Aplicación de las funciones elípticas de Fourier para la descripción de la forma de los huevos de las aves / Application of the elliptic Fourier functions to the description of avian egg shape

Egg shape is difficult to quantify due to the lack of an exact formula to describe its geometry. Here I described a simple algorithm to characterize and compare egg shapes using Fourier functions. These functions can delineate any closed contour and had been previously applied to describe several biological objects. I described, step by step, the process of data acquisition, processing and the use of the SHAPE software to extract function coefficients in a study case. I compared egg shapes in three birds’ species representing different reproductive strategies: Cuban Parakeet (Aratinga euops), Royal Tern (Thalasseus maximus) and Cuban Blackbird (Dives atroviolaceus). Using 73 digital pictures of eggs kept in Cuban scientific collections, I calculated Fourier descriptors with 4, 6, 8, 16 and 20 harmonics. Descriptors were reduced by a Principal Component Analysis and the scores of the eigenvalues that account for 90% of variance were used in a Lineal Discriminant Function to analyze the possibility to differentiate eggs according to its shapes. Using four harmonics, the first five component accounted for 97% of shape variances; more harmonics diluted the variance increasing to eight the number of components needed to explain most of the variation. Convex polygons in the discriminant space showed a clear separation between species, allowing trustful discrimination (classification errors between 7-15%). Misclassifications were related to specific egg shape variability between species. In the study case, A. euops eggs were perfectly classified, but for the other species, errors ranged from 5 to 29% of misclassifications, in relation to the numbers or harmonics and components used. The proposed algorithm, despite its apparent mathematical complexity, showed many advantages to describe eggs shape allowing a deeper understanding of factors related to this variable. Rev. Biol. Trop. 62 (4): 1469-1480. Epub 2014 December 01.

La forma de los huevos es difícil de cuantificar por la ausencia de fórmulas exactas que describan su geometría. Se describe un algoritmo para la caracterización y comparación de estas formas, basado en la aplicación de las funciones de Fourier. Estas permiten delinear cualquier tipo de contorno cerrado y han sido aplicadas efectivamente al análisis de varias formas biológicas. Se describen los pasos para la toma de datos, su procesamiento y el empleo del programa SHAPE para la obtención de los descriptores, a partir de un estudio de caso. En este se comparan las formas de los huevos de tres especies de aves que representan tres estrategias reproductivas bien diferentes: el Catey (Aratinga euops), la Gaviota Real (Thalasseus maximus) y el Totí (Dives atroviolaceus). A partir de 73 fotografías digitales a huevos depositados en colecciones, se calcularon los coeficientes de las funciones para 4, 6, 8, 16 y 20 armónicos, y se redujeron por medio de un Análisis de Componentes Principales. Los puntajes de los componentes que describen hasta el 90 % de la variabilidad fueron empleados en un Análisis de Función Discriminante Lineal para analizar la posibilidad de separar los huevos según sus formas. Con solo cuatro armónicos los primeros cinco componentes explicaron 97% de la varianza en formas. Más armónicos disminuyen la varianza explicada, requiriéndose hasta ocho componentes para explicar la misma cantidad. Los polígonos convexos en el espacio discriminante muestran una clara distinción entre especies sugiriendo la posible discriminación (errores de clasificación entre 7-15%). Los errores en las clasificaciones estuvieron relacionados a diferencias específicas en la forma entre especies. En el estudio de caso, los huevos de A. euops fueron perfectamente clasificados pero en las otras especies los errores fueron entre 5 y 29%, con este número de armónicos y componentes empleados. El algoritmo propuesto a pesar de su complejidad matemática aparente muestra muchas ventajas para cuantificar las formas de los huevos permitiendo una mayor comprensión de los factores que determinan esta variable en las aves.

Silhouette differences among cats do not suggest a general selection for paedomorphosis / 대한수의학회지

Paedomorphosis is the retention of juvenile morphology at maturity and is important in generating evolutionary change in domestic species and species in the wild. This preliminary study compared morphological characteristics of seven domestic cat pure breeds and felid species from around the world. An original procedure based on elliptical Fourier (EF) methods was applied to head lateral views of specimens and were assessed in order to analyse head profile. For comparative purposes three domestic kittens of different ages and three species of genus Lynx were also used. EF descriptors, allowed for the quantification of the head profile. Using the Fourier transform, reconstruction of the mean head profile revealed that there was a general shape difference between wild cats, domestic cats and kittens. Results suggested that variability in head profile differentiate quite well between adult cats and kittens, but domestic and wild cats appeared grouped into a similar cluster. The similarity between breeds can thus be attributed more to the general head profile than to flatness, i.e. to the general conformation rather than facial profile. Therefore, no effect of paedomorphism on the studied breeds can be undertaken. The present approach opens interesting ethnological perspectives for the aloidic characterisation for domestic breeds.

Inferring possible population divergence in Espeletia pycnophylla (Asteraceae) through morphometric and paleogeographic approaches

The phenotypic structure within and between plant populations is generally influenced by their distribution patterns in space and time; therefore, the study of their divergence is a central issue for the understanding of their microevolutive processes. We boarded the hypothesis that three populations of Espeletia pycnophylla show phenotypic divergence as one of the possible implications of their geographic isolation in the Southern Colombian Andes. We used the Elliptic Fourier Descriptors (leaf shape) and traditional leaf morphometry (leaf size) of 347 leaves to measure inter and intra-population variation and a comparison between a paleogeographic reconstruction with an actual estimate of the distribution areas of E. pycnophylla in order to identify their main changes during the last 14 000 years. The three populations showed significant differences in leaf morphometry and a positive correlation between the matrices of morphometric and geographic dissimilarities, indicating that the inter-population divergence increases between further populations, so that the morphometric structure reflects their spatial distribution. The geographical and paleogeographical estimates evidenced a conspicuous process of reduction and fragmentation of the distribution area of E. pycnophylla since the Late-Glacial until the Holocene. We suggest that these results support possible scenarios of vicariance events, which allow us to approach the divergence of these populations in terms of their historic biogeographic relations. However, genetic analyses are still needed to support these results. Rev. Biol. Trop. 58 (4): 1261-1270. Epub 2010 December 01.

La estructuración fenotípica entre y dentro de poblaciones vegetales responde generalmente a sus patrones de distribución espacio-temporales, por lo tanto, el estudio de su divergencia es un tema central dentro de sus procesos microevolutivos. En esta investigación abordamos la hipótesis que tres poblaciones de Espeletia pycnophylla presentan divergencia fenotípica como uno de los posibles efectos de su aislamiento geográfico en los Paramos del suroeste de Colombia. Utilizamos los Descriptores Elípticos de Fourier (forma foliar) de 117 hojas y algunas medidas morfológicas tradicionales (tamaño foliar) como indicadores de la variación intra e inter-poblacional, además de una comparación entre una reconstrucción paleogeográfica con una estimación del área de distribución actual de la especie para identificar sus principales cambios durante los últimos 14 000 años. Todas las poblaciones mostraron diferencias significativas y además, existió una correlación positiva entre las matrices de disimilitud morfométrica y geográfica, indicando que la divergencia incrementa entre poblaciones lejanas. Paralelamente, las estimaciones geográficas y paleogeográficas evidenciaron un proceso de reducción y fragmentación del área de distribución de E. pycnophylla desde el Tardiglacial hasta el Holoceno. Sugerimos que ambos resultados apoyan escenarios de posibles series de eventos de vicarianza para las poblaciones estudiadas y nos permiten entender su divergencia en términos de sus relaciones biogeográficas históricas.

Categorization of the main descriptors of different ampicillin crystal habits

With the purpose of enabling the analysis by digital methods of particles of multisource pharmaceutical raw materials, this study analyzed different crystal habits of ampicillin particles, by grouping the external shapes obtained from 3 different solvents (acetonitrile, ethanol, and methanol), thereby reducing the number of descriptors necessary to adequately represent each shape. For this purpose, a selection of morphological descriptors was used including: circularity, roughness, roundness, compactness, aspect ratio, effective diameter, solidity, convexity, fractal dimension, and 10 Complex Fourier descriptors. These measures cover highly diverse morphological properties and define the crystal habit of a particle. Principal Component Analysis (PCA) and the Cluster Analysis (CA) were the grouping techniques used, which demonstrated the possibility of using between 2 and 4 descriptors instead of the 18 proposed initially.

Com o objetivo de possibilitar a análise, por meio de métodos digitais, de partículas de matérias-primas farmacêuticas de múltiplas fontes, analisaram-se diferentes cristais de partículas de ampicilina através do agrupamento de formas externas obtidas de três diferentes solventes (acetonitrila, etanol e metanol), reduzindo, desse modo, o número de descritores necessários para representar adequadamente cada forma. Com esse propósito, utilizou-se seleção de descritores morfológicos, incluindo: circularidade, aspereza, arredondamento, compactação, relação de aspecto, diâmetro efetivo, solidez, convectividade, dimensão fractal e 10 descritores complexos de Fourier. Essas medidas cobrem diversas propriedades morfológicas e definem a cristalinidade de uma partícula. As análises do componente principal (PCA) e por grupamento (CA) foram as técnicas de agrupamento utilizadas, que demonstraram a possibilidade de utilizar entre 2 e 4 descritores ao invés dos 18, inicialmente propostos.