Elliptic Fourier Descriptors Research Articles

Shell shape variation of the symbiotic gastropod Phenacovolva rosea in Vietnam

This study investigates the shell variability of Phenacovolva rosea, a symbiotic gastropod inhabiting octocorals, in relation to geographical location and host coral species. We analyzed shells from 53 adult specimens collected at three locations in the north of Vietnam and one in the vicinities of Nha Trang City (southern Vietnam). To describe the shells' outlines, elliptical Fourier descriptors were applied. Based on the shell outline data, principal component analysis was performed. Additionally, height and width of P. rosea shells were measured. Only the first two principal components were effective, with the first principal component accounting for 92.8% of the variation. It closely correlated with width-to-height ratio of shells. According to dispersion analysis (ANOVA), shells in Nha Trang were significantly slimmer with longer terminal processes compared to those from the three northern locations. The coral host species also impacted shell shape when considering the entire dataset. However, this difference may have stemmed from shell variations between locations, as coral composition is not independent of location. When regional samples were analyzed separately, no significant impact of the host was detected. The factors that differed between northern locations and Nha Trang were then discussed, along with the mechanisms underlying their influence. We suggest that predation risk, influenced by water turbidity, is greater in the clearer waters of Nha Trang. This increased predator pressure may explain the presence of long terminals on P. rosea shells found in Nha Trang, potentially providing protection against some fish predators. Furthermore, the shorter and wider shells found in northern locations may be advantageous in waters with higher current speeds, whereas the long-teminal shells with narrow apertures observed in Nha Trang may be better suited for slower currents. The climate disparity, encompassing temperature and salinity mediated through precipitation, could also potentially influence shell morphology. However, the underlying mechanism remains unclear due to the complex nature of these interactions and the scarcity of literature data. Isolating host-specific shell shape traits from other factors proved challenging, given the close association between host species composition and location. Laboratory experiments modeling each factor independently may provide a solution to this issue.

Otolith Shape Analysis of Five Sillaginidae Species from the Persian Gulf and the Oman Sea

The discrimination power of sagittal otolith shape analysis is evaluated for five closely related sillaginid species from the Persian Gulf and the Oman Sea; (Sillago arabica, Sillago attenuata, Sillago indica, Sillago sihama and Sillaginopodys chondropus) besides the description of morphological characters using scanning electron microscopy (SEM). The identification of sillaginids is difficult due to the limited reliable diagnostic morphological characters. The otolith shape was described by six shape indices (Roundness, Rectangularity, Circularity, Ellipticity, Form factor and Aspect ratio) and Elliptic Fourier Descriptors (EFD). For all shape indices, there was at least an overlap between the two species and no one was significantly different among the five species. Based on EFD analysis all five species were discriminated (91.7%) evidencing the high taxonomic value of sagittal otolith for the studied taxa. SEM images revealed sulcus acusticus as homosulcoid with an inframedian position in all five species. S. arabica and S. sihama are characterized by having a pseudo-ostiocaudal, while S. indica, S. attenuate and Sillaginopodys chondropus have ostial mode of opening. The ostium was tubular and slightly curved in all studied species, which was more strongly curved in S. arabica. These findings suggest that the sagittal otolith shape is a reliable tool to recognize inter-specific diagnosis for sillginid species in the Persian Gulf and Oman Sea.

Otolith shape reveals the population structure of 'Malabar Labeo’, Labeo dussumieri (Valenciennes, 1842), in the four west-flowing rivers of India

Otolith shape variation in Labeo dussumieri from the four west-flowing rivers of India was analyzed using Wavelet coefficients and elliptic Fourier descriptors in the ShapeR package. The mean otolith shape of L. dussumieri varied significantly among sampling locations, with the posterior margin of the otolith showing the maximum variation. Otolith shape analysis also revealed variations between regions of different latitudes, with the northern (Narmada and Kundalika River) and southern populations (Achankovil and Chalakudy River) forming two distinct clusters. This variability in otolith shape might be attributed to the variation in environmental conditions prevailing in the sampling locations. The linear discriminant analysis based on elliptic Fourier descriptors and Wavelet coefficients showed an overall classification success of 89.03 % and 89.20 %, respectively. The present study validated that the lapillar otoliths are ideal for investigating the population structure of cyprinid fishes like L. dussumieri. The present study provided the first comprehensive information on the otolith shape analysis of L. dussumieri from the four west-flowing rivers of India.

New Parametric 2D Curves for Modeling Prostate Shape in Magnetic Resonance Images

Geometric shape models often help to extract specific contours in digital images (the segmentation process) with major precision. Motivated by this idea, we introduce two models for the representation of prostate shape in the axial plane of magnetic resonance images. In more detail, the models are two parametric closed curves of the plane. The analytic study of the models includes the geometric role of the parameters describing the curves, symmetries, invariants, special cases, elliptic Fourier descriptors, conditions for simple curves and area of the enclosed surfaces. The models were validated for prostate shapes by fitting the curves to prostate contours delineated by a radiologist and measuring the errors with the mean distance, the Hausdorff distance and the Dice similarity coefficient. Validation was also conducted by comparing our models with the deformed superellipse model used in literature. Our models are equivalent in fitting metrics to the deformed superellipse model; however, they have the advantage of a more straightforward formulation and they depend on fewer parameters, implying a reduced computational time for the fitting process. Due to the validation, our models may be applied for developing innovative and performing segmentation methods or improving existing ones.

Identification of Key Genes of Fruit Shape Variation in Jujube with Integrating Elliptic Fourier Descriptors and Transcriptome.

Jujube (Ziziphus jujuba) exhibits a rich diversity in fruit shape, with natural occurrences of gourd-like, flattened, and other special shapes. Despite the ongoing research into fruit shape, studies integrating elliptical Fourier descriptors (EFDs) with both Short Time-series Expression Miner (STEM) and weighted gene co-expression network analysis (WGCNA) for gene discovery remain scarce. In this study, six cultivars of jujube fruits with distinct shapes were selected, and samples were collected from the fruit set period to the white mature stage across five time points for shape analysis and transcriptome studies. By combining EFDs with WGCNA and STEM, the study aimed to identify the critical periods and key genes involved in the formation of jujube fruit shape. The findings indicated that the D25 (25 days after flowering) is crucial for the development of jujube fruit shape. Moreover, ZjAGL80, ZjABI3, and eight other genes have been implicated to regulate the shape development of jujubes at different periods of fruit development, through seed development and fruit development pathway. In this research, EFDs were employed to precisely delineate the shape of jujube fruits. This approach, in conjunction with transcriptome, enhanced the precision of gene identification, and offered an innovative methodology for fruit shape analysis. This integration facilitates the advancement of research into the morphological characteristics of plant fruits, underpinning the development of a refined framework for the genetic underpinnings of fruit shape variation.

Path synthesis of planar four-bar linkages for closed and open curves using elliptical Fourier descriptors

Path synthesis of planar four-bar linkages for closed and open curves using elliptical Fourier descriptors

Morphometric Analysis of the Tibial Attachment Shape of the Anterior Cruciate Ligament and Its Relationship With the Location of the Anterior Horn of the Lateral Meniscus

Background: The success of anterior cruciate ligament (ACL) reconstruction relies on the accurate replication of the native ACL anatomy, including attachment shapes. The tibial attachment of the ACL exhibits significant shape variations with elliptical, C, and triangular shapes, highlighting the need for objective classification methods and additional information to identify individual anatomic variations. Hypothesis: The location of the attachment of the anterior horn of the lateral meniscus (AHLM) may determine the shape of the ACL attachment. Study Design: Cross-sectional study; Level of evidence, 3. Methods: The study used 25 knees from 17 Japanese cadavers for macroscopic anatomic examination and quantitative analysis. The shape of the ACL attachment was quantified using principal component analysis with elliptical Fourier descriptors, whereas the AHLM location was quantified by measuring its mediolateral and anteroposterior positions on the superior surface of the tibia. Reliability was assessed statistically. Results: The shape of the tibial attachment of the ACL varied among individuals and was classified as elliptical, C-shaped, or triangular. Scatterplots of the principal components of the ACL attachment shape showed overlapping regions of elliptical, C-shaped, and triangular ACL attachments, indicating that a C-shaped attachment is intermediate between elliptical and triangular attachments. The location of the AHLM attachment also varied, with areas in the anterolateral, anteromedial, or posteromedial region. The ACL shape and AHLM location were related, with elliptical, C-shaped, and triangular ACL attachments corresponding to anterolateral, anteromedial, and posteromedial AHLM attachments, respectively. Conclusion: The AHLM attachment location influences the shape of the ACL attachment. Information on the location of the AHLM attachment can aid in predicting the shape of the ACL attachment during ACL reconstruction, potentially improving footprint coverage.

E(2)-equivariant features in machine learning for morphological classification of radio galaxies

Abstract With the growth of data from new radio telescope facilities, machine-learning approaches to the morphological classification of radio galaxies are increasingly being utilized. However, while widely employed deep-learning models using convolutional neural networks (CNNs) are equivariant to translations within images, neither CNNs nor most other machine-learning approaches are equivariant to additional isometries of the Euclidean plane, such as rotations and reflections. Recent work has attempted to address this by using G-steerable CNNs, designed to be equivariant to a specified subset of two-dimensional Euclidean, E(2), transformations. Although this approach improved model performance, the computational costs were a recognized drawback. Here, we consider the use of directly extracted E(2)-equivariant features for the classification of radio galaxies. Specifically, we investigate the use of Minkowski functionals (MFs), Haralick features, and elliptical Fourier descriptors (EFDs). We show that, while these features do not perform equivalently well to CNNs in terms of accuracy, they are able to inform the classification of radio galaxies, requiring $\sim$50 times less computational runtime. We demonstrate that MFs are the most informative, EFDs the least informative, and show that combinations of all three result in only incrementally improved performance, which we suggest is due to information overlap between feature sets.

A stochastic model based on Gaussian random fields to characterize the morphology of granular objects

The geometrical modeling of granular objects is a complex challenge that exists in many scientific fields, such as the modeling of granular materials or rocks and coarse aggregates with applications in civil, mechanical, and chemical engineering. In this paper, a model called SPHERE (Stochastic Process for Highly Effective Radial Expansion) is proposed, which is based on the deformation of an ellipsoid mesh using multiple 3D Gaussian random fields. The model is designed to be flexible (full control over 2D and 3D morphological properties of granular objects), ultra-fast (over 1000 aggregates in less than 5 s), and independent of the mesh and base shape used (as long as it is a star-shaped object). The flexibility of the model and its ability to reflect real data is illustrated using images of latex nanoparticle aggregates. Using 2D measurements on images from a morphogranulometer, a method based on the SPHERE model is proposed to estimate the 3D morphological properties of aggregates. A multiscale optimization process is applied, in particular using a partial reconstruction of 2D shapes from elliptic Fourier descriptors, in order to best reproduce the shape, angularity and texture of the aggregates using the SPHERE model. Validation of the method on 3D printed data shows relative errors of less than 3% for all measured 2D and 3D morphological characteristics, and validation on a population of synthetic objects shows relative errors of less than 6%. The results are compared and discussed with those obtained using other models based on overlapping spheres and show consistency with previous work. Finally, suggestions for improvement are given.

Global optimization of underwater vehicle hull shape on flow resistance

For underwater vehicle with axisymmetric revolution body, the hull shape in the rotation axis section is the key issue on flow resistance. In this paper, we propose to use the elliptic Fourier descriptors for arbitrary hull shape modeling. By doing so, we can achieve global optimization of underwater vehicle hull shape on flow resistance. Experimental results using the computational fluid dynamics show superior improvement compared to the extensive used Myring shape with only first order elliptic Fourier descriptors under the same displacement constraint. In addition, the proposed method can be easily extend to the global optimization on flow noise.

Assessment of body shape variation using Elliptic Fourier descriptors and ellipse fitting estimators and their genetic estimates in the flatfish Senegalese sole

Body shape is an important morphological trait in aquaculture. This study investigates the use of Elliptic Fourier descriptors (EFDs) analysis and ellipse fitting estimators to assess shape variation in Senegalese sole and their genetic variance components. A total of 2271 fish were individually photographed and body contours reconstructed using 20 Elliptic Fourier harmonics. Principal component analysis identified four symmetric components that explained the 68.6% of the total variation. They were mainly related to the adjustment of the body to an ellipse (PC1s and PC3s) and caudal fin morphological features (PC2s, PC3s, PC4s). Moreover, four asymmetric components related to caudal fin (PC1a, PC2a, PC3a) and head orientation (PC4a) that explained 24.5% of the total variation were also found. In addition to EFDs, body perimeter and five ellipse fitting estimators including the maximum body height to caudal peduncle height ratio (MBH/CPH), body aspect ratio (AR), ellipticity (ELL), AR from theoretical ellipse (ARe) and solidity (SOL) were calculated. PC1s was strongly correlated with ARe, AR and ELL (≥0.75), PC2s with SOL (−0.79) and PC3s with AR and ELL (0.48–0.49). Males appeared more elliptic than females as revealed by all ellipse descriptors with a tendency to caudal fins with obtuse angles (PC3a) and heads orientated toward the abdominal cavity (PC4a). Overall, heritabilities for symmetric components were higher than for asymmetric. Heritabilities for body ellipse fitting estimators including PC1s were high or very high with the highest values for AR (0.80) and ARe (0.78) for body and whole-body, respectively. Heritability for MBH/CPH was high (0.51) with low genetic correlation with other morphological traits. Heritabilities for symmetrical and asymmetrical features of caudal fin were moderate or low and indirect selection using other highly correlated traits such as PC2s through SOL and PC3a through PC4a or PC1s would facilitate progress in the selection. Perimeter showed a moderate heritability and it was more genetically correlated with growth than shape-related traits. The data provided represent a valuable tool to assess body shape in sole and in the design of genetic breeding programs in Senegalese sole.

Exploring European Eel Anguilla anguilla (L.) Habitat Differences Using Otolith Analysis in Central-Western Mediterranean Rivers and Coastal Lagoons from Sardinia

An otolith shape and morphometric analysis was performed on European eel (Anguilla anguilla) subpopulations from five rivers and three coastal lagoons of Sardinia (central-western Mediterranean) to assess the role of different habitats on otolith development. Sagittal otolith shape was described by 11 harmonics from elliptic Fourier descriptors. Comparisons among the harmonics were run through canonical discriminant analyses (CDAs). The CDA reclassification rate (75.7%) demonstrated a spatial environmental discrimination among local eel subpopulations of Sardinia. The Euclidean distance values demonstrated a dissimilarity between the river and lagoon groups. The form factor and roundness shape indices were significantly higher in the river group than in the lagoon group. The distances of the first three rings to the otolith core revealed site-specific otolith development. Moreover, the annual otolith growth rate was faster in the lagoon group than in the river group. The differences among the studied sites in terms of sagittal otolith shape could relate to changes in different local stocks potentially related to environmental peculiarities. Establishing a direct correlation between otolith morphology and environmental factors is challenging, and further studies are needed to investigate the relationship between habitat type/environmental variation and growth/body characteristics of eels. Nevertheless, the achieved results suggest that this method can be considered to be a valuable tool for studying the ontogeny of the European eel.

The use of the shape and chemistry of fish otoliths as a subpopulational discrimination tool for Eugerres brasilianus in lagoon systems in the Southwest Atlantic Ocean

The Brazilian mojarra, Eugerres brasilianus, is an economically important species for the artisanal fisheries usually found in the estuarine waters along the southwest Atlantic Ocean. Despite this, knowledge about its population structure is scarce, and no management strategies have been applied to ensure the fisheries sustainability in Brazil. Thus, the present study intended to understand the population dynamics of E. brasilianus in three costal lagoons located in Rio de Janeiro, Brasil. A total of 90 individuals were collected in the lagoon systems of Itaipu, Saquarema and Araruama, between December 2019 and March 2020. A pre-selection of 30 individuals per location from the same age group (2 years old), following age estimation by counting the annual growth increments, were used. The contour of the sagittal otoliths was evaluated using elliptical Fourier descriptors (EFD), and the multi-elemental signatures (MES) of the whole otoliths were obtained using solution-based inductively coupled plasma mass spectrometry. Data were analyzed using univariate and multivariate statistics to assess the degree of separation between individuals from different lagoons. EFD revealed significant differences among individuals from the different sampling regions. MES exhibited distinct regional patterns, mainly driven by differences in Cu/Ca, Li/Ca, Mg/Ca, Mn/Ca, and Sr/Ca ratios. Reclassification accuracy rates obtained from linear discriminant function analyses using both EFD and MES of otoliths were 100% (Itaipu), 97% (Araruama) and 90% (Saquarema). Therefore, a clear distinction was observed among these groups, which was related to the inherent characteristics of each lagoon system, their semi-restricted connectivity with the adjacent coastal zone, as well as the estuarine-opportunistic behavior of the species. Thus, the results suggest that these fisheries should be managed as different subpopulation-units. However, more studies should be carried out about the fish movements and life history events of this species in southeastern Brazil.

Otolith shape and elemental signatures provide insights into the connectivity of euryhaline Chelon labrosus inhabiting two close estuaries with different burdens of xenoestrogens in the Southern Bay of Biscay

Intersex gonads have been observed in thicklip grey mullet Chelon labrosus, inhabiting estuaries with high burdens of xenoestrogens in the Southeast Bay of Biscay, but knowledge of population connectivity among estuaries is lacking for this euryhaline fish species. This study investigates the population structure of C. labrosus using otolith shape and elemental signatures of 60 adults (overall length ∼ 38 cm) from two estuaries 21 nautic miles apart, one with a high incidence of intersex condition (Gernika), and the other one pristine (Plentzia). Otolith shape analyses were performed using elliptical Fourier descriptors, while elemental signatures of whole sagittae were obtained by inductively coupled plasma mass spectrophotometry. Univariate and multivariate statistics were applied to determine if otolith signatures show patterns of homogeneity between estuaries. The data indicated significant differences in the otolith shape and elemental composition between mullets of Gernika and Plentzia. Elemental differences were mainly driven by Sr, Li (both higher in Plentzia) and Ba (higher in Gernika). The 98% re-classification success rate obtained from stepwise linear discriminant function analysis suggests that Gernika and Plentzia individuals form separated population units. The limited connectivity between these two close estuaries would indicate a different life history of exposure to chemicals, which might explain the high prevalence of intersex condition in Gernika and its absence in Plenztia.

Genetic basis of lineage-specific evolution of fruit traits in hexaploid persimmon.

Frequent polyploidization events in plants have led to the establishment of many lineage-specific traits representing each species. Little is known about the genetic bases for these specific traits in polyploids, presumably due to plant genomic complexity and their difficulties in applying genetic approaches. Hexaploid Oriental persimmon (Diospyros kaki) has evolved specific fruit characteristics, including wide variations in fruit shapes and astringency. In this study, using whole-genome diploidized/quantitative genotypes from ddRAD-Seq data of 173 persimmon cultivars, we examined their population structures and potential correlations between their structural transitions and variations in nine fruit traits. The population structures of persimmon cultivars were highly randomized and not substantially correlated with the representative fruit traits focused on in this study, except for fruit astringency. With genome-wide association analytic tools considering polyploid alleles, we identified the loci associated with the nine fruit traits; we mainly focused on fruit-shape variations, which have been numerically characterized by principal component analysis of elliptic Fourier descriptors. The genomic regions that putatively underwent selective sweep exhibited no overlap with the loci associated with these persimmon-specific fruit traits. These insights will contribute to understanding the genetic mechanisms by which fruit traits are independently established, possibly due to polyploidization events.

Geographic Variation in Opisthonema oglinum (Lesueur, 1818) in the Southeastern Brazilian Bight Inferred from Otolith Shape and Chemical Signatures

The thread herring Opisthonema oglinum (Lesueur, 1818) is a small pelagic fish distributed in the western margin of the Atlantic Ocean from the United States to Argentina. It is a target species for diverse commercial fisheries, including the Brazilian industrial purse seine fleets that operate in the Southeastern Brazilian Bight. To investigate the geographic variation in the thread herring populations in this fishing ground, sagittal otoliths were collected from two areas: Rio de Janeiro (RJ: 23°04′ S, 44°03′ W) and Santa Catarina (SC: 26°05′ S, 48°18′ W). Otolith shape analyses and multi-elemental signatures were statistically evaluated using elliptical Fourier descriptors and elemental/Ca ratios. Remarkable differences in the thread herring otoliths between the two areas were found. The previous scenario in which the thread herring constitutes a single panmictic population in the Atlantic Ocean is now debatable. The implications of these results in terms of rational fisheries management for this species are highlighted.

Comparing otolith shape descriptors for population structure inferences in a small pelagic fish, the European sardine Sardina pilchardus (Walbaum, 1792).

Otolith shape analysis has been one of the most used approaches to study population structure in the past decades. Currently, two sets of shape descriptors are used to perform otolith shape analysis, namely, Elliptic Fourier descriptor (EFd), which focuses on the overall otolith shape differences, and Discrete Wavelet descriptor (DWd), which is sensible to local differences along the otolith contour. Here, the authors conducted a comparative analysis of the performance of both the descriptors in reconstructing the population structure and connectivity patterns in a small pelagic fish species with a wide geographical distribution and fast growth rate, the European sardine Sardina pilchardus (Walbaum, 1792), for the first time. A combination of each otolith shape descriptor and shape indices was explored using multivariate statistical methods. The two otolith shape descriptors showed similar, although limited, overall classification success associated with the population dynamic characteristics of the species. Both descriptors point to migration among adjacent areas, such as northern Atlantic locations, eastern Mediterranean and even across well-defined physical obstacles, such as the Strait of Gibraltar, among Atlantic and western Mediterranean locations. Both descriptors supported the division of the populations of Mediterranean waters into three main groups but slightly differed in the group limits of the Atlantic waters. A comparison of the present results with those from previous otolith shape analysis studies using EFd on a decadal time scale revealed differences in the population structure and connectivity patterns compared to the earlier period. These differences not only may be attributed to changes in environmental variables leading to changes in population dynamics but can also be the result of the sardine biomass sharp decrease that occurred in the past decade.

Deep convolutional neural networks accurately predict breast cancer using mammograms

Breast cancer in women is the most frequently diagnosed and major leading cause of cancer deaths. Due to the complex nature of microcalcification and masses, radiologists fail to diagnose breast cancer properly. In this research paper, we have employed a novel Deep Convolutional Neural Network (DCNN) model using a transfer learning strategy and compared the results with Machine Learning (ML) techniques such as Support vector machine (SVM) kernels and Decision Trees based on different features extracting strategies to distinguish cancer mammograms from normal subjects. In this study, we first extracted the hand-crafted features such as as texture, morphological, entropy-based, scale-invariant feature transform (SIFT), and elliptic Fourier descriptors (EFDs) and fed into machine learning algorithm for classification. We then utilized the deep learning algorithms with transfer learning approach. The deep learning models yielded the highest detection performance with default and optimized parameters i.e. GoogleNet yielded accuracy (99.26%), AUC (0.9998) with default parameters and AlexNet yielded accuracy (99.26%), AUC (0.9996) with optimized parameters. The results reveal that proposed approach is more robust for early detection of breast mammograms which can be best utilized for improved diagnosis and prognosis.

An Image-based Approach of Apex Type Descriptor State Establishment using Elliptic Fourier Analysis

An objective method to establish apex and base type descriptor states is proposed using elliptic Fourier descriptors derived from appropriately segmented images. Using pili (Canarium ovatum Engl.) kernel-in-shell apex as a model, 51 pili accessions represented by 10 kernel-in-shell images per accession were acquired using a calibrated VideometerLab3 setup. An appropriate segmentation scheme was applied by developing an algorithm that would segment blobs that cover only the apical region (upper 25%) of the closed contours using OpenCV implemented in Python 3.7. From the segmented blobs, elliptic Fourier descriptors (EFDs) were derived. Subsequently, the EFDs were analyzed using principal component analysis and cluster analysis. Two effective principal components were able to explain 94.18% of the variation which were visualized to show differences involving length to width ratio, apex angle and left-to-right leaning orientation of the segmented images. Although a single apex shape was observed, mean EFDs of three clusters were able to represent three apex type descriptor states-narrowly acute, acute and widely acute. This indicated that elliptic Fourier analysis can characterize variations in the apical regions, particularly apex shape and angle, given the proper segmentation protocol.

Taxonomy and ecology of Achnanthidium (Bacillariophyta, Achnanthidiaceae) from southeastern Brazil with the description of six new species

The present study aims to expand the knowledge on Achnanthidium species occurring in tropical areas of southern Brazil. For this purpose, 345 samples from 179 sampling sites distributed throughout the state of São Paulo were analyzed for ‘monoraphid’ diatom diversity. This paper focuses on samples with a high abundance of Achnanthidium species. The permanent slides and stubs were observed using light and scanning electron microscopy. Morphometric analysis was performed to discriminate between similar species through the Elliptical Fourier Descriptors analysis. For this, valve outlines from Brazilian species were compared to those from type material available from the literature. The ecological optimum and tolerance was calculated for taxa that presented more than 10 % of occurrence per habitat. In total, 12 Achnanthidium species were observed. Six are described as new: Achnanthidium acutum sp. nov., A. brasiliense sp. nov., A. parvicapitatum sp. nov., A. paulistanum sp. nov., A. ritae sp. nov. and A. vandevijveri sp. nov. The morphometric analysis supported the differentiation between some taxa. Nine species, with occurrences of at least 10 % per habitat, had their ecological optimum and tolerance calculated. In general, these species prefer slightly acidic to neutral pH, medium electrolyte cond. and mesotrophic water conditions.