CC BY
10АЖ_| © Амурский зоологический журнал. VII(2), 2015.166-174 | Accepted: 25.05.2015
УДК 598.293.1 | ©Amurian zoological journal. Ш(2), 2015.166-174 | Published: 30.06.2015
GEOMETRIC MODELLING OF EGG VARIABILITY IN CORVIDAE I.S. Mityay1, A.V. Matsyura2
['Митяй И.С., 2Мацюра А.В. Геометрическое моделирование оологической вариабельности у врановых птиц] 'National University of Life and Environmental Sciences of Ukraine, Heroyev Oborony str. 15, 03041, Kiev, Ukraine. E-mail: oomit@mail.ru
2Altai State University, Lenina str. 61, 656049, Barnaul, Russia. E-mail: amatsyura@gmail.com
'Национальный университет биоресурсов и природопользования, ул. Героев Обороны 15, 03041, Киев, Украина. E-mail: oomit@mail.ru
2Алтайский государственный университет, ул. Ленина 61, 656049, Барнаул, Россия. E-mail: amatsyura@gmail.com
Key words: ovoids, Corvidae, species-specific egg shapes Ключевые слова: овоид, врановые, видоспецифические формы яиц
Summary. We analyzed the egg shape in bird family Corvidae using a polynomial model and a compound ovoid model. We constructed a geometric model that reflects the relationship between cloacal and infundibular arcs, and the length and the diameter of the egg. Specifically, we quantified the shape of the egg via seven indices: the traditional index of elongation and six novel indices. Morphological parameters of bird eggs within three genera of Corvids (Corvus, Pica, and Garrulus) revealed that although there was overlap with their minimum and maximum values, the mean values remained different. Cluster analysis, using suggested indices and polynomial equations based on the absolute length and diameter of eggs, demonstrated different values within three main groups: the Hooded Crow, Carrion Crow, and Common Raven group, the European Jackdaw and Eurasian Jay group, and the Rook and Eurasian Magpie group. This is best explained by the variation in the elongation indices, suggesting that spheroid eggs are the optimal for clutches of 1-2 eggs or more than 5 eggs. Geometrical schemes, formulas of compound ovoid, and polynomial equations generated for seven species of corvids are supplied, which provide evidence of species-specific patterns of egg shapes.
Резюме. Нами были проанализированы формы яиц врановых птиц с помощью полиномиальной модели и модели составного овоида. Для каждой из форм была построена геометрическая модель, которая отражает взаимосвязь между клоакальной и инфундибулярной зоной, длиной и диаметром яйца. Количественные описание овоидов проводили по семи показателям: традиционному индексу удлиненности и шести оригинальным индексам. Анализ морфологических параметров яиц птиц трех родов (Corvus, Pica и Garrulus) показал, что их минимальные и максимальные значения перекрываются, но существуют выраженные различия в средних значениях. Был установлен кластер «серая ворона, черная ворона, ворон - галка, сойка - грач, сорока» относительно семи индексов и предложенных уравнений, базирующихся на значениях абсолютной длины и диаметра яиц, и отражающих изменение удлиненности яиц. Это может быть объяснено тем, что сфероподобные яйца вероятно являются наиболее оптимальными в кладках из одного-двух и из более чем пяти яиц. Для проверки этой гипотезы потребуется дополнительное исследование. Геометрические схемы, формулы и полученные полиномиальные уравнения для семи видов врановых птиц предложены нами в качестве исходных величин для видоспецифичных моделей форм яиц, которые могут быть использованы в систематике и филогении.
INRODUCTION
The shell of bird egg plays an important role in providing the essential conditions for the development of the embryo. It acts as a barrier from outside conditions and simultaneously provides an area for the embryo to develop [Alabi et al., 2012; Deeming, Ruta, 2014a; Demming, Ruta, 2014b; Gamauf, Haring, 2004; Hoyt, 1968; Zelenitsky et al., 2011]. The efficacy of mechanical properties of an eggshell depends on the degree of its curvature and its thickness. A perfect sphere will have maximum strength with a minimal shell thickness. However, birds typically do not produce perfect spherical eggs and thus must create a compromise between the curvature and thickness of their eggs and strength [Andersen et al., 2014; Barta, Székely, 1997; Livezey, Zusi, 2007;
Richter, Wirkner, 2014]. In addition to its mechanical functioning, a shell allows gas exchange, transpiration, and thermoregulation during incubation. All these processes are associated with the egg surface. Ultimately, these properties vary by morphometric parameters of the egg, namely, its shape and quantitative indicators. The description of the last is in many ways problematic [Alabi et al., 2012; Andersen et al., 2014; Barta, Szekely, 1997; Hoyt, 1968; Livezey, Zusi, 2007; Preston, 1968; Troscianko, 2014].
The underlying issue in bird eggs, Corvidae eggs in particular, is that there is no holistic approach of describing an egg that takes into consideration its form, geometrical diagrams and their accompanying quantitative calculations. In doing so, it would allow one to highlight the ideal shapes for any bird species, analyze their relationship with certain aspects of the
process of incubation, and the suitability of egg form to ensure the optimal development of the embryo in variable environmental conditions [Alabi et al., 2012; Barta, Szekely, 1997; Deeming, Ruta, 2014a; 2014b; Zelenitsky et al., 2011].
The purpose of this research was to analyze the eggs of certain species in the family Corvidae and to identify their species-specific shapes by geometric models and compare them with the actual egg shapes.
METHODS
Data (raw measurements and pictures) was collected in the field as well as in museums in Ukraine and Russia: National Science and Natural History Museum of National Academy of Sciences of Ukraine (Kiev), the Zoological Museum of Kiev, National Taras Shevchenko Museum of Zoology (Kiev), Lviv National Ivan Franko University, State Museum of Natural History of National Academy of Sciences of Ukraine (Lviv) , the Nature Museum of Kharkiv National University, Cherkassy Regional History Museum, the Zoological Museum of Moscow State University (Russian Federation) - see Table 1.
Index (Iiz = r / D), lateral area Index (Ilz = rl / D), and cloacal area Index (Isz = rc / D); Index of asymmetry (Ias = rc / r), Equatorial Index (I = b = L-(rc + r) and Complementarity Index Icom = (rc + b) (r + b) bL, where b = L-(rc + r), L - egg length , D - egg diameter, r , r, r - the radii of the areas.
' c' P 1
All parameters were developed with our novel approach (Fig. 1) stemming from digital pictures of eggs with the help of computer programs developed by B. Trotsenko and C. Shelestyuk on equations of piecewise continuous curve.
In addition to the above-mentioned model of the composite ovoid, the Polynomial model was used which reflects the physical nature of the eggs. A computer program calculating four-degree polynomial has been kindly offered by L.I. Frantsevich [2015]. Statistical processing was performed by Statistica 9.0 and Microsoft Excel 2010.
RESULTS AND DISCUSSION
Eggs differed in diameter (D), length (L), and arc radius of the polar (rp r3), and lateral zones (r^. We ultimately did not utilize the minimal variation
Table 1
The volume of initial data of Corvidae eggs
Species Egg number Length, mm Diameter, mm Weight, g
Corvus corax 87 49.5±0.241 33.7±0.123 28.9±0.232
Corvus corone 13 43.5±0.578 30.0±0.193 -
Corvus cornix 98 41.5±0.221 29.5±0.106 18.9±0.167
Corvus frugilegus 100 40.1±0.249 28.0±0.094 16.6±0.119
Corvus monedula 100 34.9±0.120 25.1±0.079 11.3±0.077
Pica pica 294 33.0±0.126 23.5±0.056 9.5±0.072
Garrulus glandarius 96 31.0±0.093 22.8±0.064 8.6±0.069
We processed the data from 788 eggs of the Corvidae. Data processing was realized by methods previously described in [Mityay, 2003; 2008]. To compare the characteristics of the shapes of Corvidae eggs we used a model of a composite ovoid. According to this model all the variety of shapes are obtained by drawing (combination, pairing, and smoothing) of arcs adequate to the curvature of ovoid areas [Hoyt, 1968; Preston, 1968; Troscianko, 2014]. For each of the shapes we constructed the geometric model that reflects the relationship between cloacal and infundibular arcs, along with the length and the diameter of the ovoid.
Quantified description of ovoids was performed via seven indices: a traditional index of elongation Iel (egg length/diameter ratio), and six proposed novel indices.
The six novel area indices are: infundibular area
of the latter index in the egg description, and thus our results were limited to the four former indices. Moreover, these parameters are closely united in a single system where the length serves as the whole, while the diameter and radius of the polar zones are the components. This approach makes it possible to deduce the formulas of eggs, build basic geometric models, and numerically characterize the minimum number of parameters (length, diameter, and one of the polar radii) - see Fig. 2.
Our classification was based on these settings. All the forms were divided into ovoids (r = 0.5 D), symmetric and asymmetric pseudoovoids due to equality or inequality of infundibular and cloacal radii [Mityay, Degtyarenko, 2012].
The analysis of empirical data showed that the eggs of Corvidae are predominantly asymmetric pseudoovoids (81.5 %) and ovoids (14.9 %). This
Fig. 1. Schemes of measurements from different type of eggs: Рис. 1. Схемы снятия промеров с различных типов яиц: а, псевдоовоидов; b - овоидов
ratio varies in different species. Eggs of Common Raven are dropping-shaped pseudoovoids of type 13 and 14: Group 1 (8.2 %), Group 2 (17.11 %), Group 3 (25.57 %), Group 4 (15.79 %), Group 5 (14.29 %), and Group 6 (10.53 %), see Fig. 3.
24.0 % of Hooded Crow eggs are typical ovoids (type 9-10), the other - the typical pseudoovoids of type 9-10: Group 2 (6 %), Group 3 (22 %), Group 4 (18 %), Group 5 (8 %), Group 6 (22 %) - see Fig. 4.
10.25 % of Eurasian Magpie eggs are teardrop-shaped ovoids (type 13-15) and pseudoovoids of type 13-14: Groups 1-4, respectively 12.4, 14.73, 40.31, and 22.31 % (Fig. 5).
13.13 % of European Jackdaw eggs are blunt and normal ovoids of type 8-9. The pseudoovoids of type 13-14 were also selected: Group 2 (19.19 %), Group 3 (16.17 %), Group 4 (22.22 %), Group 5 (22.22 %), and Group 6 (7.07 %) - Fig. 6.
14.6 % of Eurasian Jay eggs are ovoids, rest are the pseudoovoids, between them 3.61 % of Group 2; 4.82 % of Group 3; 15.66 % of Group 4; 46.99 % of Group 5; and 28.92 % of Group 6 - see Fig. 7.
Using these indices and the polynomial coefficients we have implemented a comparison of the egg shapes at the level of genera and species of the Corvidae family. Analysis of morphological parameters of bird eggs of three genera (Corvus, Pica, and Garru-lus) showed that their minimum and maximum values overlap, but there are differences in the mean values (Table 2).
The eggs of all three species were significantly different in length (t = 34.5, -37.0, 18.7; tav = 1.653; a = 0.05) and diameter (t = 30.1, 35.1, 13.Ctav = 1.653; a = 0.05). Genera Corvus and Pica also significantly differ in the indices of the lateral (t= 10.5; tav = 1.653; a = 0.05), infundibular (t = 7.1; tav = 1.653-a = 0.05) zones, the equatorial Index ( t = -4.2; tav = 1.653; a = 0.05), and all the polynomial coefficients (t = -12.8,
a, c - symmetric and asymmetric pseudoovoids; b - ovoids с - симметрических и асимметрических
9.2, 7.0, -2.2; ta,v = 1.653; a = 0.05).
These data indicate that the egg shapes in the genus Corvus have larger radius lateral edges and smaller angle of inclination. They have a greater distance between the centers of the infundibular and cloacal arcs together with smaller infundibular radius and diameter of the egg meridian (k0). The genera Corvus and Garrulus have significant differences in the radius of infundibular arc to the distance between the centers of the arcs of infundibular and cloacal areas and the two polynomial coefficients (k2, k3). European Jay eggs are closer to ovoid shape in all the parameters. They have higher infundibular and cloacal radius, but the distance between them is lesser. They also have a shorter diameter of egg meridian (k0). Genera Pica and Garrulus have differences only in the lateral arc radius and polynomial coefficient of the first degree. Thus, the majority of morphological parameters of Corvidae eggs at genera level is species-specific.
Our further studies were related to the certain types of shapes in Corvidae eggs. Most of the literature sources indicate the species-specific shape of eggs, but the evidence showing the benefit of this is almost non-existent. In general, each species of Cor-vus genera is characterized by a specific set of egg shapes, the parameters of which overlap to varying degrees, and the mean values differ. Some egg shapes are more regular providing a base for oological databank of bird species. Less distributed egg shapes are the abnormalities on the one hand, and on the other - the original surplus variation as a potential material for natural selection. To determine the degree of similarity of eggs of different species of Corvidae we conducted a cluster analysis by seven egg shape indices and four polynomial coefficients (Fig. 8).
For each of the clusters we made the additional comparison by the shape index (Table 3), the coefficients of the polynomial (Table 4), and geometric
Fig. 2. Basic forms and geometric diagrams of Corvidae eggs. Here 1-4 - Corvus corax; 5-8 - C. corone; 9-14 - C. cornix; 15-17 - C. monedula; 18-21 - Garrulus glandarius; 22-24 - C. frugilegus; 25-30 - Pica pica (the size of rectangle inside the schemes corresponds to the diameter of eggs, the points are the centers of the corresponding circles, horizontal and vertical lines correspond to half of the ovoid, the circles outline the contours of the polar circle zones of the egg) Рис. 2. Основные формы и геометрические схемы яиц врановых птиц: 1-4 - Corvus corax; 5-8 - C. corone; 9-14 -C. cornix; 15-17 - C. monedula; 18-21 - Garrulus glandarius; 22-24 - C. frugilegus; 25-30 - Pica pica (прямоугольник внутри схем по размерам соответствует диаметру яйца, точки - центры соответствующих окружностей, горизонтальная и вертикальная линии соответствуют половине овоида, окружности очерчивают контуры полярных зон яйца)
Fig. 3. Shape and indices of Common Raven eggs Рис. 3. Формы и индексы для яиц ворона
1.5
1
0.5
1с г
lei
las
Icom
1еС|
kO
□ Ovoids
® Pseud с ovoids E3 Pseudoovoids ElPseudoovoids HPseudoovoids
□ Pseudoovoids
Fig. 4. Egg shapes and indices of Hooded Crow Рис. 4. Формы и индексы для яиц серой вороны
Fig. 5. Egg shapes and indices of Eurasian Magpie
Рис. 5. Формы и индексы для яиц сороки обыкновенной
constructions (Fig. 7). The last one arranged so that the radius of the polar area, the length, and diameter of the egg expressed by the dependence on each other and are reflected in the compound ovoid formula. Besides, the polynomial equation was calculated for
each shape type.
Eggs in the transition pattern 'Common Raven -Hooded Crow' are very similar in shape (Fig. 7), but the significant differences on most of the indices and polynomial coefficients were found. These differenc-
Fig. 6. Egg shapes and indices of European Jackdaw Рис. 6. Формы и индексы для яиц галки
□ Ovoids ÜPseudoovoids BPseudoovoids EPse u do ovo id s BPseudoovoids
I«
llz
liz
Id las tcom kq
kO
Fig. 7. Egg shapes and indices of Eurasian Jay Рис. 7. Формы и индексы для яиц сойки
es were observed only for the length, diameter, and elongation index (t = 1.87 t = 1,70; a = 0,05).
A formula of compound ovoid egg of Common Raven:
L = 2r +2 rc; (r = LD; rc = (2D-L/2); L = 2r +3 rc; (r = L/4; rc = L/6); L = 2ri +4 rc; (r = L/4; rc = L/8).
The same for the Hooded crow: L = 2r +2 rc (ri = LD; rc = (2D-L/2); L = 2rl +3 г (ri = LD; г = (2D-L/3); L = 2rl +4 г; (ri = L / 4; rc = L/8).
Generalized polynomial equation: y(x) = 0.681+0.004(1+0.128+0.006x-0.027+0.004x2+ 0.103+0.003x3)Z
For the Hooded Crow: y(x) = 0.688+0.004(1+0.13+0.006x-0.036+0.004x2+ 0,1+0.003x3)Z
(Z-value here and below is: Z = (1-x2 )05).
There was a significant difference in the cluster 'Hooded Crow - European Jackdaw - Eurasian Jay' in absolute length (t = 23.74, 42.34, 17.31; tav = 1.66; a = 0.05) and diameter (t = 38.66, 51.41, 21.15; tav = 1.66; a = 0.05). Eggs of Hooded Crow and European Jackdaw are different in the lateral area index, the index of elongation, and polynomial coefficients of zero, first and third degree (t = -3.25, 1.73, 1.78 ,
3.15, -2.14; t = 1.66; a = 0.05).
' ' a,v ' '
The Hooded Crow and Eurasian Jay differed in the indices of infundibular area and polynomial coefficients of the second and third degree, the other differences were also significant (t = -3.22, -3.79, -3.1,
5.16, -3.18, 4.29, -4.77, 3.4; tav = 1.66; a = 0.05). The Hooded Crow and Eurasian Jay had no dif-
Conus corax -
Corvus corone -
Corvus comix -
С orvus monedula -
Garrulus glandarius -
Corvus frugüegus -
Pica pica -
* ___._I_•_I___I_i_I_____I_I_I_•_._._I___._I_._I_I_____._
0,00 0.05 0,10 0,15 0,20 0,25 030
Fig. 8. Tree diagram of Corvidae egg shapes Рис. 8. Диаграмма сходства формы яиц Врановых
Table 2
Egg shape indices and polynomial coefficients of three Corvidae genera
Index Corvus (n=473) Pica (n=295) Garrulus (96)
min Max M±m min max M±m min max M±m
K„ 0.07 0.95 0.68±0.005 0.62 0.61 0.72±0.003 0.65 0.81 0.74±0.003
ki -0.01 0.31 0.12±0.003 0.001 0.28 0.08±0.003 0.03 0.76 0.22±0.03
k2 -0.19 0.17 -0.03±0.002 -0.15 0.06 -0.06±0.003 -0.001 0.26 0.09±0.005
-0.11 0.82 0.11±0.006 -0.04 0.18 0.10±0.002 -0.11 0.14 0.04±0.004
Table 3
Indices of Corvidae egg shapes
Parameter Corvus (n=473) Pica (n=295) Garrulus (96)
min max M±m min max M±m min max M±m
L, mm 29.3 55.5 41.2±0.2 26.2 40.8 33.3±0.1 28.2 34.1 31.0±0.09
D, mm 22.4 36.1 28.9±0.1 20.0 26.2 23.7±0.1 21.1 24.2 22.8±0.06
I cz 0.2 0.4 0.2±0.002 0.1 0.4 0.2±0.003 0.2 0.4 0.3±0.005
Ilz 0.7 1.8 0.9±0.008 0.7 1.4 0.9±0.007 0.7 1.6 0.9±0.014
I iz 0.3 0.5 0.5±0.001 0.3 0.5 0.5±0.002 0.4 0.5 0.5±0.002
I as 0.2 0.9 0.5±0.005 0.3 0.9 0.6±0.008 0.3 1.0 0.6±0.011
I eq 0.3 1.1 0.7±0.005 0.3 0.9 0.7±0.01 0.4 0.8 0.6±0.008
Iel 1.2 1.7 1.4±0.004 1.2 1.6 1.4±0.005 1.2 1.5 1.4±0.005
I com 1.0 1.5 1.1±0.002 1.0 1.5 1.1±0.007 1.1 1.4 1.2±0.005
Table 4
The polynomial coefficients of Corvidae eggs
Species N k„ ki k2 k3
Corvus corax 87 0.68 0.13 -0.03 0.10
Corvus corone 13 0.69 0.13 -0.04 0.10
Corvus cornix 98 0.71 0.13 -0.03 0.08
Corvus frugilegus 1„„ 0.69 0.16 -0.02 0.07
Corvus monedula 1„„ 0.72 0.10 -0.04 0.09
Pica pica 294 0.72 0.09 -0.06 0.10
Garrulus glandarius 96 0.74 0.10 -0.04 0.09
Table 5
Indices of bird egg shape_
Species n I cz Ilz I iz Iel I as I com I eq
Corvus corax 87 0.23 1.05 0.47 1.47 0.49 1.10 0.77
Corvus corone 13 0.23 1.00 0.47 1.45 0.49 1.10 0.75
Corvus cornix 98 0.24 0.96 0.47 1.39 0.51 1.12 0.69
Corvus frugilegus 1„„ 0.23 1.06 0.48 1.43 0.49 1.12 0.72
Corvus monedula 1„„ 0.24 0.89 0.47 1.38 0.52 1.13 0.67
Pica pica 294 0.24 0.89 0.46 1.39 0.52 1.12 0.69
Garrulus glandarius 96 0.26 0.88 0.47 1.35 0.55 1.15 0.62
ference in the indices of the lateral and infundibular area and polynomial coefficients of first and second degree. The remaining differences are authentic.
Formula of composite ovoid of Hooded Crow: L = 2r+2r ; r=L-D; r =(2D-L)/2.
i c i 7 c x '
L = 2r+2r ; r=L-D; r =(D-L)/2.
i ci ' c ' '
L = 2r+3r ; r=L-D; r =(2D-L)/3.
i ci ' c ' '
L = 2r+3r ; r = D/2; r =(2D-L)/4.
i c' ï ' c ' '
L = r+4r ; r=2D-L; r =(L-D)/2.
ici c ' '
The same for European Jackdaw:
L = 2r+2r ; r=2L/3; r =L/6.
i ci ' c
L = 2r+3r ; r=L/4; r =L6.
i ci c
L = r+3r ; r = (3D-2L)/2; r =L-D.
i ci' ' ' c
For Eurasian Jay:
L = 2r+2r; r=L-D; r=(2D-L)/2). L = r+4r ; r=L/4; r =3L/16; L=2r+r ; r. = D/2; r
ici ' c ici ' c
= L-D.
Polynomial equation for egg shape of Hooded Crow:
y(x) = 0,71±0,004(1+0,133±0,006x-0,027±0,004x2+0 ,103±0,003x3)Z.
The same for European Jackdaw:
y(x) = 0,72±0,004 (1+0,099±0,006x-0,045±0,004x2
+0,103±0,098x3)Z.
For Eurasian Jay:
y(x) = 0,74±0,003(l+0,222±0,025x+0,097±0,004x2-
0,037±0,003x3)Z.
All the parameters were significantly different in the
cluster 'Rook - Magpie'.
Formula of composite ovoid for the Rook:
L=2r+2r; r=2L/3; r =L/6; L=2r+3r; r=L/4;
i c i ' c i c i
r =L6; L=r+4r; r=L/4; r =3L/8.
c i c i ' c
For Eurasian Magpie:
L=2r+2r; r=L-D; r =(2D-L)/2; L=2r+2r; r=(2D-
i c i I c i y
L)/2; r =L-D; L=2r+3r; r=L/4; r =L/6; L=r+2r; r.
' c i c i ' c i c i
= D/2; r =L/6; L=r+2r; r = D/2; r =L/6; L=r+4r;
c i c i ' c i c
r=L-D; rc = (2D-L)/2.
Polynomial equation for the Rook:
y(x) = 0,72±0,004 (l+0,099±0,006x-0,045±0,004x2
+0,103±0,098x3)Z.
For Eurasian Magpie:
y(x) = 0,74±0,003(1+0,222±0,025x+0,097±0,004x2-0,037±0,003x3)Z.
CONCLUSIONS
We suggested that each of the corvid species has typical egg shape with a set of parameters that are overlapped at some extent. Moreover, the average values of such parameters have significant differences. This contributes to the species specificity of egg shapes. We also determined that some egg shapes
occur most frequently from the whole set making the basis of species oological fund. Less distributed egg shapes are the deviations from the norm on one hand and sort of variation surplus as a potential material for natural selection on other hand.
Our data testified that the use of an integrated approach for eggs description, which includes names, geometric diagrams, standards, and quantitative characteristics presents a significant opportunity for entirely new research. This could allow to diagnose the egg shapes, to carry out a variety of comparisons towards literary data and associate each egg shape with relevant biological information.
REFERENCES
Alabi O.J., Ng'ambi J.W., Norris D., 2012. Effect of egg weight on physical egg parameters and hatchability of indigenous Venda Chickens // Asian Journal of Animal and Veterinary Advances. Vol. 7. P. 166-172. Andersen M.J., Nyari A.S., Mason I., Joseph L., Dumbach-er J.P., Filardi C.E., Moyle R.G., 2014. Molecular sys-tematics of the world's most polytypic bird: the Pachy-cephala pectoralis/melanura (Aves: Pachycephalidae) species complex // Zoological Journal of the Linnean Society. Special Issue: Birds: systematics and phylog-eny. Vol. 170 (3). P. 566-588. Barta Z., Szekely T., 1997.The optimal shape of avian eggs //
Functional Ecology. Vol. 11(5). P. 656-662. Deeming D.C., Ruta M., 2014a. Egg shape changes at the theropod-bird transition, and a morphometric study of amniote eggs //Roal Society Open Science. Vol. 1. 140311
Demming D.C., Ruta M., 2014b. Amniote egg morphology and the evolution of avian eggs // Royal Society Open Science. Vol. 1. #140311. Frantsevich L.I., 2015. Planimetria of bird egg shape. Retrieved from: http://www.biometrica.tomsk.ru/planirus. htm [in Russian].
Gamauf A., Haring E., 2004. Molecular phylogeny and biogeography of Honey-buzzards (genera Pernis and Henicopernis) // Journal of Zoological Systematics and Evolutionary Research. Vol. 42. P. 145-153.
Hoyt D.F., 1968. Practical methods of estimating volume and fresh weight of bird eggs // The Auk. Vol. 96. P. 73-77.
Livezey B.C., Zusi R.L., 2007. Higher-order phylogeny of modern birds (Theropoda, Aves: Neornithes) based on comparative anatomy. II. Analysis and discussion // Zoological Journal of The Linnean Society. Vol. 149 (1). P. 1-95.
Mityay I.S., 2003. New approach of integrated estimation of egg shape // Branta. Vol. 6. P. 179-192 [in Russian].
Mityay I.S., 2008. Use of current technologies in research of bird eggs // Bulletin of Zaporozhye National University. Biological Sciences. Vol. 1. P. 191-200 [in Russian].
Preston F.W., 1968. The shape of bird eggs: mathematical aspects // The Auk. Vol. 85. P. 454-463.
Richter S., Wirkner Ch.S., 2014. A research program for Evolutionary Morphology // Journal of Zoological Systemat-ics and Evolutionary Research. Vol. 52(4). P. 338-350.
Troscianko J., 2014. A simple tool for calculating egg shape, volume and surface area from digital images // Ibis. Vol. 156(4). P. 874-878.
Wang N., Kimball, R.T., Braun, E.L., Liang, B., Zhang, Z., 2013. Assessing phylogenetic relationships among Galliformes: a multigene phylogeny with expanded taxon sampling in Phasianidae // PLoS ONE. Vol. 8(5). e64312.
Welch A.J., Olson, S.L. Fleischer R.C., 2014. Phylogenetic relationships of the extinct St Helena petrel, Pterodro-ma rupinarum Olson, 1975 (Procellariiformes: Procel-lariidae), based on ancient DNA // Zoological Journal of the Linnean Society. Special Issue: Birds: systematics and phylogeny. Vol. 170(3). P. 494-505.
Zelenitsky D.K., Therrien F., Ridgely R.C., McGee A.R., Witmer L.M., 2011. Evolution of olfaction in non-avian theropod dinosaurs and birds // Proceedings of the Royal Society. Biological Sciences. Vol. 278. P. 3625-3634.
