Shell temperature: How shall we tell if a still gosling is under the eggshell?

The present investigation was aimed at predicting a still (i.e., dead) vs. live embryo within a hatching goose egg by measuring the eggshell cooling rate. For this, we daily measured the temperature (T) values on the shell surface of goose eggs after they were removed from the incubator and during further natural cooling. T was recorded every 0.5 h for further 1.5 h of cooling. It was possible to recognize eggs with dead embryos using the combination of T, egg weight (W), and surface area (S). The resultant indicator (TS/W) was called specific temperature index (STI). The mathematical relationship using STI measurements between Days 8-13 facilitated 80 % correct identification of the eggs with dead embryos. Additionally, we derived mathematical dependencies for shell weight (Ws) and thickness (t) by utilizing the values of W, egg volume (V), S, the average T of all measurements taken, as well as the drop in T during 1.5 h of natural cooling. The key advantage of these parameters was their measurement and/or calculation by applying non-destructive methods. The integrated application of these parameters resulted in achieving high calculation accuracy as judged by correlation coefficients of 0.908 for Ws and 0.593 for t. These novel mathematical models have the potential to decrease hatching waste by predicting embryo viability. Our research will add to a toolkit for non-invasive egg assessment that is useful in the poultry industry, research on eggs, and engineering.

Metabolic Rate and Egg Production in Japanese Quails Can Be Predicted by Assessing Growth Parameters of Laying Hens.

The aim of the current study was to assess the female metabolic rate and test the hypothesis that there is a relationship between the egg productivity of Japanese quails from eight breeds and their morphometric, or growth, parameters. Parameters measured were body weight (B), volume (V), and surface area (S), as well as the metabolism level expressed by the ratio S/V. The collected egg performance traits were as follows: the number of eggs produced (N), the average egg weight (W), and the total egg mass (M) (i.e., N multiplied by W). To measure the S and V values, a novel technique was developed that takes into account the similarity of the quail's body to an ellipsoid. An analysis of the relationships between productivity indicators allowed us to introduce a new index called the metabolic index, B·S/V, based on all three main growth parameters in quails. Using the values of this index, we were then able to judge indirectly the level of quails' egg productivity. We went on to assess the N, W, and M values, not only depending on the size of the bird's growth parameters but also according to the degree of their changes during quail growth. These changes were expressed as the slope angles of trend lines describing the growth process data. This approach produced more accurate results for predicting the egg productivity in terms of W and M.

Genotyping-by-Sequencing Strategy for Integrating Genomic Structure, Diversity and Performance of Various Japanese Quail (Coturnix japonica) Breeds.

Traces of long-term artificial selection can be detected in genomes of domesticated birds via whole-genome screening using single-nucleotide polymorphism (SNP) markers. This study thus examined putative genomic regions under selection that are relevant to the development history, divergence and phylogeny among Japanese quails of various breeds and utility types. We sampled 99 birds from eight breeds (11% of the global gene pool) of egg (Japanese, English White, English Black, Tuxedo and Manchurian Golden), meat (Texas White and Pharaoh) and dual-purpose (Estonian) types. The genotyping-by-sequencing analysis was performed for the first time in domestic quails, providing 62,935 SNPs. Using principal component analysis, Neighbor-Net and Admixture algorithms, the studied breeds were characterized according to their genomic architecture, ancestry and direction of selective breeding. Japanese and Pharaoh breeds had the smallest number and length of homozygous segments indicating a lower selective pressure. Tuxedo and Texas White breeds showed the highest values of these indicators and genomic inbreeding suggesting a greater homozygosity. We revealed evidence for the integration of genomic and performance data, and our findings are applicable for elucidating the history of creation and genomic variability in quail breeds that, in turn, will be useful for future breeding improvement strategies.

A novel model for eggs like pears: How to quantify them geometrically with a mathematical formula of two parameters?

Of the variety of bird egg shapes, perhaps the most fascinating and unusual are pyriform (pear-shaped, or conical) eggs. Among oologists, there is still no consensus on what exactly caused this evolutionary and ecological adaptation. To address this, our research was aimed to develop a minimalistic mathematical model for an accurate description of the pyriform egg contour, using the minimum number of measurements. As such, egg length (L) and its maximum breadth (B) were found to be an optimal set of parameters that were easy enough to measure with the required accuracy. We tested four analytical premises that can be used for successful pyriform egg shape modelling. To validate these four model premises, images of pyriform eggs characteristic of 32 species were used. As a result, we derived a novel mathematical dependence that we called the 'pyriform model with two parameters'. Based on this model, it is feasible to geometrically reconstruct any pyriform egg profile under study using only two egg measurements, i.e., L and B. Since pyriform eggs are characteristic of wild bird species that are most often investigated in the field, the measurement of only two parameters minimizes the time spent and, accordingly, the stress factor on the animals. The least error estimate for the new model was 3.9%, which turned out to be even more accurate than that of the previously developed model with three parameters.

A novel approach to egg and math: Improved geometrical standardization of any avian egg profile.

Developing a geometric formulation of any biological object has a number of justifications and applications. Recently, we developed a universal geometric figure for describing a bird's egg in any of the possible basic shapes: spherical, ellipsoidal, ovoid, and pyriform. The formulation proved widely applicable but had a number of drawbacks, including a very obvious join between two parts of the egg. To correct this, we developed the Main Axiom of the universal mathematical formula. This essentially involved making the ordinate of the extremum of the function correspond to half the maximum egg breadth (B), and the abscissa to the reciprocal of the parameter w that reflects the shift of the vertical axis to its coincidence with B. This, in turn, helped us develop a new, simplified mathematical model without a nonbiological join. Experimental verification was performed to confirm the adequacy of the new geometric figure. It accurately described actual avian eggs of various shapes more closely than our previous model. To the best of our knowledge, our new, simplified equation can be applied as a standard for any bird egg that exists in nature. As a rather simple equation, it can be used in a broad range of applications.

Disentangling clustering configuration intricacies for divergently selected chicken breeds.

Divergently selected chicken breeds are of great interest not only from an economic point of view, but also in terms of sustaining diversity of the global poultry gene pool. In this regard, it is essential to evaluate the classification (clustering) of varied chicken breeds using methods and models based on phenotypic and genotypic breed differences. It is also important to implement new mathematical indicators and approaches. Accordingly, we set the objectives to test and improve clustering algorithms and models to discriminate between various chicken breeds. A representative portion of the global chicken gene pool including 39 different breeds was examined in terms of an integral performance index, i.e., specific egg mass yield relative to body weight of females. The generated dataset was evaluated within the traditional, phenotypic and genotypic classification/clustering models using the k-means method, inflection points clustering, and admixture analysis. The latter embraced SNP genotype datasets including a specific one focused on the performance-associated NCAPG-LCORL locus. The k-means and inflection points analyses showed certain discrepancies between the tested models/submodels and flaws in the produced cluster configurations. On the other hand, 11 core breeds were identified that were shared between the examined models and demonstrated more adequate clustering and admixture patterns. These findings will lay the foundation for future research to improve methods for clustering as well as genome- and phenome-wide association/mediation analyses.

Egg-inspired engineering in the design of thin-walled shelled vessels: a theoretical approach for shell strength.

A novel subdiscipline of bionics is emerging in the form of 'egg-inspired engineering' through the use of egg-shaped ovoids as thin-walled tanks and building structures. Hügelschäffer's and Narushin's models of egg geometry are highly applicable within this proposed subdiscipline. Here we conducted a comparative analysis between the two models with respect to some of the most important egg parameters. These included contents volume, shell volume, and the location of the neutral axis along the shell thickness. As a first step, theoretical studies using the Narushin's model were carried out due to the lack (or limited amount) of data on the geometric relationships of parameters and available calculation formulae. Considering experimental data accumulated in the engineering and construction industries, we postulate a hypothesis that there is a correlation between location of the neutral axis and the strength of the walls in the egg-shaped structure. We suggest that the use of Narushin's model is preferable to Hügelschäffer's model for designing thin-walled shelled vessels and egg-shaped building structures. This is due to its relative simplicity (because of the requirement for only two initial parameters in the basic equation), optimal geometry in terms of material costs per unit of internal capacity, and effective prerequisites for shell strength characteristics.

Measurement of the neutral axis in avian eggshells reveals which species conform to the golden ratio.

Avian eggs represent a striking evolutionary adaptation for which shell thickness is crucial. An understudied eggshell property includes the neutral axis, a line that is drawn through any bent structure and whose precise location is characterized by the k-factor. Previous studies have established that, for chicken eggs, mean k corresponds to the golden ratio (Φ = 1.618, or 0.618 in its reciprocal form). We hypothesized whether such an arrangement of the neutral axis conforms to the eggshell of any bird or only to eggshells with a certain set of geometric parameters. Implementing a suite of innovative methodological approaches, we investigated variations in k of 435 avian species, exploring which correspond to Φ. We found that mean k is highly variable among birds and does not always conform to Φ, being much lower in spherical and ellipsoid eggs and higher in pyriform eggs. While 21 species had k values within 0.618 ± 0.02 (including four falcon species) and the Falconinae subfamily (six species) revealed a mean of 0.618, it is predominantly domesticated species (chicken, ducks, and geese) that lay eggs whose neutral axis corresponds to the golden ratio. Thus, the study of the mathematical secrets of the eggshell related to the golden ratio of its neutral axis suggests its species-specific signatures in birds.

Mathematical progression of avian egg shape with associated area and volume determinations.

Development of nondestructive techniques for estimating egg parameters requires a comprehensive approach based on mathematical theory. Basic properties used to solve theoretical and applied problems in this respect are volume (V) and surface area (S). There are respective formulae for calculating V and S of spherical, ellipsoidal, and ovoid eggs in classical egg geometry; however, the mathematical description and calculation of these parameters for pyriform eggs have remained elusive. In the present study, we derived the appropriate formulae and established that this would be not only applicable and valid for the category of pyriform eggs, but also universal and explicit for all other naturally occurring avian egg shapes. Thus, we have demonstrated "mathematical progression" of this natural object, considering the egg as a sequence of geometric figures that transform from one to another in the following sequence of shapes: sphere → ellipsoid → ovoid (whose profile corresponds to Hügelschäffer's model) → pyriform ovoid.

Egg and math: introducing a universal formula for egg shape.

The egg, as one of the most traditional food products, has long attracted the attention of mathematicians, engineers, and biologists from an analytical point of view. As a main parameter in oomorphology, the shape of a bird's egg has, to date, escaped a universally applicable mathematical formulation. Analysis of all egg shapes can be done using four geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical or pear-shaped). The first three have a clear mathematical definition, each derived from the expression of the previous, but a formula for the pyriform profile has yet to be derived. To rectify this, we introduce an additional function into the ovoid formula. The subsequent mathematical model fits a completely novel geometric shape that can be characterized as the last stage in the evolution of the sphere-ellipsoid-Hügelschäffer's ovoid transformation, and it is applicable to any egg geometry. The required measurements are the egg length, maximum breadth, and diameter at the terminus from the pointed end. This mathematical analysis and description represents the sought-for universal formula and is a significant step in understanding not only the egg shape itself, but also how and why it evolved, thus making widespread biological and technological applications theoretically possible.

Effects of Essential Oils-Based Supplement and Salmonella Infection on Gene Expression, Blood Parameters, Cecal Microbiome, and Egg Production in Laying Hens.

One of the main roles in poultry resistance to infections caused by Salmonella is attributed to host immunity and intestinal microbiota. We conducted an experiment that involved challenging Lohmann White laying hens with Salmonella Enteritidis (SE), feeding them a diet supplemented with an EOs-based phytobiotic Intebio®. At 1 and 7 days post-inoculation, the expression profiles of eight genes related to immunity, transport of nutrients in the intestine, and metabolism were examined. Cecal microbiome composition and blood biochemical/immunological indices were also explored and egg production traits recorded. As a result, the SE challenge of laying hens and Intebio® administration had either a suppressive or activating effect on the expression level of the studied genes (e.g., IL6 and BPIFB3), the latter echoing mammalian/human tissue-specific expression. There were also effects of the pathogen challenge and phytobiotic intake on the cecal microbiome profiles and blood biochemical/immunological parameters, including those reflecting the activity of the birds' immune systems (e.g., serum bactericidal activity, ß-lysine content, and immunoglobulin levels). Significant differences between control and experimental subgroups in egg performance traits (i.e., egg weight/number/mass) were also found. The phytobiotic administration suggested a positive effect on the welfare and productivity of poultry.

Spectroscopy analysis for simultaneous determination of lycopene and ß-carotene in fungal biomass of Blakeslea trispora.

Blakeslea trispora is a good alternative source for producing such carotenoids as lycopene and ß-carotene. The objective of this research was to elaborate a method for the simultaneous determination of lycopene and ß-carotene in Blakeslea trispora products using a usual UV-vis spectrophotometer. The standard solutions of the mixture of different concentrations of ß-carotene and lycopene were measured with the UV-vis method and correlation formula for the extinction coefficients of 1% standard solution of lycopene in the solvent (hexane) and the ratios of the optical densities at the character peaks of 470 and 502 nm was elaborated. This gives a possibility to calculate the concentrations of lycopene and ß-carotene in the mixture. The prediction quality of the UV-vis method was sufficient and the obtained results were very close to the ones, being measured with the HPLC technique. The proposed method can be used for both routine industrial work and academic research, providing the rapid analysis for simultaneous measurements of lycopene and ß-carotene.