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Measuring egg size using digital photography: testing Hoyt's method using Florida Scrub-Jay eggs

2007; Association of Field Ornithologists; Volume: 78; Issue: 1 Linguagem: Inglês

10.1111/j.1557-9263.2006.00092.x

1557-9263

Eli S. Bridge, Raoul K. Boughton, Robert A. Aldredge, T. J. Harrison, Reed Bowman, Stephan J. Schoech,

Animal Behavior and Reproduction

ABSTRACT Egg volumes are most often estimated using a mathematical model that incorporates length and width measurements and a species-specific shape variable. Although adequate in many respects, this technique does not account for intraspecific variation in egg shape. We developed a computer-automated technique that uses calibrated digital photographs to render precise measurements of several egg-size parameters including length, width, volume, and surface area. The system extracts egg outlines from photographs, and divides each egg into latitudinal slices that are subsequently regarded as simple geometric shapes (cylinders or cone frustra) with volumes and surface areas that can be summed to generate size parameters for the entire egg. We tested this technique using 491 eggs from Florida Scrub-Jay (Aphelocoma coerulescens) nests and compared the resulting egg volumes with volumes calculated using the preeminent method of estimating volume from linear measurements. Our method was highly accurate, and differences between the volumes from our method and the alternative method were strongly associated with variation in egg shape. Advantages of our technique include decreased handling of eggs and increased accuracy. Software resources and additional information regarding the technique are available at http://www.archbold-station.org/abs/data/birddata/Bridge-JFO-eggsize.htm. El volumen de los huevos comunmente es estimado utilizando un modelo matemático en donde se incorpora el ancho y el largo del huevo y la variable de la forma de este. Aunque es un método adecuado en muchos aspectos, esta técnica no toma enconsideracion las variaciones intraespecificas de la forma de los huevos. Desarrollamos una técnica automática con computadora, que usa fotografia digital calibrada para ofrecer medidas de los huevos incluyendo largo, ancho, volumen y área superficial. El sistema extrae parámetros de los huevos de fotografías y divide cada huevo en rebanadas latitudinales, que subsecuentemente son tomadas como formas geométricas (e.g., cilindros o conos) con volumenes y áreas superficiales, que a su vez pueden ser utilizadas para obtener el largo y el ancho. Pusimos a prueba esta técnica con 491 huevos del Azulejón (Aphelocoma coerulescens) y comparamos el volumen de los huevos obtenidos con el computador con volumenes calculados con el método usual de medidas lineales. Nuestro método fue preciso y las diferencias en los volumenes usando nuestro método y las del método clásico estuvieron asociadas a la variación en la forma de los huevos. Entre las ventajas de nuestra técnica encontramos una disminución en la manipulación de los huevos y un aumento en la presición de los datos tomados. Los recursos computacionales que se necesitan e información adicional sobre esta técnica se encuentra disponible en: http://www.archbold-station.org/abs/data/birddata/Bridge-JFO-eggsize.htm. Egg size is associated with many important aspects of avian life history, such as female mass (Nol et al. 1997), female social status (Grønstøl 1997), lay date (Flint and Sedinger 1992), egg composition (Ricklefs 1984, Arnold 1989), nesting success (Reed et al. 1999), hatchling size (Briskie and Sealy 1990, Williams 1994), and nestling survival (Galbraith 1988, Grant 1991). Egg size has been determined in a variety of ways, including mass, linear measurements (length and width), and volume. Under ideal conditions, field measurements of fresh egg mass can yield accurate measures of egg size. However, for the relatively light eggs of many passerines, detecting differences as small as 0.1 g, which can be 5% or more of egg mass, is difficult when using spring scales (Pesola, Baar, Switzerland). Furthermore, attempts to obtain egg weights in the field must address the issue of gradual water loss that occurs during the incubation period. Similarly, field measurements of length and width using calipers are prone to observer error and, by themselves, these linear measurements often fail to correspond precisely with egg size due to differences in shape. Although egg volumes can be approximated from linear measurements of length and width, any error in these measures may be amplified by the multiplicative process that yields volume estimates. Furthermore, egg volume is determined by egg shape in addition to length and width (Preston 1974), yet calculation of egg volumes from length and width measurements generally fail to account for intraspecific variation in egg shape. The most widely used method for estimating egg volume appears to be that of Hoyt (1979), where volumes are estimated on the basis of length and width measures and a species-specific shape variable. A query of the ISI Web of Science database (http://isiwebofknowledge.com) yielded 413 citations for this paper, far more than the sum of all citations found for other egg-sizing methods, including photographic techniques (Paganelli et al. 1974, Mänd et al. 1986), water displacement (Hoyt 1976, Loftin and Bowman 1978, Székely et al. 1994, Kern and Cowie 1996), and other methods based on linear measurements (Westerkov 1950, Coulson 1963, Stonehouse 1966). Here we present a new method of measuring the length, width, volume, and surface area of bird eggs using digital photography and automated computer-image analysis. We tested this approach using photographs of Florida Scrub-Jay (Aphelocoma coerulescens) eggs, and we use the resulting data to compare our technique with Hoyt's (1979). Egg photography Florida Scrub-Jays at Archbold Biological Station (27°10′50″, 81°21′00″) are highly sedentary cooperative breeders, with clutches of two to five eggs laid on consecutive days by a single female (Woolfenden and Fitzpatrick 1996). From early March to late May in 2004 and 2005, we located nests and visited them daily to mark newly laid eggs with one to five miniscule ink dots to determine laying order. When a clutch was complete, we photographed the eggs. In 2004 we also measured the length and width of eggs using dial calipers (±0.1 mm). Photographs were taken with a Nikon Coolpix 8700 digital camera (Nikon Corp., Tokyo, Japan) mounted on a custom-built, plywood stand that held the eggs and camera in place (Fig. 1). The stand had a platform base with five small holes to hold the eggs, and a solid color surface so eggs could be easily distinguished from the background. We installed screws a fixed-distance apart near the right and left edges of the platform to use as calibration points when converting pixel-based dimensions into metric units. These calibration markers were elevated to the approximate height of the middle of an egg positioned on the platform to ensure that the line between the markers was in the same plane as the outline of an egg. The distance between the two calibration points was measured 10 times to the nearest 0.01 mm, and these measurements were then averaged to give a single calibration distance measure. This measurement process was performed both before and after 4 months of use in the field to insure that the calibration points did not shift appreciably. The camera was mounted on a vertical piece of wood attached to the platform base so it could be positioned directly over the eggs with the lens pointing straight down. To take a photograph, eggs were removed from a nest and arranged by laying order on the platform with the long axis of each egg parallel to the platform. Photographs were taken in shade without a flash to diminish glare and shadows and to maximize contrast between the eggs and the background. The egg photography platform shown above an example of a photograph of a clutch. Image processing and geometrical measurements Our digital measurement system used the shareware program GraphicConverter (Lemke Software, Peine, Germany) in conjunction with Applescript, a component of Macintosh OSX system software (Apple Computer, Cupertino, CA). These two software components were integrated into a single egg-analysis procedure where GraphicConverter performed all necessary image manipulations while the user interface and mathematical calculations were performed using a set of Applescript instructions. Details concerning operation of the egg analysis procedure are available at http://www.archbold-station.org/abs/data/birddata/Bridge-JFO-eggsize.htm. Here we present a brief description of the procedure. The first step in processing an egg image was to establish a linear scale factor in pixels/cm for the entire photograph by determining the distance in pixels between the two calibration points. Next, an egg was selected from the photograph by framing it with a rectangular selection tool. This selected area was then removed to a new image window and rendered in black and white using the "threshold" feature in GraphicConverter that converts all pixels in an image to either black or white based on whether a pixel's brightness is above or below an adjustable threshold value. In the resulting image, eggs appeared as white silhouettes against a black background. The margins of the image were then trimmed so that the top, bottom, and sides of the egg defined the height and width of the image. The egg image was then inverted to show a black egg silhouette on a white background and rotated (with automatic resizing and trimming of the image as needed) to ensure that the long axis of the egg was oriented vertically (see Fig. 2). Examples of egg silhouettes used for calculating height, width, volume, and surface area. These two silhouettes represent the extremes of egg shape in our sample of Florida Scrub-Jay eggs, with the highest and lowest shape index values. The shape index value shown for each egg is the percentage of the white marginal area surrounding the egg over the entire area of the rectangle. All measurements were determined from the arrangement of pixels in these egg-silhouette images. Length and width measurements were derived from the height and width of a rotated egg silhouette and the pixels/cm scale factor. Volume was calculated by examining each row of pixels in the rectangular image and regarding the series of black pixels in each row as a cylindrical slice of the egg. Each cylinder had a radius (r) equal to half the number of black pixels in the row and a height (h) of 1 pixel, and the volume of each cylinder was calculated as V =hπr2, where h is always 1. The volumes from all rows of an egg image were summed to give a total volume in pixels. This value was then converted to cm3 using the scale factor. Similarly, surface area was calculated by dividing the egg image into small cross-sections. However, because the egg outline consisted of square pixels rather than a smooth contour, the surface area of an egg could not be calculated as the sum of the outer surface areas of the cylinders used to estimate volume. Instead, each cross-section was regarded as a right frustrum of a cone, and the surface areas of the perimeters of these frustra were calculated and summed (as in Paganelli et al. 1974). A second consideration was that the pixels in a digital image cannot perfectly trace the outline of an egg. Because each row of pixels was only a very close approximation of the width of the egg at a given point, using each row of pixels to generate a frustrum would inflate egg surface area because it would create a convoluted topology slightly less smooth than that of a real egg. Hence, for surface area estimation, the script used fewer and larger cross-sections than for volume, thereby reducing the degree of convolution in the egg surface. This problem did not apply to volume calculation because the slight errors in over- and underestimating egg diameters are averaged out over hundreds of rows of pixels. To examine relationships between egg shape and volume, we calculated a shape index for each egg. The shape index was simply the percentage of white pixels in each egg silhouette, and represented the proportion of the two-dimensional, rectangular egg image not occupied by the egg. Round or barrel-shaped eggs tended to have a low shape index value, whereas pointed or diamond-shaped eggs had relatively large shape index values (Fig. 2). Comparisons and validations We compared egg volumes derived from our digital photo analyses (henceforth referred to as digital volumes) to volumes derived from Hoyt's (1979) equations (henceforth Hoyt volumes) using our digital length and width measurements and the shape coefficient for American Robin (Turdus migratorius) eggs (0.504). We used this shape coefficient because robin eggs are more similar to scrub-jay eggs than those of other species for which Hoyt provided coefficients. We also evaluated coefficients of 0.500 and 0.510 to test the correctness of the robin-shape coefficient. To evaluate potential error in Hoyt's method caused by variation in egg shape, we compared digital and Hoyt volumes and regressed the difference between these values on the shape index. For further comparison, we also calculated Hoyt volumes for a subsample of 232 eggs (all from 2004) using caliper measurements of lengths and widths. Before processing egg images, we used several egg photographs to optimize the threshold value used by GraphicCoverter to convert color images to black and white. Similarly, we used a computer-generated image of a circle similar in size to a scrub-jay egg to determine the optimum number of cross-sections to be used in calculating surface area and to validate the accuracy of the volume measurements. To perform these operations, we regarded the circle as the outline of a sphere and compared its exact geometrical volume and surface area to measurements calculated using our image analysis system. As a practical test of the accuracy of the system, we photographed a metal disk with a diameter of exactly 24.26 mm and compared the geometrical volume and surface area of the sphere it would describe to the results from the digital photography system. We did not use actual eggs to validate the system because we had no means of estimating egg volumes that would likely exceed the accuracy of the photography system. Accuracy Tests of the egg measurement system using a simulated sphere with a diameter of 25 mm (similar in size to a scrub-jay egg) and at the same resolution as the actual egg photos indicated that our measurement system was highly accurate. The volume of the sphere was 8.181 ml (calculated as V = (4/3)πr3) and its surface area was 19.635 cm2 (calculated as S = 4πr2). These values closely matched the output from the egg processing system, which yielded 8.180 ml and 19.642 cm2 for volume and surface area, respectively, when using 80 cross-sections to assess surface area. Tests using an actual disk with a diameter of 24.26 mm further confirmed the accuracy of the system. The geometrical volume (7.476 ml) and surface area of the sphere it would outline (18.490 cm2) closely matched the volume (7.481 ml) and surface area (18.549 cm2) measured from a digital photograph. Caliper measurements of calibration points before and after use in the field differed by 0.02%, which we considered negligible. Egg volumes and comparison with Hoyt's equation The mean digital volume of the 491 eggs in our study was 5.71 ± 0.55 (SD) ml. We obtained a similar mean volume of 5.68 ± 0.56 ml using Hoyt's (1979) equation with a shape coefficient of 0.504. Alteration of the shape coefficient decreased the agreement of the average Hoyt volume with the average digital volume, with Hoyt volume averaging 5.64 ml with a coefficient of 0.500, and 5.75 ml with a coefficient of 0.510. Within-egg differences between Hoyt volumes and digital volumes (digital minus Hoyt) ranged from 0.25 ml (4.03% of the average digital volume) to −0.21 ml (3.41% of the average digital volume) and the absolute values of these differences averaged 1.15 ± 0.80% of the average digital volume. Linear regression of the differences between Hoyt volumes and those calculated from digital images on our shape index showed that egg shape explained 77% of the variation in the difference between digital volumes and Hoyt volumes (R2= 0.77, N= 491, P < 0.001; Fig. 3). Differences were greatest when the shape index was high or low, suggesting that Hoyt's (1979) equation is less robust at the extreme ends of the shape index range (i.e., for unusually round or pointed eggs). Linear regression of the difference between egg volumes calculated using Hoyt's (1979) equation and volumes from the digital photography system on the shape index (i.e., the area of the trimmed margin around each rectangular egg-outline image as a percentage of the entire image area) from our digital photo analyses. The 233 Hoyt volumes calculated using caliper measurements differed from their respective digital volumes by an average of 1.55 ± 1.28%, with differences ranging from 0.43 ml (7.83% of the average digital volume) to –0.40 ml (7.17% of the average digital volume). The difference between Hoyt volumes based on caliper measurements and digital volumes approached statistical significance (paired t-test: N= 233, t=−1.83, P= 0.068), due in part to a large sample size. However, the mean volumes from the two methods were very similar: 5.545 ± 0.517 ml for Hoyt volumes and 5.532 ± 0.522 ml for digital volumes. Advantages of the digital photography system Measuring egg volume using digital photographs has the advantage of being accurate for eggs of almost any species, regardless of intraspecific variation in egg shape. The only assumption about egg shape inherent in our method is that of circular symmetry around the long axis. In addition, digital photographs can be taken quickly and require little handling of eggs, especially compared to taking caliper measurements, reducing the risk of accidental breakage, abandonment of the nest, or both. Finally, digital photographs provide a permanent record, permitting review of photographs for error checking and general reference. Hoyt (1979) noted that egg shape varied considerably among species and provided a table of volume coefficients so equations could be customized for each species. On the basis of a study of Black Swan (Cygnus atratus) eggs (Stonehouse 1966), Hoyt (1979) also predicted that error associated with intraspecific variation in egg shape would rarely, if ever, exceed 2%. Although few investigators have documented intraspecific variation in egg shape, Kern and Cowie (1996) and Ojanen et al. (1981) suggested that that Pied Flycatcher (Ficedula hypoleutica) eggs were particularly variable, with some nearly spherical and others strongly pointed. Johnson et al. (2001) reported similar variation in House Wren (Troglodytes aedon) eggs. Less variation in shape might be expected for species with spherical eggs (e.g., Strigiformes) or those experiencing strong selection for a particular shape (e.g., the pointed eggs of cliff-nesting species such as murres, Uria spp.; Lack 1968). The eggs of Florida Scrub-Jays appear to be intermediate in terms of variation in shape. Of the 491 eggs we measured, 78 of the Hoyt volumes differed from corresponding digital volumes by more than 2%. Thus, a simple volume coefficient may be insufficient to account for egg-shape variation in some species. Our analysis of the shape index and differences between Hoyt volumes and digital volumes revealed that 77% of the error associated with the application of Hoyt's equation was due to egg shape, indicating that about three-fourths of the error associated with Hoyt's equation can be eliminated by incorporating individual egg shape into estimates of egg volume. This comparison uses the same pixel-based length and width measurements for both digital and Hoyt volumes. When we calculated egg volumes using Hoyt's equation and caliper measurements of length and width, the range of error almost doubled. However, error associated with caliper measurements may vary with the skill of the observer and the size of the eggs measured. Our method follows several other techniques for measuring egg volumes that account for individual egg shape. For example, Preston (1974) and Tatum (1975) combined linear measurements with parameters describing the ellipse formed by the profile of an egg to provide accurate assessments of volume and surface area. Previous investigators have also used photography to estimate egg size. Paganelli et al. (1974) and Mänd et al. (1986) used film photography to facilitate digitizing the outlines of eggs. In addition, Paganelli et al. (1974) divided digitized egg outlines into 16 latitudinal slices for which volume and surface-area calculations were performed. Our technique is similar, but we use a computer-based system to make the process more accurate and less labor intensive. Volumeters (graduated cylinders used to measure water displacement by an immersed egg) have also been used to measure egg volume (Tarassov 1977, Loftin and Bowman 1978, Thomas and Lumsden 1981, Székely et al. 1994, Kern and Cowie 1996). Volumeters are usually used for larger eggs because small eggs require a specialized volumeter with a narrow measurement tube (but see Kern and Cowie 1996). In addition, because eggs are immersed in water, volumeters can only be used for eggs that are not cracked or pipped. Recommendations and software acquisition We have several recommendations for those interested in using digital photographs to estimate egg volumes. First, the photography platform may need to be customized for use with the eggs of some species. The color and texture of the background material should provide good contrast with the eggs and minimize reflection. We tried several materials and found that black velvet provided the greatest contrast with scrub-jay eggs. For eggs of other species, a different background color may be needed and some image preprocessing may be necessary to obtain images to which a brightness threshold can be applied. Several digital image software packages, including GraphicConverter, can perform (and often automate) the needed brightness adjustments and color filtering. Second, each egg must be positioned on the photography platform with the long axis parallel with the surface of the platform. Deviation from this position will effectively shorten the resulting image of the egg and lead to underestimates of length, volume, and surface area. Proper positioning can usually be assured by viewing mounted eggs from the side. In addition, the calibration component of the photography platform should be as large as possible (i.e., almost the entire width of the photograph) to facilitate accurate translation of pixel-based measures to metric units. Careful and repeated measures of the distance between the calibration points are necessary because all resulting digital measurements are based on this calibration value and transport and handling for use in the field may cause movement of the calibration points. Third, image resolution must be considered. Extremely low resolution will reduce accuracy, and extremely high resolution may slow the processing of photographs. In our photographs, eggs were generally from 600 to 1000 pixels in height. We recommend this range of resolution for those using our methods. Finally, although any camera with adequate resolution can be used, we suggest avoiding cameras that exhibit a high degree of barrel distortion, which may result when using inexpensive zoom lenses. This distortion "warps" photographs so that straight lines appear slightly curved near the edge of the field of view. To test for barrel distortion, photograph a perfect rectangle or a series of straight lines and note any discrepancies in the resulting image. If a camera that causes barrel distortion must be used, this problem can and should be corrected using imaging software before any analyses are performed. GraphicConverter is a shareware program available for $30 (US; http://www.lemkesoft.com/en/index.htm). The applescript used in our study is available for download (http://www.archbold-station.org/abs/data/birddata/Bridge-JFO-eggsize.htm) or by request from ESB. These tools are designed for use with the apple OS X operating system, and we have not developed a fully automated system for PC users. However, the procedures necessary to implement our technique can be performed manually using PC-based software. More specifically, PC users would have to manually derive scale factors for each photograph, edit egg images to generate silhouettes, save these images as xmp files (or some other text-based format), and use a spreadsheet program (e.g., Excel; Microsoft Corp., Seattle, WA) to open each xmp file to calculate the desired parameters. If automated PC-based methods come to our attention, they will be noted on our Web site. This technique was developed for use in studying the reproductive biology of Florida Scrub-Jays as part of NSF grants IBN 0346328 to S. Schoech and R. Bowman and IBN 0508418 to S. Schoech and R. Boughton. The photography stand prototypes were built by L. Riopelle. We wish to thank all the research assistants and interns who helped find and monitor nests, especially T. Grieves, J. Atwell, R. Atwell, R. McKee, and C. Pitt. Thanks also to T. Lemke for advice on using GraphicConverter with Applescript and to the staff of Archbold Biological Station for support of our research.