Introduction

Body size is a crucial parameter determining the ecological and evolutionary attributes of animals1,2. Its phenotypic variation may be caused by both genetic and environmental components3. As a result, body size contributes to the fitness and varies substantially among individuals, populations, and species4,5,6. The final body size is not just a static trait, but is a product of an ontogenetic trajectory typically involving the growth process.

Growth trajectories are perfectly understood in fast-growing avian species7. A collection of datasets covering the entire period of growth is sometimes extremely laborious and time-consuming, especially in case of species with slow ontogenetic trajectories and/or indeterminate growers (but see in squamates reptiles8,9,10,11,12,13,14 and in fishes15,16,17,18,19). This subsequently simplifies the description of body growth as a function of growth increments (typically used in agri- and aqua-culture).

The growth trajectories typically consist of two major components contributing to the final body size. In a typical case, these are an intrinsic growth rate and a duration of exponential growth period. The latter one is not estimated as a separate parameter by some widely-used theoretical growth models (e.g. von Bertalanffy, West production model), which are applicable even when the data points do not cover the whole course of ontogeny20,21. The logistic growth model fits the empirical data concerning a detailed description of growth trajectories and produces the required information about the duration of exponential growth period further referred to as an inflexion point. The estimates from this model are the growth rate, inflexion point, and asymptotic body size22. Both the growth rate and the growth duration may contribute to the final body size and are inherently inter-correlated.

Besides the growth trajectories and their components (parameters), life-history variables comprise of the body size, maturation, longevity, mortality rates, reproductive investments, etc. In many animal taxa, these variables are tightly inter-correlated and arranged along a common gradient, typically forming an axis from slow to fast life-histories23,24. Thus, the composite measure of life-histories from a multivariate data set is used to classify the position across the current concept of the “fast-slow” continuum (e.g.,24,25,26,27). Even in the absence of complex data, it is possible to estimate an approximate position of individual species/populations on this axis according to a limited number of reliable life-history variables. In this respect, growth rates and/or duration of exponential growth may be, under some circumstances, helpful.

In our study, we monitored three closely related species of eyelid geckos of the genus Eublepharis. During the last century, leopard gecko (Eublepharis macularius, Blyth, 1854) became a laboratory animal as well as a captive bred pet. It is routinely used as a model species for studies of incubation temperature and its hormonal consequences influencing brain development28,29,30,31, antipredatory strategies, etc.32,33. Eublepharid geckos (Eublepharidae) vary considerably in body size – the largest species E. angramainyu (Anderson and Leviton, 1966) is more than 20 times heavier than the smallest Coleonyx brevis (Stejneger, 1893). Thus, the family was repeatedly used as a model for studies dealing with the evolution of body size34, parental investment35,36, growth37, allometries of cell size, DNA content, and metabolism38,39,40.

Growth rates and trajectories may properly reflect the animal’s life-history strategy only if these parameters were solely determined by the underlying trade-offs and the corresponding strategic decisions concerning an investment. Growth may be constrained by fitness (performance, health status) of the animal. In this respect, the efficiency of growth can be useful during the monitoring of the processes that are suspected to cause deleterious effects.

We compared the growth parameters to explore the effect of experimental crossing of the species/populations of the eublepharid geckos. The view on the real size of the effect of hybridization on fitness is still controversial. Both negative and positive outcomes were associated with hybridization in natural and experimental conditions41,42,43; for reviews, see44,45,46,47. Historically, natural hybridization was considered as exceptional and erroneous events48, but the current increase of literature concerning the importance of hybridization for both speciation and adaptation implies the opposite44,47,49,50,51. Genomic and epigenetic insights into the molecular bases of heterosis are indicating that the role of natural hybridization is important in the formation of new species. Because of exceptional time demands, experimental studies dealing with hybridization covering the observation of real parameters of fitness (fertility, viability, body growth) are still very scarce43,52,53,54.

The aims of our study were 1) to compare the growth parameters of leopard geckos to demonstrate contrasting life-history strategies of selected parental species/populations; and 2) to compare the growth parameters of parental species with parameters of F1 and F2 hybrids and subsequent backcrosses to reveal the putative beneficial (heterosis in F1 generation of hybrids) and/or deleterious (incompatibilities leading to segregation load in F2 and backcrosses) effects of hybridization on fitness.

Results

The estimated growth parameters for distinct populations/species, their F1 and F2 hybrids, and backcrosses are presented in Table 1. The logistic regression model fits well our longitudinal growth data (Table 1 and Fig. 1).

Table 1 The estimated values (mean ± SE) of the asymptotic body mass a (g), growth rate K and inflexion point T (days), and variance explained by the model (R2) with a number of individuals (N) for the examined species, hybrids, and backcrosses of eublepharid geckos.
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Figure 1
figure 1

Histogram of variance explained (R2) by a logistic regression model for all studied individuals.

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Comparisons among parental species/populations

Growth parameter a significantly differed (Table 1) among distinct species/populations (ANOVA: F3,132 = 88.337, P < 0.001). Moreover, E. angramainyu exhibited significantly lower growth rate K (ANOVA: F3,132 = 16.3791, P < 0.001) and bigger inflexion point T (ANOVA: F3,132 = 37.057, P < 0.001) than all of the other species/populations. The growth parameters revealed from the logistic regression model were inter-correlated. The asymptotic body weight (a) was closely correlated to parameter T (r = 0.64, 0.75 and 0.65 for yellow, white, and dark species/populations, respectively). No such correlation was found between a and K parameters. The whole course of body growth of distinct species/populations is illustrated by Fig. 2.

Figure 2
figure 2

Mean body weight as a function of age predicted by the logistic growth model in studied species of eyelid geckos. Growth parameters were estimated from pooled records of either species/populations. Dotted curves are ± 95 confidence intervals for means of studied species/populations. Abbreviations: (M) yellow population of E. macularius, (W) white population of E. macularius, (A) E. angramainyu, (D) dark population of E. sp.

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Changes in mean absolute and relative body weight increments (computed from real body weighting) during the post-hatching ontogeny are shown in Fig. 3.

Figure 3
figure 3

Absolute body weight increments (aBWI) as a function of age (A) and relative body weight increments (rBWI) as a function of actual body weight for distinct species/populations (B). Abbreviations: (M) yellow population of E. macularius, (W) white population of E. macularius, (A) E. angramainyu, (D) dark population of E. sp.

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Comparison among parental species (E. angramainyu and E. macularius), their F1 and F2 hybrids, and backcrosses

Growth parameters significantly differed among parental species of A and M and their F1 hybrids (ANOVA: a: F(2,81) = 57.725, P < 0.0001; K: F(2,81) = 10.0467, P = 0.000127; T: F(2,81) = 24.9932, P < 0.0001). F2 hybridization was not successful (except for one individuum, which had poor body growth with the lowest prediction of parameter a = 36.546 g) in comparison with the parental population and F1 hybrids. The course of body growth of the parental species and F1 and F2 hybrids is depicted in Fig. 4. The asymptotic body weight significantly differed in both backcrosses (MAxM and MxMA) from the parental species of E. angramainyu and F1 hybrids (ANOVA: F(4,104) = 29,771, P < 0,0001). The estimations of asymptotic body mass were similar for both backcrosses (see Table 1).

Figure 4
figure 4

Mean body weight as a function of age predicted by the logistic growth model in parental species of yellow population of E. macularius (M) and E. angramainyu (A) and their F1 (MxA) and F2 (MAxMA) hybrids. Growth parameters were estimated from the pooled records of either species and the hybrids. Dotted curves are ± 95 confidence intervals for means of studied groups. Note the growth curve of F1 hybrids (N = 27), which is between the parental species’curves and the poor growth of F2 hybrid.

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Comparison among parental species (yellow and white E. macularius and dark E. sp.) and their F1 and F2 hybrids

The growth parameters significantly differed among the parental species of M and D and their F1 hybrids (ANOVA: a: F(3,116) = 31.980, P < 0.0001; K: F(3,116) = 9.8493, P = 0.000008; T: F(3,116) = 5.4302, P = 0.001571). The parental species differed in all growth parameters (all p < 0.01). This difference is in accordance with our prediction of the parental species’ genetic distinction. F1 hybrids differed in parameter a (p = 0.019977 and 0.005097 in comparison with M and D, respectively). Moreover, F1 hybrids also differed in parameter K in comparison with D (p = 0.006029). The inflexion point T was similar in F1 and F2 hybrids in comparison with the parental species. The course of body growth of the parental species and F1 and F2 hybrids is shown in Fig. 5.

Figure 5
figure 5

Mean body weight as a function of age predicted by the logistic growth model for parental species of the yellow population of E. macularius (M), the dark population of E. sp. (D), F1 (MxD) and F2 (MDxMD) hybrids. Growth parameters were estimated from pooled records of either species and the hybrids. Dotted curves are ± 95 confidence intervals for means of studied groups. Note the growth curves of F1 (N = 19) and F2 (N = 11) hybrids which are between the parental species’ curves.

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Hybridization of W with D also revealed distinctiveness of the parental species. Growth parameters of F1 and F2 hybrids were intermediate compared with values among the parental species (see Table 1).

Discussion

Leopard geckos of the genus Eublepharis are long-living animals (maximum lifespan > 25 years, personal observation) laying multiple clutches per season. The clutches are of an invariant size, each consisting of two eggs, which are extraordinarily large compared to the maternal body35,55. This place their life-history strategy close to the “slow” end of the “fast-slow” continuum reported in lizards. Our analyses uncovered strong differences in growth trajectories among the examined species which were clearly associated with the asymptotic body weight. This suggests that the examined species/populations still significantly differ in their position along the fast-slow axis.

A three-parameter logistic regression model fits our long-term data covering the course of ontogeny from hatching to adulthood very well. Parental species/populations (A, M, W and D) differed significantly in the estimated asymptotic body weights and growth rates (except the growth rate and inflexion point, which were similar for two closely related populations of the yellow and white form of E. macularius).

We found that the growth parameters estimated by the logistic regression model were inter-correlated. Asymptotic body weight is tightly predicted by parameter T. Given the mutual relationship of growth parameters, we decided to compute separately the growth rate expressed as absolute and relative body weight increments. This approach allowed us to compare real increments of studied species/populations across the ontogeny (Fig. 3) and revealed similar results as those deduced from the estimates of parameter K. The growth rate was counterintuitively the lowest in large E. angramainyu (A) and highest in small E. sp. (D). The final body size was determined by the inflexion point parameter (T). The inflexion point reflects that the duration of the exponential growth period increases with mean asymptotic body size and thus easily overcompensates the effect of decreasing growth rates in the larger-bodied species.

A general life-history relationship described as the Rosa Lee phenomenon56,57 may provide an explanation for the decrease in the growth rate parameter (K) with asymptotic body size (a) found in our data set. Lee’s studies concerning age and growth determination in fishes demonstrated that individuals in a population with slower growth rates suffer less from mortality when they are young, which points to the existence of a trade-off between the growth rate and survival. This phenomenon was traditionally examined in fishes58,59,60,61 and only exceptionally applied to other vertebrates62,63,64,65. If further proved in geckos, large-bodied species might be selected to avoid mortality risk by reducing the growth rates. A preliminary inspection of our unpublished data sets suggests that within each species/population, the fast-growing individuals of the leopard gecko tend to suffer equal or even lower rates of juvenile mortality. However, the mortality pattern under laboratory conditions substantially differs from that under natural conditions. Thus, we have to search for alternative explanations for the reported reduced growth rates in larger geckos. Metabolic rates may be slightly constrained, e.g., by a positive allometric relationship between erythrocyte size and body size, which has been demonstrated in lizards including the eublepharid geckos38,66. Body growth of the whole organism, as well as the growth of particular organs and body segments, is orchestrated by hormones, growth factors and cell-cycle regulations67. These represent fundamental proximate mechanisms controlling growth rate and final body size. Beside growth hormones, there are sexual steroids, which are reported either to stimulate or to inhibit body growth. This was demonstrated especially in sexually dimorphic species68,69,70,71,72,73. Recent studies revealed that the deceleration of body growth is caused by the suppression of cell proliferation and is driven primarily by local rather than systemic mechanisms67.

Clear differences detected among the examined species/populations can be interpreted in terms of the “fast – slow” continuum of life-history strategies. E. angramainyu is a large-bodied species with a slow growth rate. This species attained the body weight close to asymptotic values at the age of about three years, but the first copulation was recorded at the age of five years. On the contrary, E. macularius is smaller, grows more slowly, and matures earlier (1–2 years). The sexual maturation is not known from the nature, but it is reasonable to suppose that it takes more time due to seasonality. However, the clutch size is invariant in eublepharid geckos and the relationship between body size and egg size is isometric35.

A similar analysis of the growth parameters is ideal for the comparison of parental and descendant individuals in the experimental crossing of the species/populations. It may also contribute to our knowledge of the influence the hybridization has on fitness, viability and competitiveness of F1 and F2 hybrids and backcrosses. Both positive and negative effects of hybridization are discussed in current literature52,74,75,76,77. A heterosis effect accompanying hybridization is traditionally used in agriculture and aquaculture because of an increased vigour (e.g., larger body size, faster growth rate, higher reproductive output, enhanced tolerance to environmental conditions). Similar experiments dealing with the effect of hybridization on body growth in squamate reptiles are completely missing. A pioneering study of hybridization among species of the genus Lacerta54 provided the first insight into the issue concerning hybridization in reptiles. Rykena reported intriguing data concerning hatchability, survival, fertility, and physical deformities of F1 and F2 hybrids and backcrosses54. The lacertids have genetic sex determination (GSD)78 and conclusions concerning the hybridization of GSD species may differ from those with temperature sex determination (TSD). Species with TSD are more abundant and are considered to be ancestral within the squamate reptiles79. However, information about the patterns of hybridization in TSD species is completely missing47.

Our study is a continuation of a long-term project dedicated to experimental hybridization of eyelid geckos. E. macularius belongs among the species with TSD80. Although sex determination of the E. angramainyu has never been experimentally tested, we expect it to be TSD as well, similarly like the closely related Hemitheconyx caudicinctus79. Moreover, the analysis of the karyotype in eyelid geckos revealed the absence of sex chromosomes81, which implies that the genome is the same in both sexes.

Preliminary results concerning the fitness indicators of F1 and F2 hybrids and backcrosses were published by Jančúchová-Lásková and her colleagues43. It was demonstrated that M is able to hybridize with congeneric A and produces viable and fertile hybrids without apparent malformations. Moreover, the introgression of the E. angramainyu genes into the E. macularius genome is possible via backcrossing. To examine the real competitiveness of hybrids and backcrosses with parental species and consequent advantages of hybridization, the observation of growth parameters is crucial. Hybridization produces novel genotypes that may be able to outperform their parental species and persist in unoccupied niches if necessary. The individual fitness and the extent to which hybrids interact with their parents (e.g., assortative mating or differential habitat use) is essential for evolutionary consequences of hybridization.

Our results of growth parameters revealed that F1 hybrids are an intermediate form between the parental species (Fig. 4). The body growth of only one F2 hybrid was very poor with asymptotic body size smaller than the parental yellow population of E. macularius (M). Poor fitness of this F2 hybrid is in congruence with the whole poor hatchability (6%) and viability (25%) of F2 hybrids demonstrated previously43. The growth parameters unequivocally corroborated that the putative fitness losses affect more hybrids of F2 generation, which is in accordance with the general Dobzhansky-Muller incompatibilities82,83,84,85 and empirical evidence86. MAxM and MxMA backcrosses had better hatchability and survival rate than F2 hybrids. The egg hatchability also dramatically differed between MAxA backcross and MAxM and MxMA backcrosses. While the latter one was possible to incubate (for details, see43), the hatchability of the opposite backcrosses (MAxA) was zero, even though the females laid eggs regularly. This fact again points to some genetic incompatibilities.

Concerning the growth parameters, backcross MAxM did not differ in the asymptotic body size and growth rate from the MxMA backcross. The only difference was in the timing of the deceleration of the body growth. These backcrosses attained larger body size than the parental yellow population of E. macularius. In this case, the effect of hybridization on body growth was positive. It is expected that the advantages of hybridization for backcrosses exert in an increased heterozygosity, avoidance of the inbreeding depression and more successful occupation of new habitats87.

Parental species of the yellow population of E. macularius and dark E. sp. differed in all of the growth parameters (all p < 0.01). Such a difference is in accordance with our prediction of genetic distinctiveness of these parental species. Hybridization of these two species reveals a similar effect on F1 hybrids. The growth parameters a and T were intermediate, but the growth rate was close to the smaller E. sp. in F1 hybrids. The success rate of gaining F2 hybrids was better than in the hybridization of M with A. The growth parameters of F2 hybrids were close to the F1 hybrids. The distribution of E. macularius and E. sp. is most probably allopatric, but the sequence divergence is not as striking as in M vs. A. The growth parameters of backcrosses (MxMD) were not monitored; nevertheless, the egg hatchability was high (92%, Landová et al., in prep.)

The crossing of the white population of E. macularius (W) with dark E. sp. revealed intermediate values of growth parameters in F1 and F2 hybrids in comparison with the parental species. It was not possible to test exactly the differences among the F1 and F2 hybrids due to the low number of hybrids, but the mean values of estimated growth parameters were comparable. Substantial differences in the results of hybridization of M/W with D were probably caused by the body size of the parental species (i.e., the body size of W is very similar to D).

In conclusion, we demonstrated that the growth parameters revealed by the three-parameter logistic regression model described the pattern of body growth of the studied species/populations of leopard geckos well. The pattern of body growth supports the “fast-slow” life-history continuum with species growing slowly but attaining large asymptotic body size and vice versa. Based on estimated growth parameters, it is possible to distinguish among these species/populations. We used this approach to study the effect of hybridization on fitness. We enriched our knowledge concerning the ability to hybridize in distinct species of the genus Eublepharis, which was previously observed in long-term geographic and evolutionary separated species of E. macularius and E. angramainyu by the additional experimental crossing of E. macularius with E. sp. The current approach tested competitiveness of F1 and F2 hybrids and backcrosses by comparison of their body growth parameters. Our results revealed that growth parameters are intermediate in both F1 hybrids. The poor fitness of F2 hybrid (MAxMA) is corroborating the outbreeding depression usually observed in F2 and other segregating generations of between-species hybrids. However, the introgression of A genes into M genome is enabled via backcrossing. This fact employs natural hybridization into the concept of species adaptation and speciation. A similar pattern concerning the occurrence of fertile hybrids of distinct species may be also expected in other taxa of Squamata.

Methods

Experimental animals and their maintenance

In the breeding stock of parental species, there were 51 E. macularius individuals of the yellow population (M), 40 E. macularius individuals of the white population (W), 6 individuals of large-bodied E. angramainyu (A), and 39 individuals of E. sp., which we further refer to as a dark population (D). Authors of the previous studies examining D geckos of the same stock considered the description of E. fuscus (Börner, 1981), and referred to this taxon, which is closely related to E. macularius sensu stricto, as E. cf. fuscus38,39,88.

The distribution of E. macularius covers large territories of Afghanistan, Pakistan and India89, althought a detailed distribution of the white and yellow form is not available. The B, W, and D populations were imported directly from unknown localities in Pakistan. E. angramainyu is native to Mesopotamia and SW Iran90. M and A are allopatric, their territories are separated by the Iranian Plateau and Zagros Mountains that are at least several million years old89. Thus, there was a long-lasting geographical isolation between E. macularius complex and E. angramainyu (cf. great sequence divergences between mitochondrial genes; uncorrected p-distances for 303 bp fragment of cyt b gene exceed 19%; Palupčíková, unpublished data).

All experimental parental species (M, W, D, and A) were the first generation of descendants of wild-caught animals. Parental A individuals were wild-caught as well, a putative locality of origin is Choqa Zanbil, Khuzestan province, Iran, 32“00’N 48'31’E, for more details about the locality see91.

The adult animals were housed individually in glass terrariums (60 × 30 × 20 cm or 30 × 30 × 20 cm, according to their body size). The floor of each cage was covered with bark substrate. Feeding and drinking dishes, as well as paper shelters, were provided. During the laying season, containers with adequately humid coconut substrate for egg deposition were added. The geckos were fed crickets and mealworms dusted with vitamins and minerals (Nutri Mix) weekly; AD3 and E vitamins were provided once per 14 days. The ambient temperature in the breeding room was about 28 °C with the permanent presence of basking sites in every terrarium to maintain a temperature gradient. During the egg-laying season (February to September), we checked the egg-deposition containers three times per week. The eggs were placed in the incubator and temperature was set to 28 ± 0.5 °C, which is the optimal and preferred temperature of E. macularius32,92,93. The incubation temperature of E. angramainyu was set lower (26 ± 0.5 °C) according to our previous experience with this species’ incubation. The hatchlings were housed individually in plastic boxes (20 × 20 × 15 cm) and were fed exclusively with crickets dusted with vitamins up to the three months of age.

To acquire F1 hybrids, females of the selected parental species/population were allowed to copulate with one breeding male of the second parental species/population. The resulting F1 hybrids were reared to sexual maturity and further bred to obtain F2 hybrids and/or backcrosses with either of the parental species. As the geckos of the studied genus Eublepharis can store sperm for several months, each experimental female was allowed to copulate exclusively with a single male during a given mating season (lasting from January/February to July/August). In contrast, males could copulate with multiple females within a single breeding season. From this hybridization, we got 68 viable F1 hybrids, 36 F2 hybrids, and 27 backcrosses.

All the individuals were weighed regularly by a digital balance to the nearest 0.01 g initially once per week (up to the age of 5 months), subsequently twice a month and later only once a month.

We studied the following thirteen categories of parental species/populations, their hybrids, and backcrosses that are further referred to as follows (the abbreviations are given in parentheses; there is always an abbreviation for a female followed by the one for a male with a cross (x) between:

  1. 1.

    M - a parental generation of the yellow population of E. macularius, both parents belong to the yellow population of E. macularius (M);

  2. 2.

    W - a parental generation of the white population of E. macularius, both parents belong to the white population of E. macularius (W);

  3. 3.

    A - a parental generation of E. angramainyu, both parents belong to E. angramainyu (A);

  4. 4.

    D – a parental generation of the dark population of the genus Eublepharis, both parents belong to this dark population (D);

  5. 5.

    MxA - the first-generation hybrid (F1), the mother of the yellow population of E. macularius (M) and the father of E. angramainyu (A);

  6. 6.

    MxD – the first-generation hybrid (F1), a mother of the yellow population of E. macularius (M) and a father of the dark population of E. sp. (D) grouped together with the mother of the dark population of E. sp. (D) and the father of the yellow population of E. macularius (M), we did not examine the mother’s identity effect;

  7. 7.

    WxD – the first-generation hybrid (F1), a mother of the white population of E. macularius (W) and a father of the dark population of E. sp. (D);

  8. 8.

    MxW – the first-generation hybrid (F1), a mother of the yellow population of E. macularius (M) and a father of the white population of E. macularius (W) grouped together with a mother of the white population of E. macularius (W) and a father of the yellow population of E. macularius (M), we did not examine the mother’s identity effect;

  9. 9.

    MAxMA - the second-generation hybrid (F2), both parents are F1 hybrids of the yellow population of E. macularius and E. angramainyu (MxA);

  10. 10.

    MDxMD – the second-generation hybrid (F2), both parents are F1 hybrids of the yellow population of E. macularius and the dark population of E. sp. (MxD);

  11. 11.

    WDxWD – the second-generation hybrid (F2), both parents are F1 hybrids of the white population of E. macularius and the dark population of E. sp. (WxD);

  12. 12.

    MAxM – the first-generation backcross with the yellow population of E. macularius, a mother is an F1 hybrid (MA) and a father belongs to the yellow population of E. macularius (M);

  13. 13.

    MxMA – the first-generation backcross with the yellow population of E. macularius (reciprocal to 12), a mother belongs to the yellow population of E. macularius (M) and a father is an F1 hybrid (MA)

Experiments were performed in accordance with the Czech law implementing all corresponding European Union regulations and were allowed by institutional Animal Care and Use Committee of the Charles University in Prague, and approved by Ethical Committee of Ministry of Education, Youth and Sports of the Czech Republic license no. 18147/203 and 24773/2008–10001.

Statistical methods

We applied a three-parameter logistic regression model (Equation 1) to analyse the growth trajectories of the overall sample of a given species, hybrids, backcrosses. We have previously found that this model22 fits very well the data covering the body growth of reptiles from hatching to adulthood9. We used the Levenberg-Marquardt algorithm (with 1000 maximum number of iterations), which minimized the sum of squares between the predicted and observed growth values.

$${\rm{Body}}\,{\rm{weight}}\,[{\rm{grams}}]={\rm{a}}/(1+{{\rm{e}}}^{-{\rm{K}}({\rm{age}}-{\rm{T}})})$$
(1)

Growth parameter a predicts the asymptotic body size, parameter K estimates the growth rate, and the last one, parameter T, expresses the age at the inflexion point (i.e., a place of the maximal growth rate where the growth curve changes from convex to concave and the individual growth rate starts decreasing). We set these parameters’ starting values as follows: a = 30, K = 0.005 and T = 150. Growth equations were computed separately for each individual. As the number of females (290) highly exceeded the number of males (35) and the intersexual differences were much smaller than the interspecific ones, we pooled the data of both sexes in distinct groups for a comparison between species, hybrids, and backcrosses.

Interspecific differences in growth curve parameters were tested by a general linear model (ANOVA, post-hoc Tukey’s test for unequal N). The effect of growth rate and inflexion point on asymptotic body weight was tested by multiple regression separately for each group. All calculations were performed using STATISTICA, version 6.0.

In addition to the comparison of growth parameters revealed by the logistic regression model, we compared body weight increments from real measurements calculated as an absolute body weight increment (aBWI = actual body weight - previous body weight) and a relative body weight increment (rBWI = aBWI/actual body weight).

Data availability

All data generated or analysed during this study are included in this published article (and its Supplementary Information files).