Bayesian Structure Learning Reveals Disconnected Correlation Patterns Between Morphometric Traits and Blood Biomarkers in White Stork Nestlings

Simple Summary

We examined nestling White Storks from eastern Croatia to evaluate how their growth traits (body mass, beak length, tarsus length, body condition index) relate to biomarkers (detoxification enzymes and oxidative stress markers) in blood. Morphometric traits were strongly intercorrelated and also showed selective associations with physiological biomarkers. In particular, body mass, tarsus length, and body condition index were connected to several plasma biomarkers, while S9 biomarkers formed a distinct community. The Bayesian undirected graphical model indicated that morphometric traits were selectively integrated with plasma biomarkers (body mass with reduced glutathione, acetylcholinesterase, carboxylesterase, and tarsus length with proteins), while S9 biomarkers formed a distinct community. This pattern further suggests that residual body condition indices alone are poor predictors of physiological stress, as their explanatory value was weaker than plasma biomarker links. Biomarker responses showed interannual variability when compared with previous years of monitoring, highlighting the influence of fluctuating agricultural practices and environmental conditions. These results demonstrate that combining morphometry with biochemical assays provides a more complete picture of nestling condition and environmental stress than either approach alone. This integrated framework strengthens the value of white storks as sentinels for ecological change in the environment.

Abstract

Environmental stressors, particularly agricultural pesticides, can influence both growth and physiology in developing birds, yet the relationship between morphometric condition indices and biochemical biomarkers remains poorly understood. We investigated body mass, beak length, tarsus length, and body condition index (BCI) alongside plasma and S9 biomarkers, including the activities of acetylcholinesterase (AChE), carboxylesterase (CES), and glutathione S-transferase (GST), as well as the levels of glutathione (GSH) and reactive oxygen species (ROS) in nestling White Storks (Ciconia ciconia) from Croatia. Bayesian undirected graphical model (BUGM) inferred a disconnected correlation structure composed of two communities, with a strong beak length–GSH association. Biomarkers further exhibited plasma-specific affinity: plasma markers reflected short-term adjustments, whereas S9 enzymes represented distinct metabolic pathways. Overall, morphometry and physiological status showed only limited integration, restricted mainly to plasma biomarkers, and residual body condition index did not serve as a reliable proxy for physiological stress. We conclude that integrated monitoring approaches, combining morphometric and biochemical profiling, provide a more nuanced assessment of nestling condition and strengthen the use of White Storks as sentinels of agroecosystem health.

1. Introduction

Environmental pollutants pose significant threats to avian species, with numerous studies documenting adverse effects across physiological, behavioural, and reproductive domains [1,2]. These impacts are particularly pronounced during ontogenetically sensitive life stages, such as early development, when birds are more vulnerable to toxicant-induced physiological disruption [3]. Nestling birds are widely employed as bioindicators of environmental pollution due to their developmental sensitivity, limited mobility, and capacity to integrate local exposure burdens [4,5,6]. In addition to nestlings, higher trophic-level bird species function as non-target recipients of agrochemical runoff, especially in wetland and agroecosystems where bioaccumulation through diet is prevalent [7]. Avian physiological status, including hormonal profiles and immune function, is closely influenced by dietary inputs, with tissue pollutant [8,9,10] loads reflecting trophic position and exposure pathways. Therefore, nestling physiological and biochemical traits offer a valuable, integrative proxy for assessing localised pollutant pressures and broader ecosystem-level pollutant dynamics [9].

Pollution has been shown to significantly affect avian morphometry. For example, House Sparrows (Passer domesticus) exhibited altered morphometric traits such as body mass, feather length, and beak dimensions in response to tissue concentrations of copper and zinc, suggesting both positive and negative associations depending on metal type [11]. Similarly, Eurasian Tree Sparrows (Passer montanus) from polluted environments showed reduced body size and elevated fluctuating asymmetry in tarsus, wing, and toe measurements, which correlated strongly with tissue levels of lead, cadmium, copper, and zinc [12]. Great Tit (Parus major) nestlings from areas near smelters also demonstrated decreased body mass, delayed fledging, and abnormal leg growth compared to those in cleaner environments, pointing to ontogenetic vulnerability to metal exposure [13]. These findings collectively underscore the utility of morphometric traits, particularly fluctuating symmetry and growth indices, as bioindicators of sub-lethal toxicological stress in birds.

Biomarkers such as the activities of acetylcholinesterase (AChE), carboxylesterase (CES), and glutathione S-transferase (GST), as well as the levels of reduced glutathione (GSH) and reactive oxygen species (ROS), are routinely employed to evaluate pollutant exposure and sublethal physiological stress in avifauna [14,15,16,17,18,19]. These biomarkers can be quantified through venous blood sampling, a minimally invasive technique that offers an ethically preferable alternative to lethal methods such as decapitation or organ excision [20,21,22].

Despite the widespread use of biomarkers like AChE, CES, GST, GSH, and ROS in ecotoxicology [23,24], no studies to date appear to have explicitly tested correlations between these biomarkers and bird morphometric measures (e.g., tarsus, beak length, body mass). This gap persists despite the widespread use of these biomarkers in avian ecotoxicology. However, different endpoints have been studied in White Stork (Ciconia ciconia). Kosicki and Indykiewicz [25] analysed nestling growth dynamics over multiple breeding seasons and showed that short-term weather conditions, rather than breeding parameters, were the main drivers of variation in morphometrics. Tryjanowski et al. [26] investigated brood structure and found that apparent sex differences in body mass were largely explained by age and hatching order, suggesting that ontogenetic stage rather than sex per se accounted for most of the variation. Jerzak et al. [27] focused on blood biochemistry and reported modest sex- and age-related differences in analytes such as proteins, uric acid, and cholesterol, while Kamiński et al. [28] studied haematological indices and demonstrated that sex effects were minor compared with stronger influences of sampling year and hatch date.

The White Stork is a long-standing bioindicator of farmland ecosystems across Europe because of its central-place foraging ecology, accessible nests, and strong reliance on agro-wetland prey during the nestling period. Adults provision nestlings from fields and meadows within a limited radius of the nest; therefore, nestling blood chemistry integrates exposures from the immediate agricultural area. Nestlings are physiologically sensitive to changes in food availability and to agrochemical inputs that modulate cholinesterase activity, detoxification demand, and redox balance [17,18]. The species’ extensive monitoring tradition, spanning morphometry, ringing, and non-lethal blood sampling, enables standardised deployment of biomarker panels across sites and years, and facilitates coupling with simple morphometric indices for scalable biomonitoring. Previous work on White Stork nestlings in our study area has primarily examined spatial and sex-related variation in biomarker responses in relation to agricultural practices and landfill exposure [19]. That study showed how land use can modulate physiological stress markers, but it treated biomarkers largely as independent endpoints and relied on classical area-based contrasts.

Statistical approaches capable of resolving complex, nonlinear dependencies are particularly valuable in this context [29]. Bayesian undirected graphical models (BUGM), recently applied in reptile ecotoxicology, provide a powerful framework to infer structural associations and assess uncertainty in biological networks [29]. This framework moves beyond univariate contrasts to explore how growth and physiological stress responses covary within nestlings, offering novel insight into the integration of oxidative and detoxification processes during development. Applying such network-based approaches to avian biomonitoring offers a novel opportunity to test whether morphological traits and physiological biomarkers form communities, thereby advancing our understanding of how environmental stressors shape development.

We hypothesised that morphometric traits and biochemical biomarkers do not form a single integrated system in nestling White Storks but instead show selective cross-links. We had three main study hypotheses. Firstly, we hypothesised that body condition index will show limited association with physiological biomarkers because growth-based indices reflect longer-term developmental reserves, whereas biomarkers capture short-term biochemical state [30,31,32,33,34,35,36]. Secondly, we hypothesized that growth-related traits will show trait-specific links to oxidative status; in particular, beak length should be positively associated with ROS and/or GSH, as rapid keratin/tissue accretion elevates metabolic demand and redox turnover [37,38,39,40,41,42]. And lastly, we hypothesized that within the biomarker set, fraction-level structure will dominate: biomarkers will group by fraction, plasma (systemic) versus blood cell S9 (intracellular), rather than with morphometry, reflecting distinct physiological domains [16,40,43].

To evaluate these predictions, we (I) analysed biomarker response in plasma and S9 blood cell homogenate alongside morphometric traits; (II) tested pairwise conditional (in)dependence among biomarkers and morphometric traits using Hoeffding’s D correlation coefficients; and (III) inferred the conditional partial correlation network structure among biomarkers and morphometric traits using a BUGM to evaluate whether key functional traits such as body condition (residual body condition index) are linked to nestlings’ responses to environmental pollution exposure. This approach enables the determination of whether morphometry and biomarkers are interchangeable or complementary indicators for biomonitoring, and how developmental variation modulates biomarker responses in an ecotoxicological context.

2. Materials and Methods

2.1. Sampling Procedure and Blood Processing

The study was conducted with authorisation from the Ministry of Environment and Energy of the Republic of Croatia (Permit: UP/I-352-04/25-08/85; Ref. No: 517-06-1-2-25-2). Sampling was conducted during the 2025 breeding season in eastern Croatia, near the Danube River (Figure 1). Blood from 20 White Stork nestlings (n = 20 individuals, from 17 nests) aged from 6 to 8 weeks was sampled. Nestlings were selected based on size, with the largest individual sampled from each nest; when two nestlings per nest were included, the two largest were chosen. Age was determined by measuring beak length and applying back-calculation based on known growth rates from nestlings of known age [28,44]. All birds were sampled as nestlings on 23 June 2025 within a single breeding season and area. Sampling procedures were conducted between 08:00 and 12:00 h to limit exposure to heat stress and to minimise interference with the natural feeding schedule. The distance between nests was less than 5 km. Previous studies have shown that when White Stork nests are located within 5 km of each other, parents often forage in overlapping areas [45,46,47]. Therefore, parents from different nests exploit overlapping foraging areas, and nestlings were provisioned from the same feeding sites.

Molecular sex and exact day-age were not determined, as our analyses targeted population-average nestling patterns. However, approximate age was inferred using growth-based criteria following Tryjanowski et al. and Kania [28,44], allowing us to report an age range, while precise day-age estimates were not central to our study objectives. Prior cohorts using the same biomarker panel detected no sex differences [17,19]. Nests were accessed using a truck-mounted telescopic crane. Nestlings were gently extracted from the nest and placed into a cloth bag, which was subsequently lowered to the ground via a rope system. To minimise handling-induced stress, each nestling was positioned in a supine posture with a soft cloth placed over the head to reduce visual stimuli.

For each White Stork nestling, morphometric measurements were recorded, including body mass (BM), beak length (BL), and left tarsus length (TL). The BM was measured using an Etekcity digital scale (± 0.01 kg), while BL and TL were measured with a Walter-brand calliper (± 0.10 mm). The TL is commonly used as a proxy for structural body size, especially in nestlings and juveniles, as it is one of the earliest skeletal elements to ossify and stabilise [48]. The BL, meanwhile, often reflects feeding ecology and ontogenetic stage, and may vary by sex or population in response to ecological pressures [49]. Both traits are widely used in calculating body condition indices (BCIs), such as mass-to-tarsus ratios or size-corrected mass, helping researchers estimate energetic reserves independent of body size [50].

Approximately 4 mL of blood was drawn from the brachial vein using a 0.80 mm needle and sterile 5 mL syringe and transferred into lithium heparinised tubes. Samples were kept at 4 °C in the dark for 6–8 h prior to processing. The blood was centrifuged at 3000× g for 10 min at 4 °C to separate plasma, which was aliquoted into sterile tubes and stored at −80 °C for subsequent biomarker assays. Cell pellets were processed following the protocol described in Bjedov et al. [16]. Briefly, blood cell pellets were resuspended in 5 mL phosphate buffer (0.10 M, pH 7.20), sonicated, and centrifuged at 9000× g for 20 min at 4 °C to isolate the post-mitochondrial supernatant (S9 fraction). S9 aliquots were stored at −80 °C until biomarker quantification. All biomarkers were analysed in both plasma and S9 fractions.

2.2. Chemicals

The following analytical grade chemicals were used: 5,5′-dithiobis-(2-nitrobenzoic acid) (DTNB) ([-SC₆H₃(NO₂)CO₂H]₂, CAS 69-78-3, 396.35 g·mol⁻¹), (2-Mercaptoethyl) trimethylammonium iodide acetate (acetylthiocholine iodide) (CH₃COSCH₂CH₂N(CH₃)₃I, CAS 1866-15-5, 289.18 g·mol⁻¹), acetonitrile (C₂H₃N, CAS 75-05-8, 41.05 g·mol⁻¹), p-nitrophenyl acetate (C₈H₇NO₄, CAS 830-03-5, 181.15 g·mol⁻¹), 1-chloro-2,4-dinitrobenzene (CDNB) (C₆H₃ClN₂O₄, CAS 97-00-7, 202.55 g·mol⁻¹), dimethyl sulphoxide (DMSO) (C₂H₆OS, CAS 67-68-5, 78.13 g·mol⁻¹), CellTracker™ Green CMFDA Dye (C₂₅H₁₇ClO₇, CAS 136832-63-8, 464.86 g·mol⁻¹) (ThermoFisher Scientific, Waltham, MA, USA), CM-H₂DCFDA (C₂₇H₁₉Cl₃O₈, CAS 1219794-09-8, 577.80 g·mol⁻¹) (ThermoFisher Scientific), disodium hydrogen phosphate (NaH₂PO₄, CAS 7558-79-4, 141.96 g·mol⁻¹), sodium dihydrogen phosphate dihydrate (NaH₂PO₄ × 2H₂O, CAS 13472-35-0, 156.01 g·mol⁻¹). For the determination of the protein concentration, the Pierce™ BCA Protein Assay Kit was used.

2.3. Biomarker Measurements

All biomarker assays (

Table 1. Detailed information on conducted biomarker assays.

		Method	Reaction Mixture	Measurement Settings
Enzymatic biomarkers	Acetylcholinesterase (AChE) Activity	Ellman et al. [51]	5 µL plasma (5× dilution in 0.10 M phosphate buffer, pH 7.20) or 25 µL S9 (10× dilution in phosphate buffer) 180 µL phosphate buffer 10 µL DTNB (1.6 mM in buffer) 10 µL acetylthiocholine iodide (156 mM in distilled water)	Absorbance was recorded at 412 nm over 5 min. The specific activity was calculated using the molar extinction coefficient ε = 13.60 · 103 M−1·cm−1.
	Carboxylesterase (CES) Activity	Hosokawa and Satoh [52]	10 µL undiluted plasma sample or 20 µL S9 (10× dilution in phosphate buffer) 150 µL p-nitrophenyl acetate (1 mM in acetonitrile, diluted in distilled water)	Absorbance was recorded at 405 nm over 5 min. The specific activity was calculated using the molar extinction coefficient ε = 16.40 · 103 M−1·cm−1.
	Glutathione S-Transferase (GST) Activity	Habig and Jakoby [43]	5 µL plasma or 20 µL S9 (10× dilution in phosphate buffer) 160 µL CDNB (1 mM in ethanol/phosphate buffer, 0.10 M, pH 7.2), 40 µL GSH (25 mM in distilled water)	Absorbance was recorded at 340 nm over 2 min (plasma) or 5 min (S9). The specific activity was calculated using the molar extinction coefficient ε = 9.60 · 103 M−1·cm−1.
Non-enzymatic biomarkers	GSH Detection	Bjedov et al. [16]	2 µL sample (for both plasma and S9) 90 µL phosphate buffer (0.10 M, pH 7.20) 5 µL CellTracker™ Green CMFDA (9.78 µM in DMSO)	Fluorescence was recorded at 5 min intervals for 15 min with excitation of 485 nm and emission of 530 nm (gain: 50).
	ROS Detection	Bjedov et al. [16]	10 µL sample (for both plasma and S9) 90 µL phosphate buffer 10 µL CM-H2DCFDA (7.87 µM in DMSO) for plasma or 5 µL CM-H2DCFDA (7.87 µM in DMSO) for S9	Fluorescence was recorded at 5 min intervals for 15 min with excitation of 485 nm and emission of 530 nm (gain: 50).

) were optimised for the Tecan Spark 10M microplate reader. Plasma and S9 fractions, along with blanks, were analysed in three technical replicas. Enzymatic activity was derived from changes in absorbance and expressed as specific activity. Measurements conducted using fluorescent probes were expressed in fluorescent units. Total protein concentration was determined using the Pierce™ BCA Protein Assay Kit with bovine serum albumin (BSA) as a standard. Measurements were conducted according to the kit instructions.

2.4. Body Condition Estimation and Descriptive Analysis

To assess body condition independently of structural size, a Body Condition Index (BCI) was calculated using linear regression analysis. Body mass was regressed against tarsus length, as tarsus length is considered a reliable proxy for structural body size in nestlings. Before regression analysis, the assumptions necessary for linear regression were assessed. Linearity between mass and tarsus length was visually confirmed through scatterplots. The residuals (observed minus predicted mass) were checked for normality using a Quantile-Quantile (Q-Q) plot, confirming that the residuals approximated a normal distribution. Homoscedasticity, or equal variance of residuals, was visually evaluated using a residuals vs. predicted mass scatterplot, revealing no evident patterns or heteroscedasticity. Regression residuals (residual BCI) were then used as an indicator of size-corrected energetic reserves. Nestlings with a positive value, i.e., positive residual, were considered to be in better body condition than nestlings with a negative residual [50,53]. Descriptive statistics for both biomarkers and morphometric traits were computed using a mixed-method approach that incorporated parametric measures (mean, standard deviation [SD], and standard error [SE]) alongside non-parametric, quantile-based statistics (median, first quartile [Q1], and third quartile [Q3]). It is necessary to clarify that all analyses and inferences were conducted using the total sample size of n = 20 nestlings. These analyses were performed in the R 4.4.0 environment with a 95% significance level. To contextualise the 2025 measurements, we compiled means for the same biomarkers from the same sampling area for 2020–2024 (Table S4). These data are used descriptively to compare 2025 values against the previously observed local range; no between-year hypothesis tests were performed, as our a priori hypotheses concern the 2025 trait–biomarker responses.

2.5. Multivariate Analysis

2.5.1. Imputation of Missing Records in BCI, TL, and S9 Fraction

Due to missing values in the first nestling’s BCI and TL records, as well as a missing ROS activity measurement in the S9 fraction for the second nestling, multivariate imputation was performed using an unsupervised machine learning approach via the Super Learner ensemble algorithm [54], which implements a weighted combination of predictive models through the sl3 package integrated within the misl (Multiple Imputation by Super Learning) package [55]. The models included non-negative least squares regression (NNLS) to ensure plausible predictions, a Bayesian generalised linear model with normally distributed errors and a Cauchy-distributed prior on its coefficients (BGLM) to incorporate uncertainty during imputation, and multivariate adaptive regression splines (MARS) to capture complex nonlinear influence patterns [56].

Imputations were conducted under the Missing Not At Random (MNAR) assumption, as missing BCI, TL, and S9 fraction ROS activity values resulted from the first nestling’s unmeasurable TL due to its fragility and vulnerability, posing a considerable risk of potential injury during handling, while ROS activity remained undetected in the second nestling’s blood S9 fraction [57,58,59]. Accordingly, the ensemble of three regression models was calibrated as the basis for multiple multivariate imputation by chained equations via the MICE package [60], combined through Rubin’s rules with a post hoc delta adjustment correction factor of 0.15 to mitigate potential MNAR-related biases [61]. All imputations were executed in R 4.40 using n = 10 datasets and 10 iterations per dataset.

2.5.2. Detection and Recoding of Multivariate Outliers

Multivariate outliers were identified in plasma GST, CES, and PAChE enzymatic activities (Figures S1 and S2) using the unsupervised Random Forest implementation described by Chandola et al. [62], an advanced adaptation of this machine learning technique designed to detect both local and global outliers through distance calculations based on k neighbours within the complete set of study variables, highlighting its robustness against outlier influence and multicollinearity. Specific parameters included k = 10 neighbours, a stringent detection threshold of 3.7, 500 decision trees, and 100 iterations to enhance analytical precision. Subsequently, identified outliers in GST, CES, and PAChE multivariate distributions were recoded using k = 10 neighbours and a detection threshold of 3.5, incorporating predictive mean matching (pmm) to preserve univariate conditional distributional properties of studied variables, as described by Horton and Lipsitz [63,64] and Cai et al. [64]. All methodological steps were executed using the outForest package in R 4.40.

2.5.3. Evaluation of Multivariate Normality

The multivariate normality assumption for the distribution encompassing nestling BCI, BM, TL, and BL, alongside plasma biomarker activities and concentrations (Pprot, PAChE, PCES, PGST, PGSH, PROS) and S9 fraction activities and concentrations (S9Prot, S9AChE, S9CES, S9GST, S9GSH, S9ROS), was evaluated through sequential analysis employing Royston’s test, Doornik-Hansen omnibus test, Energy test, Henze-Zirkler test, and Generalised Shapiro–Wilk test, all rejecting multivariate normality (Table S1). Analyses were conducted in R 4.40 using the MVN and mvShapiroTest packages with a 95% significance level.

2.6. Conditional and Structural Associations Between Blood Biomarkers and Morphometry of White Stork Nestlings

2.6.1. Conditional Associations

Conditional independence among variables was assessed by estimating nonparametric Hoeffding’s D correlation coefficients, which, unlike standard correlation tests (Pearson, Spearman, and Kendall), determine conditional relationships between variable pairs through their joint marginal occurrence probabilities, simultaneously accounting for nonlinear, monotonic, and non-monotonic associations [65,66]. Hoeffding’s D statistic is defined for n > 5, and its performance, specifically the exact distribution for small sample sizes (n = 5, 6, 7), demonstrates that in our case (n = 20), the test provides practical evidence of conditional dependence among random variables under an asymptotically approximated limit distribution of nD_n [67,68]. This test was conducted using the dplyr, tidyr, and independence packages in R 4.40 with a 95% significance level.

2.6.2. Bayesian Structure of Conditional Partial Associations

To assess the association structure between White Stork nestling morphometric parameters (BCI, BM, TL, and BL) and plasma biomarkers (Pprot, PAChE, PCES, PGST, PGSH, and PROS) alongside S9 fraction biomarkers (S9Prot, S9AChE, S9CES, S9GST, S9GSH, and S9ROS), a Bayesian undirected graphical model, BUGM, based on conditional partial correlations was implemented [69]. The model was constructed using a continuous birth-death Markov chain Monte Carlo (BDMCMC) sampler via the BDgraph package [70], representing a substantial improvement over classical samplers such as Metropolis-Hastings or Gibbs in efficiency and accuracy for inferring plausible structures in undirected graphical models [71], given the Rao-Blackwellized estimator implementation [72].

A critical aspect of this analysis was the empirical configuration and model tuning based on informative priors, grounded in previously estimated Hoeffding coefficients (Section 2.6.1), which identified significant sparse conditional associations relevant to study objectives (D > 0.10, p < 0.05) (Table S2). These results led to a restrictive prior for inferred correlation estimation probabilities, with a restrictive posterior inclusion probability of g.prior = 0.2 and an informative level of df.prior = 8. This strategy is particularly relevant given the small sample size (n = 20), where informative priors are essential to reduce posterior distribution uncertainty and minimise noisy precision matrix estimates [73,74]. Notably, as it is emphasised in Kundu et al. [75], thorough calibration of priors in Bayesian graphical structure learning, combined with Bayesian model averaging (BMA) [76] and theoretical domain of conditional partial correlation graphical model principles [77,78], provides an effective framework for modelling complex relationships even in the presence of multicollinearity. Thus, in small samples, well-justified and calibrated priors not only enhance inference precision but also mitigate spurious and confounding events introducing noise and bias into sampling [79,80]. In this regard, studies by Mukherjee and Speed [81] and Leday and Richardson [82] confirm that empirically grounded informative priors within Bayesian biological network modelling constitute best practice when performing inferences in small datasets.

Sampling was conducted over 100,000 total iterations, discarding 40,000 burn-in iterations (40% of total), within acceptable limits (<50%) for stable convergence as suggested per Huth et al. [83], additionally to control autocorrelation and ensure stationarity of the posterior distribution, five iterations were skipped between samples (jump = 5) with a convergence threshold of 1 × 10⁻⁸. Given prior rejection of multivariate normality (Table S1), the correlation network was constructed as a Gaussian copula graphical model (GCGM) [84] using a G-Wishart distribution as a conjugate prior, enabling correlation modelling under non-normal and multimodal distributions. The final network structure (S) and conditional partial correlations (Θ) were selected via BMA with the BUGM stored samples, performing robust weighted selection based on probabilities of plausible structures with the least uncertainty [85]. Subsequently, Bayes Factor 10 (BF₁₀) was estimated to determine evidence strength in favour of edge inclusion (null hypothesis) against the evidence in favour of edge exclusion (alternative hypothesis) in the BMA-selected structure [86]. Subsequently, to assess uncertainty in inferred partial correlations, 95% highest density intervals (HDIs) were quantified using the easybgm package [87]. Convergence quality was verified through autocorrelation function (ACF) and partial autocorrelation function (PACF) plots alongside the convergence diagnostic (CODA). BUGM inference and structure learning were executed in R 4.40.

3. Results

3.1. Descriptive Aspects and Interannual Context

Plasma and S9 fraction biomarkers in White Stork nestlings showed different response in regard to blood fraction, with generally higher protein concentrations and GSH levels in the S9 fraction, while AChE activity was higher in plasma (

Table 2. Descriptive statistics of biochemical parameters measured in plasma and S9 fractions from White Stork (C. ciconia) nestlings (n = 20) sampled during the breeding season 2025 from eastern Croatia. Parameters include proteins, acetylcholinesterase (AChE), carboxylesterase (CES), glutathione S-transferase (GST), glutathione (GSH), and reactive oxygen species (ROS). Values presented as minimum, percentiles, median, maximum, range, mean, standard deviation (SD), and standard error (SE).

		Proteins (mg∙mL−1)	AChE (nmol·min−1·mgPROT−1)	CES (nmol·min−1·mgPROT−1)	GST (nmol·min−1·mgPROT−1)	GSH (RFU)	ROS (RFU)
Plasma	n (individual)	20	20	20	20	20	20
	Min	10	11.30	2.57	2.65	5493	127
	25% Percentile (Q1)	42.29	22.96	3.45	4.26	6851	135
	Median	54.01	29.61	4.65	6.15	7625	143
	75% Percentile (Q3)	58.68	36.47	5.83	9.63	9513	150
	Max	74.09	120.30	26.25	34.64	13,382	205
	Range	64.09	109	23.69	31.99	7889	78
	Mean	50.43	33.21	5.68	8.39	8266	145
	SD	13.46	21.81	4.99	7.04	1848	17
	SE	3.00	4.88	1.12	1.58	413	4
S9	n (individual)	20	20	20	20	20	19
	Min	91.74	0.62	1.04	0.82	10,575	59
	25% Percentile (Q1)	173.40	0.75	1.13	1.09	16,684	82
	Median	193.00	0.88	1.23	1.48	20,155	94
	75% Percentile (Q3)	235.90	0.96	1.53	1.68	22,435	118
	Max	322	2.28	2.74	3.28	30,113	290
	Range	230.20	1.66	1.71	2.46	19,538	231
	Mean	195.10	0.98	1.39	1.51	19,947	115
	SD	58.32	0.40	0.43	0.56	5004	61
	SE	13.04	0.09	0.09	0.12	1119	14

). CES and GST activities followed the same pattern across both fractions, although absolute values were lower in S9. ROS concentrations were broadly comparable between fractions.

Regarding the interannual context, in plasma, 2025 specific AChE activity was about 8.71% higher than the previous activity in 2021, while the specific CES activity was 76.83–84.78% lower than all prior years (Table S4). Specific plasma GST activity remained within the prior range, close to its lower half. The concentration of plasma ROS in 2025 was only 3.33% below that of 2023, and the GSH concentration was 26.73% below that of 2020, but 173.26% higher than that of 2023 (Table S4). In the S9 fraction, 2025 specific AChE activity was 78.84% lower than that of 2022 but still above that of 2024. The specific CES activity in S9 reached the lowest series value, 85.21% lower than in 2022. The specific S9 GST activity was also at the series low, 95.54% lower than in 2021. In contrast, S9 ROS concentration in 2025 was the highest, exceeding that in 2023 by 8.49%. The concentration of S9 GSH in 2025 was 34.58% below that of 2020 but more than threefold (228.51%) higher than in 2024. These comparisons are descriptive only (Table S4).

Morphometric traits also varied among nestlings (

Table 3. Morphometric measurements of White Stork (C. ciconia) nestlings (n = 20) sampled during the 2025 breeding season in eastern Croatia. Measurements include body mass (kg), beak length (mm), and left tarsus length (mm). Values presented as minimum, percentiles, median, maximum, range, mean, standard deviation (SD), standard error (SE) and body condition index (BCI).

	Mass (kg)	Beak (mm)	Tarsus (mm)	Residual BCI
n (individual)	20	20	19	19
Min	2.35	97.00	136.00	−0.72
25% Percentile (Q1)	3.13	107.80	160.00	−0.11
Median	3.40	115.50	174.00	0.01
75% Percentile (Q3)	3.69	125.80	188.00	0.11
Max	4.20	140.00	237.00	0.58
Range	1.85	43.00	101.00	1.31
Mean	3.36	116.80	177.00	0
SD	0.43	12.30	23.73	0.32
SE	0.10	2.75	5.45	0.07

). The BM averaged around 3.4 kg, with moderate variation in BL and high variability in TL, reflecting developmental differences. Residual BCI values centred around zero, with a narrow interquartile range, indicating moderate variability in size-corrected mass.

3.2. Conditional Associations

Assessment of conditional independence through nonparametric Hoeffding’s D correlation coefficients revealed a selective pattern of associations among variables analysed in White Stork nestlings, with only 14 of 120 possible correlation pairs (11.66%) showing appreciable and significant evidence of conditional dependence (D > 0.10, p < 0.05), spanning an association range of D = 0.103–0.206. In this context, the magnitude and nature of associations were relatively low and entirely positive, with the strongest association observed between plasma CES activity and protein accumulation in the same fraction (D = 0.206, p < 0.001); meanwhile, all other plasma and S9 fraction biomarkers were exclusively associated with activities and concentrations of other biomarkers measured within their respective fractions. Morphometric traits predominantly exhibited conditional associations among themselves, with BL describing the highest number of associations (3 associations) and being the only variable correlating with a biomarker—plasma ROS activity (Table S2). Consequently, 88.34% (106) of analysed correlation pairs reflected substantial conditional independence, suggesting a particularly fragmented dependency structure within the studied biological system.

3.3. Bayesian Structure of Conditional Partial Associations

Structure learning via BUGM inference further indicates that the most probable posterior structure exhibits notable uncertainty, reflected in a posterior structure probability S = 0.383, representing a relatively moderate probabilistic magnitude. Specifically, only 15 of 120 possible correlation pairs (12.50%) demonstrated strong conclusive evidence (BF₁₀ > 10) favouring their inclusion in the most probable inferred correlation structure, while 18 of 120 possible partial correlation pairs (15%) showed inconclusive evidence for structural inclusion, as well the remaining 72.50% of possible correlation pairs, represented by 87 edges, exhibited conclusive evidence favouring their exclusion (Table S3). Notably, there is substantial alignment between the inferred partial correlation structure and the number of conditionally significant pairs identified via Hoeffding’s correlations, as well as between the BUGM’s structural posterior uncertainty and the magnitude of Hoeffding’s coefficients, indicating appreciable evidence.

In contrast, the magnitudes of conditional partial correlations (Θ) generally encompassed positive changes or increments, ranging from low to moderate and notably strong correlations, in which the weakest correlation was observed between changes in nestling BM and changes in plasma CES activity, whereas the strongest association linked changes in BM and TL. Remaining morphometric associations exhibited moderate to strong magnitudes, with the correlation between changes in BCI and TL being the sole negative yet moderate association, consistent with the natural BCI’s inverse relationship to TL increments. Collectively, changes in nestling TL were weakly and moderately associated with protein concentration changes in both plasma and S9 fraction, while changes in BM correlated weakly and moderately with plasma enzymatic biomarker activities (PAChE and CES). Similarly, BM changes in nestlings correlated at comparable magnitudes with non-enzymatic biomarker concentrations such as plasma GSH, with the association between BL changes and plasma GSH concentrations being markedly strong (Table S3). Exclusive biomarker associations indicated that increases in plasma CES and GST activities were positively and moderately linked, whereas ROS concentration changes in both plasma and S9 fraction moderately correlated with plasma CES activity changes. Additionally, S9 fraction GST activity changes moderately associated with GSH concentration changes and AChE and CES activity changes exclusively within the S9 fraction, revealing a pattern of structural specificity and isolation (Table S3).

These dynamics are evident in Figure 2a, as the BUGM-inferred correlation structure (S), concatenated through physical projection using the ForceAtlas2 algorithm, reveals two isolated node or variable communities describing a disconnected graph, within the first community is dominated in terms of weight and centrality by nestlings’ BM and TL alongside plasma CES activity, while the second community is monopolised by S9 fraction GST activity, exclusively comprising biomarkers from this fraction—consistent with correlation patterns documented in Table S3. Complementarily, Figure 2b indicates that uncertainty in conditional partial correlations, reflected in their 95% HDIs, was inversely proportional to association magnitudes, varying from narrow intervals for prominent correlations to moderate-to-high amplitude intervals for moderate and low-magnitude correlations, respectively. The chord diagram in Figure 2c extends structural findings from Figure 2a, showing sequential clockwise reduction in node weights, with nestlings’ BM and TL and S9 fraction GST activity exhibiting the highest number and edge strength and overall network relevance. Conversely, variables such as S9 fraction protein concentrations, plasma AChE activity, and S9 fraction ROS concentrations displayed the lowest structural weights and impact. In general, plasma biomarkers constituted an exclusive component of Community 1 and were directly and indirectly associated with the measured morphometric traits of White Stork nestlings, while most S9 fraction biomarkers were characterised by mutual associations within Community 2, with no evidence of co-occurrence with morphometric traits.

Furthermore, the BUGM convergence diagnostic represented by ACF and PACF indicates that autocorrelation was fully controlled around 20 lags, while partial autocorrelation monitored via PACF suggests that samples comprising the posterior distribution achieved total stability around 10 lags, as well, the structural exploration of posterior correlation configurations reveals that the BDMCMC sampler explored networks ranging from 11 to 35 edges, with the 15-edge network selected as the most probable structure (Figure S3a). Consequently, Figure S3b illustrates that, among 12,000 iterations, sampling traces became completely independent around 4800 iterations (dotted red baseline), indicating that the posterior distribution of the inferred structure reached stationary behaviour, confirming correct convergence of the structural learning process.

4. Discussion

Biomarker responses in plasma (systemic, short-term state) and S9 blood cell homogenate (intracellular processes) were characterised in nestlings from eastern Croatia and, when compared to recent-year baselines, were consistent with fraction-specific physiology under agricultural exposure. Pairwise dependence of morphology–physiology quantified by Hoeffding’s D was sparse and positive. Inference using BUGM resolved a modular separation between morphometry and biomarkers, with biomarker nodes forming communities by fraction and BCI showing limited association with biochemical status; posterior support for a single dominant BUGM structure was moderate. In the following sections, the environmental context, the pairwise structure, and the BUGM are addressed in turn.

4.1. Biomarker Response and Environmental Context

Biomarker responses vary among years in both plasma and S9 fractions within the same foraging area. This interannual variability is ecologically plausible: plasma markers typically index systemic, short-term state (e.g., redox balance and circulating enzyme activities), whereas S9 markers reflect intracellular pathways of detoxification and oxidative metabolism. Year-to-year differences in rainfall and temperature, crop phenology, timing and formulation of agrochemical applications, prey composition, and parental condition can all shift these processes on the timescale relevant to nestling development [88,89,90,91]. The position of 2025 values relative to prior years from the same area, fits the expectation that biomarkers behave as sensitive, area-level sentinels of changing exposure and physiological demand rather than as fixed trait values.

Interpreted alongside our BUGM results, the interannual context reinforces fraction-specific biology: plasma captures rapid systemic adjustments under fluctuating conditions, while S9 emphasises intracellular detoxification capacity. This separation is consistent with our a priori predictions of modularity and supports the use of combined plasma-S9 panels for biomonitoring. Identifying the specific drivers behind annual shifts will require targeted designs (e.g., coordinated pesticide application records, climatic covariates, and concurrent residue measurements in prey and blood), but even without pinpointing single causes, the observed patterns argue for continued biomarker monitoring in the agricultural environment.

4.2. Hoeffding’s Dependence Analysis: Sparse but Informative Links

Hoeffding’s analysis indicated a sparse dependency structure, with only 14 of 120 pairs showing significant dependence. This confirms that morphometric traits and biomarkers show limited integration, with only a single morphology–biomarker edge detected (BL–ROS), while the strongest dependencies were confined to fraction-internal physiology (CES–protein). In practical terms, how a nestling looks (size, BM, TL or BL) and how its physiology functions (detoxification, antioxidant balance) do not strongly overlap. Morphometric traits primarily describe structural development, skeletal growth and mass accumulation, which change gradually and are influenced by long-term nutrition and ontogeny [30,31]. By contrast, biomarkers capture physiological state, acute biochemical responses to oxidative stress or xenobiotic exposure, which can shift on much shorter timescales [32,33,34,35,36]. Because these two dimensions operate on different biological timescales and reflect distinct processes, their associations are weak. Ecologically, this means that a nestling can appear morphometrically robust while still showing elevated oxidative stress if exposed to pesticides, or conversely, a smaller nestling may display unremarkable biomarker values if not under immediate stress.

The strongest association was between plasma CES and plasma proteins, suggesting a fraction-internal link where detoxification activity may scale with overall protein turnover or nutritional status. CES is a broad-spectrum detox enzyme acting in circulation, and its positive link with protein levels could reflect increased synthesis of plasma proteins under dietary sufficiency, which simultaneously supports greater enzymatic capacity [92,93]. Such fraction-specific communities are consistent with the idea that detoxification potential is tightly tied to metabolic resources, rather than external morphology. All other biomarker associations occurred within the same fraction (plasma-plasma or S9-S9), reinforcing that plasma reflects systemic short-term responses while the S9 fraction captures intracellular detoxification pathways, with little detectable cross-talk between them [16].

Morphometric traits are associated mainly among themselves, with BL showing the highest number of links. The only morphometric-biomarker association was BL with plasma ROS. We interpret this association cautiously: the dataset if from a single season and sampling area and the BUGM evidence for this edge was moderate, not decisive. Given the large number of pairwise screens, the possibility of a spurious correlation cannot be excluded. Our methods quantify conditional association, not causation or directionality and owing to that fact, we treat BL–ROS as hypothesis-generating and consistent with our a priori expectation of sparse, trait-specific bridges, pending replication in independent cohorts/years. This may reflect the rapid growth of beak tissue, where elevated metabolic activity and cellular turnover generate oxidative load, or it could indicate diet-related differences in feeding frequency and nutrient assimilation. ROS are sensitive markers of both endogenous metabolism and exogenous stressors [37,38], meaning that individuals with faster beak development might experience higher oxidative turnover. In an ecological context, beak size also influences prey capture and feeding efficiency in white storks, which could further modulate oxidative status via nutrient uptake. This single connection suggests that growth in certain traits may transiently align with oxidative status, whereas overall body condition does not. In conclusion, consistent with our prediction of sparse integration, only 14/120 pairs showed conditional dependence. The strongest and most consistent signal was the plasma CES–protein link, whereas BL–ROS represented the only morphology–biomarker edge and should be considered tentative until replicated.

4.3. BUGM: Disconnected Corrleation Structure and Key Bridges

BUGM confirmed the sparse association structure, with a moderate posterior probability (S = 0.383) and only 15 of 120 possible edges (~12%) retained with strong evidence. This indicates that the conditional structure inferred by the BUGM among morphometrics and biomarkers was fragmented and uncertain, consistent with the weak dependencies observed in Hoeffding’s analysis.

The inferred structure is separated into two communities. Community 1 grouped BM, TL, BCI, and BL with multiple plasma biomarkers (PGSH, PAChe, PCES, PROS, PGST, protein, ROS), indicating selective integration between morphometry and plasma physiology. Rather than CES acting as the only bridge, several plasma biomarkers (e.g., PGSH, PAChe, PCES) showed modest connections to morphometrics. The CES role likely reflects both its location and function: circulating in plasma, CES engages in immediate detoxification of xenobiotics but does not anchor broader intracellular metabolic processes, preventing it from becoming a dominant hub [39,40,92,93]. Its substrates overlap partially with GST and oxidative stress markers, producing weak bridges when detoxification and antioxidant systems are co-activated. However, CES activity is highly variable across individuals and contexts, influenced by diet, environment, and transient exposures. Such variability renders its bridging role modest and inconsistent.

A notable exception was the BL and plasma GSH edge, which emerged as one of the most robust associations in the BUGM. This link is biologically plausible; rapid beak growth may elevate metabolic demand and ROS generation, necessitating upregulation of GSH as a compensatory antioxidant defence. Both beak development and glutathione synthesis also depend on dietary protein and sulphur amino acid intake [41,42], while hormonal regulation of growth could further synchronise morphological development with redox status [94,95].

Posterior uncertainty intervals highlighted that only a handful of associations were reliable; the BL–PGSH link stood out as robust, with additional but weaker support for edges such as CES–ROS and BM–PAChE. This emphasises that fraction-level community was clear, with morphometry partly integrated with plasma biomarkers but separated from S9 enzymes; individual cross-links should still be interpreted with caution and ideally replicated in larger or repeated datasets. Such caution is warranted because growth-oxidative stress relationships are well known to be variable. In the Yellow-Legged Gull (Larus michahellis) nestlings, experimental supplementation with a mitochondrial-targeted antioxidant showed that rapid early growth elevates ROS production, and that scavenging ROS can partly alleviate this cost without altering developmental trajectories [96]. Similarly, comparative work across birds and mammals demonstrates that fast growth rates are typically associated with higher oxidative damage, with antioxidant defences such as GSH mobilised to buffer this stress [97]. These findings lend support to the BL and GSH edge as a plausible signal of a growth-redox trade-off. Likewise, the CES and ROS link is consistent with detoxification processes that overlap with oxidative pathways, though the strength of such associations may fluctuate depending on diet, environmental exposures, and developmental stage.

Community 2 was composed entirely of S9 enzymes, grouped around GST and showing links with S9 GSH, AChE, and CES. This fraction-specific isolation reinforces the interpretation that plasma captures short-term systemic responses, whereas S9 is well established as a source of intracellular detoxification enzymes such as GST, AChE, and CES [15,43,52]. In line with our prediction, BUGM revealed that morphometry integrated selectively with plasma biomarkers, while S9 biomarkers formed a distinct community.

4.4. Broader Ecological and Biomonitoring Implications

Our results showed that morphometry and biomarkers in White Stork nestlings formed distinct but selectively connected communities. Morphometric traits (BM, TL, BCI, BL) grouped tightly, while showing modest bridges to several plasma biomarkers, most notably the robust BL–GSH association and weaker links to plasma AChE and CES. These connections suggest that larger or faster-growing nestlings may possess slightly greater detoxification or antioxidant capacity, but such effects were minimal compared to the overall separation of growth and physiology. Similar patterns have been documented in White Storks. Kosicki and Indykiewicz [25] showed that nestling growth dynamics are driven mainly by short-term weather conditions rather than breeding parameters, indicating that morphometrics primarily track environmental variability. Tryjanowski et al. [26] further demonstrated that apparent male-female differences in body mass diminish once age and brood structure are accounted for. Jerzak et al. [27] reported only small sex- or age-related differences in selected blood chemistry parameters, while Kamiński et al. [28] found minor sex effects in haematology that were overshadowed by far stronger influences of sampling year and hatch date. In line with these studies, our work focused on a different set of physiological endpoints, for which previous research has not detected significant sex effects [17,19].

These patterns echo broader findings in other taxa where condition indices have shown limited explanatory power. In polar bears (Ursus maritimus), absolute BM predicted reproductive success more reliably than condition indices, which often obscure biologically relevant variation [98]. Furthermore, in many regions, the sparse terrestrial food supply sustains only small populations of brown bears (Ursus arctos), which are better adapted to exploit these lower-quality resources and may compete with polar bears. Rode et al. [98] show that in areas where polar bears consume land-based foods, their condition and survival tend to decrease despite greater use of terrestrial habitats. In European badgers (Meles meles), body condition influenced survival and reproduction only below threshold values, with effects mediated by environment and life-history stage [99]. The study also showed that most individuals exhibited substantial annual variation in BCI unrelated to immediate stressors, highlighting that condition indices alone can be misleading. This mirrors our findings in nestling White Storks, where BCI showed no robust associations with biomarkers, the real-time indicators of oxidative stress and detoxification. A study on Bonelli’s Eagles (Aquila fasciata) found that nestling diet strongly shaped physiological condition: higher consumption of preferred prey, the European rabbit (Oryctolagus cuniculus), improved antioxidant balance and reduced oxidative stress, while greater diet diversity was linked to elevated oxidised GSH and poorer condition [100]. Antioxidant enzymes and oxidative stress markers were also influenced by sex, age, and sampling time, but these physiological measures showed only weak and inconsistent associations with morphometric condition [100]. In Imperial Shags (leucarbo atriceps), morphometric indices proved to be strong predictors of nestlings’ survival, where BM explained up to half the variation in survival probabilities [101]. This was particularly pronounced in subordinate b-nestlings, i.e., the second-hatched nestlings, which are smaller, disadvantaged and often face sibling competition. Plasma biochemical markers (triglycerides, proteins, alkaline phosphatase) reflected short-term nutritional status and varied with age, sex, and season, but they explained little of the longer-term condition or survival outcomes and showed inconsistent predictive value [101]. Morphometry captured developmental reserves relevant for survival, whereas blood chemistry reflects immediate physiological state. A similar pattern emerged in our White Stork nestlings, where morphometric traits and biomarkers formed two separate communities, and condition indices alone did not reliably indicate oxidative or detoxification status.

Taken together, these results emphasise that biomarkers capture physiological dimensions not visible in growth metrics, and condition indices may even obscure size-related information. For biomonitoring, this means residual BCI alone cannot serve as a reliable proxy for physiological state. Instead, combining morphometry with biochemical profiling provides a more nuanced window into developmental conditions and environmental stress, strengthening our ability to detect how agricultural environments shape early-life health in wild bird populations.

4.5. Future Directions and Challenges

Future work should increase sample sizes across multiple colonies and years and incorporate repeated measures within individuals. Pairing biomarker panels with direct exposure data (residues in blood and prey, or environmental matrices) will strengthen causal links. Given prior evidence in this species that sex does not significantly modulate the selected biomarker responses in White Stork nestlings, subsequent studies may prioritise diet and environmental variation.

In future research, endpoints known to be sensitive to age or sex should be incorporated, alongside a broader spatial design covering multiple colonies with contrasting feeding grounds and pollution sources. Expanding the biomarker panel with additional physiological endpoints and complementing these with pollutant analyses in White Storks will provide a more comprehensive understanding of how environmental stressors shape nestling health. Finally, targeted tests of the beak length-redox associations (BL–ROS/GSH) in larger cohorts, with repeated measurements of the same nestlings across developmental stages and ideally with integrated dietary data, would clarify whether these links reflect growth-redox trade-offs or context-dependent environmental signals.

5. Conclusions

This study provides one of the first integrated assessments of morphometry and blood biomarkers in wild birds. The application of a BUGM provides a novel framework for evaluating conditional associations in ecotoxicology, moving beyond pairwise correlations to identify grouping structure and trait-specific links. This approach offers unique insights into how morphometric and biochemical dimensions are selectively integrated. The BUGM analysis revealed two communities: one combining morphometric traits with plasma biomarkers, and a second formed by S9 biomarkers. This indicates that morphometry is selectively linked with plasma oxidative and detoxification measures (e.g., associations of BM, TL, and BCI with PGSH, PAChe, PCES, and PROS), while S9 biomarkers represent a distinct physiological community. Thus, rather than being fully separated, morphometric traits and plasma biomarkers share modest but consistent connections, whereas fraction-level separation is clear. These results further suggest that residual BCI alone is not a reliable proxy for physiological stress state but that combining morphometric measurements with a minimal plasma biomarker panel (e.g., CES, GST, GSH, ROS) provides a more nuanced picture of nestling condition. Inter-annual comparisons also underscore the need for repeated, fraction-specific biomarker measurements to track shifting exposures in agricultural areas. Future work should (I) validate the observed morphology–biomarker links in larger and longitudinal samples, (II) integrate direct exposure data (e.g., pesticide residues, metals) to connect biomarkers with specific stressors, and (III) test threshold-type effects in body condition under varying environmental contexts. This integrated, multi-metric approach will strengthen inference about early-life health and enhance the sentinel value of White Storks in agroecosystems.