Fieldwork was carried out in central Argentina (Córdoba province), in an ecoregion originally characterized by a dry woodland forest (the Espinal ecoregion corresponding to the NT0801 world ecoregion according to Olson et al. [22]). The original vegetation has been cleared for agriculture to a large extent. Samples were collected in two localities from central Argentina (Córdoba province), 20 km apart: Marull (31° 40’ S, 62° 49’ W) and Miramar (32° 55’ S, 62° 40’ W). We consider that samples belong to a single population taking into account the short distance between sites and also that previous work found evidence of a lack of genetic structure and of homogeneity in allelic frequencies between these two sites [20].

Nests were examined during the last week of November and the first week of December, 2000. Nests were located in eucalyptus tree rows along fences, over 15 m above ground level. We reached the nests during the night using a cherry picker truck. Parakeets were trapped from the nests at night using a specially designed funnel net placed below each nest entrance [23]. During night time parakeets do not leave the nest even if under moderate disturbance, whereas during day time they disperse well before observers can even approach the nest.

Nestlings were removed by hand from the nest after capturing the adults. All individuals were kept in specially designed boxes during the remaining of the night to avoid stress and predation if released. Early in the following morning nestlings were relocated to their nest chambers, and the remaining individuals (able to fly) were released in the proximity of their nests.

We were unable to capture all adult individuals in nests, because some escaped when we were approaching the nests. However, we are certain that all of the trapped individuals were roosting in the chambers where they were captured as we did not find openings between chambers that could allow adults to move at the moment of trapping. No information is available on the social status of the trapped adults besides their chamber location.

A total of 28 nests were sampled (Miramar = 19, Marull = 9): 21 nests had a single chamber, six nests had two chambers, and one nest had four chambers. A total of 195 individuals were genotyped (154 nestlings, and 41 adults, including 21 candidate fathers, 20 candidate mothers). The following six measurements were taken from each individual: weight (in g), wing length (from the bend of the wing to the tip of the longest primary feathers), tarsus length (from the inner bend of the tibiotarsal articulation to the base of the toes), tail length (from the base of the tail to the tip of the longest feathers), and bill length and width (all in mm). Measurements were taken by the same person using calipers and rulers.

For testing heritability of morphological traits, we took into account the average mass at fledging in this species estimated to be between 88.7 and 105.5 g [24]. Accordingly, we decided to include all individuals whose weight was over 82 g, considering that this value corresponds to the minimum weight found in an adult in our sample, which is close to the cut-off value of 88 g estimated by Navarro and Bucher [24].

Pearson correlation test, in the Hmisc package in R [25, 26], was used to estimate the relationships between the traits in nestling data set. Adult sexual differences in the traits were evaluated using ANOVA and MANOVA for univariate and multivariate analyses, respectively. Assortative mating was analyzed by means of Pearson correlation test between trait values from males and females.

Analyses of animal models included 133 individuals with genetic pedigree information (122 both full-siblings and half sibling nestlings and 11 adults) and 86 founders (i.e., the individuals for which both the father and the mother are unknown) (see S1 Table for pedigree information); the remaining individuals sampled were not considered. Thus, the main contribution to heritability estimates appears to be based on between-nestlings relationships instead of parent-offspring relationships.

As described in detail previously [20], we assigned relationship among individuals using seven microsatellite loci. Briefly, genomic DNA was extracted from blood samples and analyzed as in Martínez et al. [20]. Seven microsatellite loci were used for relatedness and parentage analyses: AgGT19, AgGT29, AgGT90 [27], MmGT046, MmGT054, MmGT057 and MmGT060 [28]. The combined exclusion probability with one-parent known was 0.985, while the combined probability of excluding two putative parents was 0.999. The sex of adults was determined molecularly as indicated in Griffiths et al. [29] using the specific markers P2 and P8 for ZW sexual chromosomes.

We estimated genetic relationships between individuals to reconstruct more accurately the population genetic pedigree (see S1 Table for pedigree information). Values of genetic relatedness among individuals were taken from Martínez et al. [20]. Presence of null alleles was investigated in the whole data set using the software Micro-Checker v2.2.3 [30]. The ML-Relate program [31] was used to adjust allelic frequencies for null alleles. Allelic richness, observed and expected heterozygosity, and tests for deviation from Hardy-Weinberg equilibrium and linkage disequilibrium were calculated with Arlequin 3.5 [32].

Full-sibs, and paternity and maternity of nestlings were identified by using the maximum likelihood method implemented in Colony 2.0.1.1 [33]. We used the full likelihood method option, the long option for the length of run and the allelic frequencies adjusted for null alleles. Longer runs (10 replicates) are more likely to find the maximum likelihood configuration. Finally, the possibility of parentage and sibship was excluded from the alternative locality. The probability threshold to assign parentage was 0.99. For further details, see Martínez et al. [20] as we estimated quantitative genetic parameters in the same individuals from that study.

The narrow-sense heritability (h²) of a trait is the proportion of its total phenotypic variance that is determined by additive genetic variance, and that is available for selection to act upon [12]. Contributions of genetic and environmental effects on morphological traits were estimated using animal model analyses as implemented in MCMCglmm package in R [26, 34]. For univariate models, the posterior distribution was sampled every 100 iterations with a burn-in 100,000 for a total of 9,000 samples. For both G (random effects) and R (residuals) priors, we specified V = (trait’s variance*0.05) and nu = 1. The bivariate models were performed in nestling data set and sampled every 1,000 iterations with a burn-in of 400,000 for a total of 3,600 samples. For bivariate models, we used V = diag(2) and nu = 1.002 for G and R priors.

Variance parameters were estimated as the posterior mode with 95% credible intervals (CI) based on the posterior distribution of the parameter. At each MCMC iteration, all variance ratios and correlations were estimated based on variance-covariance components, thus providing a posterior distribution. The posterior distribution of heritability (h²) is equal to the ratio of V_A (additive genetic variance) to V_P (phenotypic variance). Additionally, using a bivariate form of the model, we calculated the genetic correlation (r_G) between each pair of morphological traits from their genetic variance (V_x or V_y) and covariance (Cov_xy): r_G = Cov_xy / (V_x V_y)^1/2.

As variance parameters are bounded above zero, we estimated the importance of random effects by looking at the deviance information criteria (DIC) [35]. The DIC is analogous to the Bayesian version of Akaike information criterion (AIC). We used a delta DIC value under seven [36] to identify potentially important random effects.

Summary statistics for the six morphological traits taken on our sample (parents and nestlings) are shown in Table 1. We found high levels of trait correlation between tail length and wing length (r = 0.71) and between wing length and bill length (r = 0.69). Length and width of the bill were moderately correlated (r = 0.32). Also, moderate correlations were found between tail length and bill length (r = 0.32), between bill width and wing length (r = 0.33) and bill width and tail length (r = 0.27; Table 2). Low but still significant phenotypic correlation was found between weight and wing length (r = 0.23) and between weight and bill width (r = 0.20).

There was significant assortative mating in two of six traits: weight and bill length have high and significant positive correlation in both parents (N = 6 pairs) (r = 0.933; p = 0.0065 and r = 0.887; p = 0.018, respectively). The ANOVA for univariate traits (p ranged from 0.055 to 0.728) and MANOVA (Wilk’s lambda = 0.745; df1 = 6; df2 = 19; p = 0.407) indicated no sexual differences in the values of the different traits measured in adults.

In the six morphological traits, all animal models that included additive genetic and maternal effects fell within a delta DIC of seven (Table 3) being equally plausible as the best model. We found nonzero heritability in all the morphological traits (from 0.023 to 0.314; Fig 1, S2 Table). The heritability of weight equaled h² = 0.314 (95% CI = 0.005–0.679), for the tarsus length the heritability equaled h² = 0.122 (95% CI = 0.004–0.390) and for bill width the heritability equaled h² = 0.127 (95% CI = 0.003–0.426). Maternal effects were particularly high in the following traits: wing length (m_e² = 0.800, 95% CI = 0.701–0.891), bill length (m_e² = 0.77, 95% CI = 0.659–0.869) and tail length (m_e² = 0.899, 95% CI = 0.843–0.946; Fig 1, S2 Table).

Bivariate animal models of nestlings that included only additive genetic variance were by far the best models according to DIC values, although some exceptions occurred (Table 4). We found significant genetic correlations between wing length and bill length, wing length and bill width and wing length and tail length. Also, genetic associations were positive between bill length and bill width, bill length and tail length and bill width and tail length. We found only one significant nest correlation between wing length and tail length (Table 4).

Common environmental effects can have an important contribution to the estimation of heritability, especially in a communal breeding bird as the monk parakeet. Sharing a common place, like the colonial nest in this parakeet, did not have an effect on the estimation of heritability of morphological traits. Nest effects were negligible in the univarite animal models since those that included the nest as a random effect presented higher DIC values than models that did not include this effect.

Contrary, we found evidence of maternal effects on morphological traits, being highest in the traits with lower heritability: wing length, bill length and tail length. Price [21] proposed that probably the maternal effects on structural size traits diminish throughout the development and are no longer detectable when the adult size is reached. Nevertheless, there appears to be mounting evidence for enduring maternal effects on some size traits in Darwin’s finches [18].

Maternal effects can have long-term consequences on individuals at evolutionary and ecological time-scales [38, 39]. Multigenerational studies on house finches [40, 41] have highlighted how phenotypic plasticity in maternal effects can have ecological consequences by enabling the colonization of new environments; morphological traits that evolved most rapidly are those that have the greatest maternal and environmental effects [41]. Although we did not evaluate the phenotypic change across generations, we suggest that maternal effects may play a key role on the magnitude and trajectory of the morphological traits in monk parakeets.

Positive phenotypic correlations were high for wing length-tail length (r = 0.71) and wing length-bill length (r = 0.71), and from moderate to low but significant in most of the remaining traits. Those high correlations would indicate strong evolutionary constraints among morphological traits, particularly with those related to flight requirements. It is important to highlight that phenotypic correlations are not always good indicators of genetic correlations because Vpe (permanent environment variance), which is a very special case of common environment effect, and maternal effects may obscure such a correlation [42].

However, we also found high genetic correlations between two groups of traits whose phenotypic correlations were from moderate to high, and significant: a) among wing length and bill length, bill width and tail length and b) among the last three traits together. Of the eight comparisons with significant phenotypic correlation in our sample, six presented positive and significant genetic correlations, implying that the observed correlations are due, in part, to additive genetic variance.

Our results are in line with Teplisky et al. [9], who found that genetic correlations among four traits (weight, wing length, tarsus length and bill length) in multigenerational data sets of seven bird species averaged 0.35 (ranging from 0 to 0.76), indicating that genetic correlations can impose significant constraints on the evolution of avian morphology.

The morphological traits assessed in monk parakeet are, in general, to be moderately constrained in terms of evolutionary potential due to the significant values of genetic correlations, except for weight and wing length, and weight and bill width.

Our results also suggest the occurrence of assortative mating for weight and bill length, as heavier males tend to mate with heavier females, and males with larger bills tend to mate with females with larger bills. Assortative mating in body condition was evidenced in the Neotropical burrowing parrot Cyanoliseus patagonus [43]. However, as pointed out by these authors, a possible explanation for the observed correlation could be that burrowing parrots form long-lasting pair-bonds from an early age. However, all the traits measured in the monk parakeet (this study) show a significant heritability value and therefore could be the focus of mate choice and sexual selection. Therefore, active mate choice or male-male competition by monk parakeets might not be discarded.