deviations from the classically described pattern (Cottarelli & Mura, 1984) were observed, based on the height and density of the ridges ornamenting the surface of the egg. Up to 12 different morphotypes were described for the populations of C. ruffoi examined (Mura & Rossetti, 2010). However, until now the mechanisms underlying this variation are not known, and differences among groups are not even described through quantitative approaches. The complex geometry of the crests cannot be quantified by common traditional morphometrics methods, and it is generally approached with qualitative descriptions. Quantification of variation and differences are necessary to compare different groups, to evaluate the effect of environmental factors, and to test hypotheses according to common statistical procedures.

The height of the crests characterizing the surface of the tertiary shell in C. ruffoi is only slightly correlated with the body size of the egg, as represented here by its diameter. Within the same population there is no clear correlation between the two variables, and when considering the population average figures the variation of the body diameter only explains 33% of the variation in the crests height. It is worth noting that, while the body size is normally distributed, the crests height is skewed towards higher values. This means that generally there are more cysts with high crests than with low crests. This asymmetry in the distribution may be associated with a real adaptive function of the crests, or else to a secondary physiological response to environmental factors. In both cases, this result will merit further attention in following studies, and compared with the metric distribution in other taxa.

The geometrical pattern of the crests, as quantified by its FD, shows instead a clear bimodal distribution. The main differences separate cysts with large and dense crests from cysts with small and more separated crests. However, there is a definite morphological gap within the distribution, associated with a very low frequency of cysts with large but more separated crests. Such bimodal distribution may reveal two different kinds of cysts, possibly associated with differences between temporary pools (e.g. temperature, salinity) or nutritional conditions of the females. Otherwise, it may be associated with morphogenetic constraints intrinsic of their anatomical systems (e.g. differences in oviduct anatomy). Actually, structural and functional limits within the biological models may confine variation within certain ranges, creating ‘empty’ regions of the morphospace (McGhee, 2006). Interestingly, this pattern of increasing/decreasing coverage of the crests is not related to the body size of the cyst. In the case of the procedure used in this study, the present data does not support an allometric component for the pattern of complexity of the crests. This result suggests that genetic, environmental and/or maternal components are more relevant than the general structural organization of the egg in shaping the cyst morphology. Molecular and ecological analysis should be put forward to investigate the existence of two morphotypes, and the larger prevalence of the one associated with lower FD (denser and higher crests).

These results suggest that the quantification of the FD of the cyst could be a widely applicable descriptor. For example, it can be applied to investigate the causes and consequences of differences between individuals or populations in phenotypic plasticity, the variation in maternal investment in reproduction and its effects on offspring development and survival, or the population-specific response to local environmental changes.

The correlation between FD and crests height is more difficult to interpret. It may reflect a biological factor (eggs with high crests are less variable and do not display simple morphological patterns), a sample bias (the distribution is due to the presence of separate groups following different biological models), or a methodological bias (FD value, as calculated here, shows different sensitivity to the crests height, possibly because of effects associated with the orthogonal projection of the pattern).

It is important to remind that this study focuses on a specific character of the cysts, namely the geometry of the surface, but the morphological variation of these structures is not restricted to the complexity of the crests. Information on other morphological aspects like colour or texture may provide relevant data, and a complete biological study must integrate all these different sources of variation.

In conclusion, we have proposed a method to quantify the degree of morphological complexity of the crests in the tertiary shell of the anostracans cysts. Taking into consideration the large intra-specific variants, it is unlikely that the crests can be used for taxonomic purposes. In contrast, the crests morphology could supply information on environmental factors or life-history variables, providing data on ecology and physiology of these taxa. The approach presented here allows us to investigate and quantify a character that could otherwise only be discussed through descriptive approaches. The method should be further verified through different image processing approaches, improving the efficiency to capture more detail and information. We use C. ruffoi as case study, and the method should be applied to other taxa to have a more complete perspective of both its limits and potentialities.



We are grateful to Melina Marrocco for her contribution in the preliminary analyses on the crests morphometrics. Thanks to Lyndsey Stewart for comments and suggestions on the manuscript. Three reviewers provided further advices and appreciated encouragements on this manuscript. The authors do not have any actual or potential conflict of interests.


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Emiliano Bruner
    • 1
  • David Costantini
    • 2
  • Graziella Mura
    • 3
  1. 1.Centro Nacional de Investigación sobre la Evolución HumanaBurgosSpain
  2. 2.University of GlasgowGlasgowUK
  3. 3.Universitá La SapienzaRomeItaly

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