Generation Mean Analysis of Gene Action for Photosystem II Fluorescence Parameters in Two Bread Wheat Crosses

Abstract

Chlorophyll fluorescence parameters are sensitive indicators of photosystem II (PSII) functionality and overall photosynthetic performance; however, their genetic architecture in wheat remains poorly understood. This study aimed to elucidate the gene action governing chlorophyll fluorescence traits in two bread wheat (Triticum aestivum L.) crosses: N-92-9 × Ehsan and Kohdasht × Ehsan. Six generations (P₁, P₂, F₁, F₂, BC₁, and BC₂) were evaluated under a randomized complete block design (RCBD) with three replications. Sixteen OJIP-based fluorescence parameters were recorded, including Fo, Fm, Fv, Fv/Fm, ABS/RC, TRo/RC, ETo/RC, REo/RC, φ(Po), ψ(Eo), ABS/CSo, DIo/CSo, TRo/CSo, ETo/CSo, ABS/CSm, and DIo/CSm. Significant generation effects were detected for 14 of the 16 parameters in N-92-9 × Ehsan and for 12 parameters in Kohdasht × Ehsan. These statistical patterns and the subsequent generation mean analyses indicated cross- and trait-dependent contributions of additive, dominance, and epistatic effects. The ratio |F|/√(D×H) was less than unity for the majority of traits in both crosses, indicating an asymmetrical distribution of dominant and recessive alleles between the parents and confirming the importance of dominance in controlling these traits. Broad-sense heritability ranged from moderate to high, reaching 0.991 for Fv/Fm in N-92-9 × Ehsan and 0.697 for ABS/CSm in Kohdasht × Ehsan. Dominance gene effects were predominant for most traits in both crosses, suggesting that hybrid breeding strategies would be more effective for improving these traits. An exception was TRo/CSo in Kohdasht × Ehsan, where additive effects were more prominent, making it amenable to improvement through selection-based methods. These findings provide a cross-specific quantitative-genetic assessment of gene action for PSII fluorescence parameters and illustrate the potential value of combining generation mean analysis with marker-based approaches when integrating photosynthetic efficiency into wheat breeding programs.

1. Introduction

Wheat (Triticum aestivum L.) remains the most strategically important cereal crop globally, contributing approximately 20% of total caloric and protein intake for the human population [1]. Meeting the growing demand for wheat in the face of climate change, expanding population, and shrinking arable land requires a continued acceleration of genetic gains in yield and stress resilience. A prerequisite for effective genetic improvement is a thorough understanding of the gene action underlying agronomically important traits, knowledge that directly informs the choice of breeding strategy, selection intensity, and generation advancement method [2].

In wheat genetics, generation mean analysis is best understood as a family-based method that uses the mean performance of a set of related generations from the same cross to infer the kinds of gene effects behind a quantitative trait. It is widely described as a simple, useful, and statistically reliable approach for estimating the main genetic effects, especially additive and dominance effects, and also the interaction effects among genes such as additive × additive, additive × dominance, and dominance × dominance [2,3,4,5,6].

Generation mean analysis is a well-established, family-based quantitative genetics approach that uses the mean performance of a defined set of related generations, typically P₁, P₂, F₁, F₂, BC₁, and BC₂, derived from the same cross to partition genetic effects into additive [d], dominance [h], and epistatic components ([i], [j], [l]) [7]. It is widely regarded as a simple, reliable approach for estimating both main genetic effects and digenic interactions. Unlike variance component methods, it provides direct estimates of the direction and magnitude of gene effects, making it particularly informative for choosing between selection-based and hybrid breeding strategies [6,8]. This method has been widely applied in wheat to dissect the genetic architecture of grain yield, yield components, plant height, days to heading, and stress-related morphological traits [9,10]. Collectively, these studies demonstrate that wheat traits are frequently governed by both additive and non-additive gene effects, and that epistatic interactions are particularly prominent for complex polygenic traits [11,12].

In wheat, the main genetic result from generation mean analysis is a partition of trait control into additive effects, dominance effects, and epistatic effects. This matters because wheat traits are often quantitatively inherited and genetically complex, and that complexity is increased by the polyploid nature of wheat, which makes genetic dissection harder than in simpler genomes [11]. In practical terms, the analysis can show whether steady selection is likely to work well, which is more favorable when additive effects are important, or whether inheritance is strongly shaped by non-additive effects and gene interactions, which can make selection less straightforward and may favor delayed selection or breeding schemes that better capture recombination and interaction effects. A second recurring finding is that traits tied to yield are rarely governed by only a simple additive–dominance model. Grain yield in wheat is built from many underlying developmental steps and component processes, including the generation and loss of reproductive organs and the final setting of grains, so the genetic signal seen in generation mean analysis often reflects this layered biology rather than a single direct pathway [12]. This helps explain why studies of wheat yield commonly look for not only additive effects but also epistatic effects, and why newer work continues to explicitly partition grain-yield variation into additive and epistatic components [13].

Conceptual breeding implications of gene action detected through generation mean analysis. Predominantly additive effects support selection in segregating and advanced inbred generations; dominance effects may favor exploitation of heterosis or evaluation of hybrid combinations; additive × additive effects may become partly fixable after recombination and inbreeding; and duplicate epistasis may reduce the efficiency of early-generation selection and support delayed selection or recurrent crossing. These recommendations are conditional on the parental combination, trait, and target environment (Figure 1).

Photosynthesis is the primary physiological engine driving biomass accumulation and, ultimately, grain yield in cereal crops. Among the components of the photosynthetic apparatus, Photosystem II (PSII) plays a pivotal role as the entry point of light energy into the photosynthetic electron transport chain [14]. The efficiency of PSII energy conversion is a critical determinant of overall photosynthetic performance and is directly linked to crop productivity under both optimal and stress conditions [15]. Chlorophyll fluorescence analysis, particularly the OJIP transient test (also known as the JIP-test), provides a rapid, non-invasive, and highly sensitive method for characterizing PSII structure and function at the level of individual reaction centers and leaf cross-sections [16,17]. The JIP-test yields a comprehensive suite of biophysical parameters including energy absorption, trapping, electron transport, and dissipation fluxes per active reaction center (ABS/RC, TRo/RC, ETo/RC, REo/RC) and per excited cross-section (ABS/CSo, TRo/CSo, ETo/CSo, DIo/CSo, ABS/CSm, DIo/CSm), along with quantum efficiency parameters (Fv/Fm, φ(Po), ψ(Eo)) that collectively describe the energetic and functional state of the PSII complex [16]. These parameters have been extensively validated as sensitive indicators of photosynthetic stress responses to heat, drought, salinity, and nutrient deficiency in a wide range of plant species, including wheat [18,19,20].

Recent Genome Wide Association (GWAS), Quantiiative Trait Loci mapping (QTL-mapping), and other genomic studies have demonstrated that chlorophyll fluorescence and related photosynthetic traits in wheat possess a detectable genetic basis and are associated with multiple genomic regions [21,22,23,24]. These studies have been valuable for identifying marker–trait associations and candidate genomic intervals. However, association mapping and generation mean analysis address different components of quantitative inheritance. GWAS evaluates statistical associations between markers and phenotypic variation across genetically diverse populations, whereas generation mean analysis partitions phenotypic means from a defined biparental cross into additive, dominance, and digenic epistatic effects. Consequently, marker-based genetic architecture and biparental gene action should be considered complementary rather than interchangeable concepts.

Although genomic studies of photosynthetic traits in wheat are increasing, relatively limited information is available on the additive, dominance, and epistatic gene effects governing a broad set of OJIP-derived fluorescence parameters within six-generation biparental populations. The present study therefore focuses specifically on cross-dependent gene action rather than claiming the first genetic investigation of chlorophyll fluorescence in wheat. In the context of wheat breeding, heritability estimates and gene action studies for PSII fluorescence parameters are also needed to evaluate whether indirect selection for photosynthetic efficiency is feasible in early generations and to determine whether heterosis for these traits can be exploited in hybrid wheat systems [25]. Two crosses were therefore chosen for this study, (N-92-9 × Ehsan) and (Kohdasht × Ehsan), to represent contrasting genetic backgrounds in terms of parental mean performance for the fluorescence traits, thereby maximizing the information content of the generation mean analysis. Accordingly, the present study was designed to: (i) assess the presence and type of gene action (additive, dominance, and epistatic effects) governing 16 OJIP-derived chlorophyll fluorescence parameters in two bread wheat crosses using the six-generation design; (ii) estimate broad- and narrow-sense heritability for each parameter; (iii) calculate model-dependent effective-factor estimates for each parameter under the assumptions of the applied quantitative-genetic formulae; and (iv) provide genetically informed recommendations for breeding strategies aimed at improving PSII photosynthetic efficiency in wheat.

2. Materials and Methods

2.1. Plant Materials and Experimental Design

Two bread wheat (Triticum aestivum L.) crosses were used in this study: (N-92-9 × Ehsan) and (Kohdasht × Ehsan). Hybridization was carried out at the Gorgan Agricultural and Natural Resources Research Center, Gorgan, Iran. In each cross, N-92-9 and Kohdasht served as the female parents, respectively, with Ehsan as the common male parent. Subsequent segregating generations were developed and evaluated at Gonbad Kavous University Research Farm.

Six generations (P₁, P₂, F₁, F₂, BC₁, and BC₂) were established for each cross. The experiment was conducted during the 2020 growing season using a randomized complete block design with three blocks. Each generation was represented by one plot within each block; therefore, the generation plot within a block constituted the experimental unit. Plot areas were 1.5 m² for P₁, P₂, and F₁, 4.0 m² for BC₁ and BC₂, and 5.0 m² for F₂, with an inter-row spacing of 25 cm.

The established field populations comprised 40 plants for P₁, 40 for P₂, 80 for F₁, 100 for F₂, and 80 plants for each backcross generation. These values describe the sizes of the field populations and should not be interpreted as the confirmed numbers of plants individually phenotyped for chlorophyll fluorescence. These population sizes were determined by seed availability, generation-specific plot requirements, and the logistical demands of fluorescence phenotyping. They are smaller than would be ideal for precise characterization of the tails of segregating distributions.

2.2. Experimental Site Characteristics

The experiment was conducted at the Gonbad Kavous University Research Farm (37°16′ N, 55°12′ E; altitude: 45 m above sea level), located in the eastern part of Golestan Province, Iran. The region has a semi-arid climate with mean annual precipitation of approximately 450 mm, the majority of which falls during the autumn–winter growing season. Mean daily temperature during the wheat growing season (November–June) ranges from 5 °C to 28 °C. Soil texture at the experimental site was silty loam, with the following physicochemical properties: pH = 7.8, electrical conductivity (EC) = 1.0 dS m⁻¹, organic matter content = 1.5%, and calcium carbonate (CaCO₃) = 18–19%.

2.3. Measurement of Chlorophyll Fluorescence Parameters

Chlorophyll fluorescence was measured on fully expanded flag leaves using a portable Plant Efficiency Analyzer (Handy PEA; Hansatech Instruments Ltd., King’s Lynn, UK). Prior to measurement, leaf clips were applied for 20 min to achieve complete dark adaptation and ensure that all PSII reaction centers were in the open (oxidized QA) state. Measurements were conducted during the grain-filling stage under field conditions. Fluorescence intensity was detected using a PIN photodiode after passing through a long-pass filter (>700 nm). The OJIP fluorescence transient was recorded from 10 µs to 1 s under a saturating red light pulse (3000 µmol m⁻² s⁻¹; peak wavelength 650 nm). Data acquisition was performed at 10 µs intervals with 12-bit resolution during the initial phase, with sampling frequency subsequently reduced for the slower phases.

Three flag-leaf fluorescence measurements were obtained within each generation × block plot. The plot was regarded as the experimental unit, the three blocks as independent field replications, and the three leaf measurements within a plot as subsamples. Consequently, nine leaf observations were recorded per generation per cross, corresponding to 54 leaf records per cross and 108 leaf records across both crosses.

Raw fluorescence transients were processed using PEA Plus software var 1 (Hansatech Instruments Ltd.) according to the JIP-test framework [26,27]. The symbols, definitions, and principal physiological interpretations of the 16 OJIP-derived parameters evaluated in this study are summarized in

Table 1. Definitions and physiological interpretations of the OJIP-derived chlorophyll fluorescence parameters evaluated in this study.

Parameter	Definition	Principal Physiological Interpretation
Fo	Minimum fluorescence intensity of a dark-adapted leaf	Basal fluorescence when PSII reaction centers are predominantly open and the primary quinone acceptor QA is oxidized
Fm	Maximum fluorescence intensity of a dark-adapted leaf exposed to a saturating pulse	Maximum fluorescence when PSII reaction centers are functionally closed
Fv	Variable fluorescence, Fv = Fm−Fo	Variable component of fluorescence associated with the photochemical reduction of PSII electron acceptors
Fv/Fm	Maximum quantum yield of primary PSII photochemistry, (Fm−Fo)/Fm	Maximum potential efficiency of PSII photochemistry in the dark-adapted state
ABS/RC	Absorption flux per active PSII reaction center	Apparent antenna size or absorbed excitation energy available per active reaction center
TRo/RC	Trapped excitation-energy flux per active reaction center at t = 0	Energy trapped by PSII and used for reduction of QA per active reaction center
ETo/RC	Electron-transport flux beyond $Q_A^{-}$ per active reaction center at t = 0	Electron transport from reduced QA into the intersystem electron-transport chain
REo/RC	Electron flux reducing the terminal acceptors on the PSI acceptor side per active reaction center	Efficiency of electron transfer toward the terminal acceptors beyond PSI
φ(Po)	Maximum quantum yield of primary PSII photochemistry, TRo/ABS	Probability that an absorbed photon is trapped by PSII and reduces QA; mathematically equivalent to Fv/Fm
ψ(Eo)	Probability that a trapped exciton moves an electron beyond $Q_A^{-}$, ETo/TRo	Efficiency with which trapped excitation energy supports electron transport beyond the primary quinone acceptor
ABS/CSo	Absorption flux per excited cross-section at t = 0	Excitation energy absorbed per leaf cross-section at the onset of illumination
DIo/CSo	Dissipated energy flux per excited cross-section at t = 0	Non-photochemical loss of absorbed excitation energy per cross-section at the onset of illumination
TRo/CSo	Trapped energy flux per excited cross-section at t = 0	Excitation energy trapped by PSII reaction centers per leaf cross-section
ETo/CSo	Electron-transport flux per excited cross-section at t = 0	Electron transport beyond QA per leaf cross-section
ABS/CSm	Absorption flux per excited cross-section at maximum fluorescence	Absorbed excitation energy per cross-section at the maximum-fluorescence state
DIo/CSm	Dissipated energy flux per excited cross-section at maximum fluorescence	Energy dissipated as heat and fluorescence per cross-section at the maximum-fluorescence state

Flux parameters are relative JIP-test quantities. RC, PSII reaction center; CS, excited leaf cross-section; QA, primary quinone electron acceptor of PSII; PSI, photosystem I.

. The subscript “o” denotes the onset of fluorescence induction, whereas CSo and CSm refer to the excited leaf cross-section at the onset of illumination and at maximum fluorescence, respectively. The parents and the first generation data provided for all traits in Table S1.

2.4. Generation Mean Analysis

Generation mean analysis was performed following the methodology of Mather and Jinks [7] to detect and characterize the genetic effects underlying each fluorescence parameter.

2.4.1. Scaling Test

To test for the presence and type of non-allelic (epistatic) interactions, three scaling tests (A, B, and C) were computed as:

A = 2(BC₁) − P₁ − F₁;

B = 2(BC₂) − P₂ − F₁;

C = 4(F₂) − 2(F₁) − P₁ − P₂.

Significant departure of A, B, or C from zero indicates the presence of epistasis.

2.4.2. Six-Parameter Model

The generation mean for each generation (Ȳ) was modelled as:

Ȳ = m + α[d] + β[h] + α²[i] + 2αβ[j] + β²

(1)

where m is the mid-parental value, [d] is the additive effect, [h] is the dominance effect, [i] is the additive × additive epistatic interaction, [j] is the additive × dominance interaction, and [l] is the dominance × dominance interaction. The generation-specific coefficients (α, β) are as defined by Mather and Jinks [7]. Parameters were estimated using weighted least squares, where weights were assigned as the reciprocal of the variance of each generation mean (w = 1/Var). The adequacy of the fitted genetic model was evaluated using a chi-square ${\mathrm{\chi }}^2$ goodness-of-fit test. A non-significant ${\mathrm{\chi }}^2$ result $p>0.05$ indicated that there was no significant evidence of lack of fit and that the fitted model adequately described the observed generation means. Conversely, a significant ${\mathrm{\chi }}^2$ result $p\le 0.05$ indicated inadequate model fit.

2.4.3. Variance Components

Genetic variance components were estimated from the six-generation variances as follows [2,7]:

(1)

Ew = 1/4(${\mathrm{V}}_{{\mathrm{P}}_1}$ + ${\mathrm{V}}_{{\mathrm{P}}_2}$ + 2${\mathrm{V}}_{{\mathrm{F}}_1}$);

(2)

D = 4${\mathrm{V}}_{{\mathrm{F}}_2}$ − 2(${\mathrm{V}}_{{\mathrm{BC}}_1}$ + ${\mathrm{V}}_{{\mathrm{BC}}_2}$ − Ew);

(3)

H = 4(${\mathrm{V}}_{{\mathrm{BC}}_1}$ + ${\mathrm{V}}_{{\mathrm{BC}}_2}-{\mathrm{V}}_{{\mathrm{F}}_2}$ − Ew);

(4)

F = ${\mathrm{V}}_{{\mathrm{BC}}_1}-{\mathrm{V}}_{{\mathrm{BC}}_2}$

Where EW is the non-genetic (environmental) variance component, D is the additive genetic variance, H is the dominance genetic variance, and F represents the covariance between additive and dominance effects across loci. The sign and magnitude of F indicate the average direction of dominance, and the ratio H/D reflects the degree of dominance.

2.4.4. Heritability Estimates

Broad-sense heritability (H²bs) was estimated as:

$${\mathrm{H}}^2\mathrm{bs}=({\mathrm{V}}_{{\mathrm{F}}_2}-\mathrm{EW})/{\mathrm{V}}_{{\mathrm{F}}_2}$$

where EW was estimated by five alternative methods (mean of VP₁ and VP₂; geometric mean; ${\mathrm{V}}_{{\mathrm{F}}_1}$; mean of three environmental estimates; and the weighted mean formula) to assess the stability of the heritability estimate. Narrow-sense heritability (H²ns) was estimated using the Warner [28] formula:

$${\mathrm{H}}^2\mathrm{ns}=(2{\mathrm{V}}_{{\mathrm{F}}_2}-({\mathrm{V}}_{{\mathrm{BC}}_1}+{\mathrm{V}}_{{\mathrm{BC}}_2}\left)\right)/{\mathrm{V}}_{{\mathrm{F}}_2}$$

2.4.5. Estimation of the Number of Effective Segregating Factors

The minimum number of gene loci (N) controlling each trait was estimated using six alternative formulae proposed by Lande [29], based on the squared difference between parental means relative to the segregating variance:

1: N = (${\overline{\mathrm{X}}}_{{\mathrm{P}}_2}$ − ${\overline{\mathrm{X}}}_{{\mathrm{P}}_1}$)²/8(${\mathrm{V}}_{{\mathrm{F}}_2}-{\mathrm{V}}_{{\mathrm{F}}_1}$);

2: N = (${\overline{\mathrm{X}}}_{{\mathrm{P}}_2}-{\overline{\mathrm{X}}}_{{\mathrm{P}}_1}$)²/8[${\mathrm{V}}_{{\mathrm{F}}_2}$ − (0.5${\mathrm{V}}_{{\mathrm{F}}_1}$ + 0.25${\mathrm{V}}_{{\mathrm{P}}_1}$ + 0.25${\mathrm{V}}_{{\mathrm{P}}_2}$)];

3: N = (${\overline{\mathrm{X}}}_{{\mathrm{P}}_2}-{\overline{\mathrm{X}}}_{{\mathrm{P}}_1}$)²/8(${\mathrm{V}}_{{\mathrm{BC}}_1}-{\mathrm{V}}_{{\mathrm{BC}}_2}$);

4: N = (${\overline{\mathrm{X}}}_{{\mathrm{P}}_2}$ − ${\overline{\mathrm{X}}}_{{\mathrm{P}}_1}$)²/{8[(${\mathrm{V}}_{{\mathrm{BC}}_1}-{\mathrm{V}}_{{\mathrm{BC}}_2}$)] − [(2${\mathrm{V}}_{{\mathrm{F}}_1}$ + 0.5${\mathrm{V}}_{{\mathrm{P}}_1}$ + 0.5${\mathrm{V}}_{{\mathrm{P}}_2}$)]};

5: N = (${\overline{\mathrm{X}}}_{{\mathrm{P}}_2}-{\overline{\mathrm{X}}}_{{\mathrm{P}}_1}$)²/{4[${\mathrm{V}}_{{\mathrm{BC}}_1}$ − 0.5(${\mathrm{V}}_{{\mathrm{F}}_1}$ + ${\mathrm{V}}_{{\mathrm{P}}_1}$)]};

6: N = (${\overline{\mathrm{X}}}_{{\mathrm{P}}_2}-{\overline{\mathrm{X}}}_{{\mathrm{P}}_1}$)²/4[${\mathrm{V}}_{{\mathrm{BC}}_2}$ − 0.5(${\mathrm{V}}_{{\mathrm{P}}_1}$ + ${\mathrm{V}}_{{\mathrm{P}}_2}$)].

The median value across the six estimates was used as the final reported estimate of N for each trait.

Under ideal model assumptions, these formulae estimate the minimum number of effective segregating factors rather than the literal number of causal genes. Their assumptions include the absence of epistasis and linkage, approximately equal allelic effects, and substantial allelic divergence between the parents. Because some of these assumptions may be violated in the present crosses, particularly for traits showing significant scaling tests, the resulting values were treated as descriptive, model-dependent indices. Negative, near-zero, or otherwise inadmissible values were considered non-estimable and were not assigned a biological locus-count interpretation.

2.5. Statistical Analysis

Before the RCBD analysis, the three within-plot leaf observations were averaged to obtain one plot-level value for each generation within each block. For each cross and trait, the following model was considered:

$${\mathrm{Y}}_{\mathrm{ij}}=\mathsf{\mu }+{\mathrm{G}}_{\mathrm{i}}+{\mathrm{B}}_{\mathrm{j}}+{\mathsf{\epsilon }}_{\mathrm{ij}}$$

where ${\mathrm{Y}}_{\mathrm{ij}}$ is the plot-level mean of the $\mathrm{i}$th generation in the $\mathrm{ij}$th block, $\mathsf{\mu }$ is the overall mean, ${\mathrm{G}}_{\mathrm{i}}$ is the fixed effect of generation, ${\mathrm{B}}_{\mathrm{j}}$ is the random effect of block, and ${\mathsf{\epsilon }}_{\mathrm{ij}}$ is the residual term. With six generations and three blocks, the degrees of freedom were 5 for generation, 2 for block, and 10 for error. Generation effects were tested against the residual mean square. Significance was assessed at $p<0.05$ and $p<0.01.$

For each cross and fluorescence parameter, the three leaf measurements within each generation × block plot were treated as subsamples and averaged to provide one plot-level observation.

Generation mean parameters were estimated by weighted least squares, with weights defined as the reciprocal of the variance of each generation mean. The significance of the estimated genetic effects was evaluated using their associated standard errors. The adequacy of the fitted genetic model was evaluated using a chi-square goodness-of-fit test, with $p<0.05$ indicating no significant lack of fit. No separate Least Significate Differences (LSD) grouping is reported. Analysis of variance (ANOVA) for all traits was performed to assess differences among generations within each cross using SAS software (version 9.4; SAS Institute Inc., Cary, NC, USA [30]).

3. Results

3.1. Analysis of Variance Among Generations

The analysis of variance (ANOVA) revealed highly significant differences (p ≤ 0.01) among generations for the majority of OJIP-derived chlorophyll fluorescence parameters in both crosses (

Table 2. Analysis of variance of traits in different generations.

N-92-9 × Ehsan
S.O.V	df	Means of Squares
		Fo	Fm	Fv	Fv/Fm
Repeat	2	341.458	16,743.779	6635.086	0.009
Generations	5	8346.91 **	137,162.449 **	125,276.458 **	0.139 **
Error	10	226.607	12,834.382	11,961.747	0.044
C.V(%)		21.942	30.288	35.961	30.693
		ABS/RC	TRo/RC	ETo/RC	REo/RC
Repeat	2	0.177	0.103	0.014	0.003
Generations	5	4.361 **	1.24 **	0.277 **	0.084 **
Error	10	0.25	0.118	0.016	0.014
C.V(%)		30.507	38.601	16.228	26.828
		φ(Po)	ψ(Eo)	ABS/CSo	DIo/CSo
Repeat	2	0.005	0.016	202.178	8.756
Generations	5	0.103 **	0.119	5517.664 **	229.084 **
Error	10	0.028	0.068	180.724	10.95
C.V(%)		24.011	35.294	17.941	22.93
		TRo/CSo	ETo/CSo	ABS/CSm	DIo/CSm
Repeat	2	7.642	77.015	47.792	107.022
Generations	5	4950.399 **	2086.955 **	93,824.339 **	4105.855 **
Error	10	101.472	108.591	12,491.94	222.392
C.V(%)		20.466	24.706	33.204	22.189
Kohdasht × Ehsan
S.O.V	df	Means of Squares
		Fo	Fm	Fv	Fv/Fm
Repeat	2	2.098	3860.409	318.571	0.01
Generations	5	205.389 **	67,360.38 **	38,110.024 **	0.034 **
Error	10	118.306	10,122.920	9314.849	0.01
C.V(%)		10.877	19.502	24.742	13.007
		ABS/RC	TRo/RC	ETo/RC	REo/RC
Repeat	2	0.009	0.002	0.11 **	0.002
Generations	5	1.383 **	0.307 **	0.114 **	0.137 **
Error	10	0.128	0.008	0.012	0.005
C.V(%)		20.095	6.371	12.286	17.003
		φ(Po)	ψ(Eo)	ABS/CSo	DIo/CSo
Repeat	2	0.021	0.01	0.094	10.486
Generations	5	0.062 **	0.015 **	1238.893 **	73.143 **
Error	10	0.017	0.009	94.596	4.327
C.V(%)		17.532	13.957	10.541	11.201
		TRo/CSo	ETo/CSo	ABS/CSm	DIo/CSm
Repeat	2	84.788	40.986 *	2573.126	141.425
Generations	5	35.114	553.749 **	14,872.625	1079.755 **
Error	10	62.356	13.710	8484.507	58.941
C.V(%)		10.749	7.205	20.021	8.265

*, **: significant at 5% and 1% probability levels, respectively. S.O.V: source of variation. C.V: coefficient of variation.

). In the N-92-9 × Ehsan cross, significant differences among generation plot means were detected for 14 of the 16 fluorescence parameters. Thirteen parameters were significant at $p<0.01$ whereas φ(Po) was significant at $p<0.05$. Fv/Fm and ψ(Eo) were nonsignificant. Coefficients of variation (CV) in this cross ranged from 16.23% to 38.60%, reflecting moderate to high phenotypic variability within generations (a pattern expected given the genetic segregation occurring in F₂ and backcross generations).

In the Kohdasht × Ehsan cross, significant generation effects were detected for 12 parameters. Fv, Fv/Fm, and φ(Po) were significant at $p<0.05$ while Fm, ABS/RC, TRo/RC, ETo/RC, REo/RC, ABS/CSo, DIo/CSo, ETo/CSo, and DIo/CSm were significant at $p<0.01$ ψ(Eo), and TRo/CSo and ABS/CSm were nonsignificant. The CV values in Kohdasht × Ehsan were comparatively lower, ranging from 6.37% to 20.10%, indicating greater phenotypic uniformity relative to the N-92-9 × Ehsan cross. This cross-specific pattern of significance suggests that the genetic divergence between parental lines differs between the two crosses for certain PSII-related traits, and that the information content of generation mean analysis will therefore differ accordingly between crosses.

The significant mean squares for generations in the majority of traits confirm the presence of heritable genetic variability in chlorophyll fluorescence parameters, which is a fundamental prerequisite for genetic improvement through selection and hybridization in wheat.

3.2. Generation Means and Phenotypic Expression

In the N-92-9 × Ehsan cross, the parental lines showed distinct mean values for several parameters, confirming adequate genetic divergence between N-92-9 (P₁) and Ehsan (P₂) as a prerequisite for generation mean analysis. For instance, mean values for Fo were 97.11 (P₁) and 95.78 (P₂), while the F₁ generation exhibited a mean of 103.17–104.36, exceeding both parental values. Similarly, Fv/Fm in F₁ (0.812) exceeded both P₁ (0.799) and P₂ (0.806), providing evidence for dominance gene action in the expression of this critical PSII efficiency parameter.

For the majority of traits, the F₁ mean exceeded the mid-parent value, indicating positive dominance in the direction of higher photosynthetic efficiency. The proximity of F₁ means to one of the parental values for certain traits indicated partial-to-complete dominance, where alleles from the dominant parent exert a predominant influence on phenotypic expression.

Consistent with theoretical expectations under positive dominance gene action, the F₂ generation mean was intermediate between the mid-parent value and the F₁ mean for most traits. This is a direct and mathematically expected consequence of the reduction in heterozygosity from 100% in F₁ to 50% in F₂ following one generation of self-pollination. Under the additive–dominance model, the expected F₂ mean is:

$${\overline{F}}_2=m+{\displaystyle \frac{1}{2}}\left[h\right]$$

which is necessarily less than ${\overline{F}}_1=m+\left[h\right]$ when [h] > 0. This reduction in mean performance from F₁ to F₂ therefore reflects the halving of dominance expression as heterozygosity declines, and should not be interpreted as inbreeding depression in the strict sense. Across both crosses, the fluorescence parameters exhibited a mixture of positive and negative heterotic deviations from the mid-parent value, with performance-related indices such as the performance index (PIABS) and quantum yield parameters (ΦPo, ψEo) generally showing positive heterosis, indicating hybrid superiority for photosynthetic efficiency, whereas parameters reflecting initial fluorescence rise and energy dissipation (e.g., Fo, Vj, Mo) tended to display smaller or negative heterotic responses (Figure 2). The occurrence of substantial heterosis for the majority of these traits points to a considerable contribution of dominance and/or non-additive gene action in governing chlorophyll fluorescence-related photosynthetic efficiency. Correspondingly, inbreeding depression was detected for most parameters in both crosses (Figure 3), generally in the same direction as, but proportionally attenuated relative to, the heterosis observed in Figure 2, consistent with the theoretical expectation that traits controlled by dominant gene action lose part of their heterotic advantage upon selfing due to the fixation of homozygous genotypes in the F₂ generation. Furthermore, the cross-specific differences in both the sign and magnitude of heterosis and inbreeding depression between the Kohdasht × Ehsan and N-92-9 × Ehsan crosses suggest that the genetic background of the parental lines modulates the expression of non-additive effects underlying chlorophyll fluorescence traits, a finding with direct implications for parental selection in breeding programs aimed at improving photosynthetic performance under field conditions.

3.3. Generation Variances and Genetic Segregation

As expected from genetic theory, the F₂ generation consistently exhibited the highest phenotypic variance among all generations, owing to maximum genetic segregation and recombination in this population [7]. In the N-92-9 × Ehsan cross, the variance for Fo in F₂ (444.91) was approximately 9.4-fold and 10.9-fold higher than in P₁ (47.36) and P₂ (40.70), respectively. The variance for Fm in F₂ (31,629.75) substantially exceeded parental variances (P₁ = 2192.19; P₂ = 1323.53). Comparable trends were observed in the Kohdasht × Ehsan cross, though with less pronounced variance inflation, consistent with the lower overall CV values observed in that cross.

The environmental variance component (EW), estimated as the weighted mean of parental and F₁ variances following the method of Mather and Jinks [7], was used to partition total phenotypic variance into genetic and non-genetic components prior to estimation of D, H, and F. The consistently low EW values relative to total F₂ variance confirm that the majority of phenotypic variation in segregating generations is genetic rather than environmental in origin.

3.4. Scaling Tests and Selection of Genetic Model

In the N-92-9 × Ehsan cross, one or more scaling tests were significant (p ≤ 0.05) for Fo, ABS/CSo, DIo/CSo, and TRo/CSo, indicating the inadequacy of the simple additive–dominance model and the presence of non-allelic gene interactions (epistasis) for these traits. For the remaining twelve parameters in this cross (including Fm, Fv, Fv/Fm, ABS/RC, TRo/RC, ETo/RC, REo/RC, φ(Po), ETo/CSo, ABS/CSm, DIo/CSm, and ψ(Eo)) all three scaling tests were non-significant, confirming that the simple additive–dominance model (m, [d], [h]) was adequate.

In the Kohdasht × Ehsan cross, significant scaling tests were obtained for Fv, ABS/RC, TRo/RC, ETo/RC, REo/RC, ψ(Eo), DIo/CSo, and ETo/CSo, necessitating the full six-parameter model ([m], [d], [h], [i], [j], [l]) for these traits. For the remaining parameters in this cross, the additive–dominance model provided an adequate fit, as confirmed by non-significant chi-square (χ²) goodness-of-fit statistics (p > 0.05).

These results indicate that the genetic architecture of chlorophyll fluorescence parameters is both trait-specific and cross-specific, reflecting the differing allelic compositions and gene interaction structures of the two parental combinations.

3.5. Gene Effects from Generation Mean Analysis

3.5.1. Additive Effects [d]

The additive effect [d] reflects one-half the difference between parental means and indicates which parent contributes the increasing alleles for a given trait [7]. In the N-92-9 × Ehsan cross, positive [d] values (indicating that N-92-9 (P₁) contributes more increasing alleles) were observed for Fo, TRo/RC, REo/RC, φ(Po), ABS/CSo, TRo/CSo, ABS/CSm, and DIo/CSm. In the Kohdasht × Ehsan cross, positive [d] values were detected for Fo, ABS/RC, TRo/RC, ETo/RC, ψ(Eo), ABS/CSo, DIo/CSo, and DIo/CSm, indicating that Kohdasht (P₁) carries more increasing alleles for these parameters (Table 2).

3.5.2. Dominance Effects [h] and Their Predominance

The net dominance effect [h] exceeded the additive effect [d] in absolute magnitude for all traits in both crosses, with the sole exception of TRo/CSo in the Kohdasht × Ehsan cross. In the two crosses examined under the environmental conditions of this experiment, the absolute estimate of [h] exceeded that of [d] for most traits. This pattern indicates an important contribution of non-additive gene action within these specific parental combinations. It should not be interpreted as evidence that dominance universally predominates for PSII fluorescence parameters across wheat germplasm or environments.

It is important to note, however, that [h] from generation mean analysis represents the net algebraic sum of dominance deviations across all segregating loci. When dominance deviations act in opposing directions at different loci, they partially cancel in the mean, potentially yielding a moderate net [h] even when individual locus dominance effects are large. This property of [h] must be considered when comparing it with the dominance variance component H from variance component analysis.

3.5.3. Epistatic Effects [i], [j], and [l]

For traits requiring the full six-parameter model, the magnitudes and signs of the epistatic components are presented in

Table 3. Estimates of gene effects for chlorophyll fluorescence parameters in wheat cross.

N-92-9 × Ehsan
Traits	Additive effect [d]	Dominant effect [h]	Additive × Additive [i]	Additive × Dominant [j]	Dominance × Dominance [l]
Fo	0.667 ± 2.875	−751.189 ± 48.354 **	−258.712 ± 19.915 **	−29.934 ± 12.855 *	499.2 ± 29.872 **
Fm	−2.723 ± 23.455	−2673.528 ± 394.574 **	−927.445 ± 162.501 **	−126.667 ± 104.894	1768.612 ± 243.752 **
Fv	−2.667 ± 22.207	−2919.834 ± 373.568 **	−1013.5 ± 153.850 **	−126.056 ± 99.310	1991.889 ± 230.775 **
Fv/Fm	−0.004 ± 0.043	−3.094 ± 0.723 **	−1.042 ± 0.298 **	0.119 ± 0.193	2.062 ± 0.447 **
ABS/RC	−0.065 ± 0.115	−18.977 ± 1.934 **	−7.039 ± 0.797 **	−0.75 ± 0.514	12.341 ± 1.195 **
TRo/RC	0.002 ± 0.075	−8.768 ± 1.255 **	−3.235 ± 0.517 **	−0.581 ± 0.334	5.819 ± 0.776 **
ETo/RC	−0.006 ± 0.029	−4.461 ± 0.488 **	−1.585 ± 0.201 **	−0.201 ± 0.130	2.966 ± 0.302 **
REo/RC	0.00003 ± 0.022	−2.355 ± 0.364 **	−0.928 ± 0.15 **	−0.105 ± 0.097	1.608 ± 0.225 **
φ(Po)	0.011 ± 0.037	−2.737 ± 0.615 **	−0.962 ± 0.254 **	−0.22 ± 0.164	1.81 ± 0.38 **
ψ(Eo)	-0.007 ± 0.059	−2.749 ± 0.981 **	−1.149 ± 0.404 **	−0.024 ± 0.261	1.802 ± 0.606 **
ABS/CSo	0.459 ± 2.874	−568.863 ± 48.334 **	-195.506 ± 19.906 **	-55.756 ± 12.849 **	376.427 ± 29.859 **
DIo/CSo	−0.014 ± 0.739	−135.385 ± 12.428 **	−47.776 ± 5.119 **	−8.169 ± 3.304 **	90.976 ± 7.678 **
TRo/CSo	0.155 ± 2.23	−443.962 ± 37.499 **	−130.385 ± 15.444 **	−29.004 ± 9.969 **	292.469 ± 23.165 **
ETo/CSo	−1.133 ± 2.602	−376.596 ± 43.762 **	−134.926 ± 18.023 **	−10.789 ± 11.634	249.913 ± 27.035 **
ABS/CSm	4.667 ± 20.824	−2438.122 ± 350.304 **	−861.374 ± 144.27 **	−148.041 ± 93.126	1650.304 ± 216.404 **
DIo/CSm	0.5 ± 2.969	−535.889 ± 49.942 **	−191.389 ± 20.568 **	−16.278 ± 13.277	349.556 ± 30.852 **
Kohdasht × Ehsan
Traits	Additive effect [d]	Dominant effect [h]	Additive× Additive [i]	Additive× Dominant [j]	Dominance × Dominance [l]
Fo	0.112 ± 2.25	−106.889 ± 37.842 **	−44.667 ± 15.585 **	−3.556 ± 10.06	70.667 ± 23.377 **
Fm	−14.889 ± 21	−2041.834 ± 353.271 **	−747.834 ± 145.491 **	−101.945 ± 93.914	1379.889 ± 218.236 **
Fv	−1.75 ± 21.791	−1504.445 ± 366.576 **	−504 ± 150.97 **	−192.723 ± 97.451 *	1009.112 ± 226.455 **
Fv/Fm	−0.008 ± 0.019	−1.373 ± 0.308 **	−0.427 ± 0.127 **	−0.15 ± 0.082	0.959 ± 0.19 **
ABS/RC	0.004 ± 0.079	−10.262 ± 1.328 **	−3.829 ± 0.547 **	−0.261 ± 0.354 **	6.757 ± 0.821 **
TRo/RC	0.041 ± 0.02 *	−4.472 ± 0.32 **	−1.658 ± 0.132 **	−0.286 ± 0.085 **	2.956 ± 0.198 **
ETo/RC	0.011 ± 0.026	−2.945 ± 0.428 **	−1.068 ± 0.177 **	−0.243 ± 0.114 *	1.92 ± 0.265 **
REo/RC	−0.009 ± 0.015	−3.419 ± 0.242 **	−1.313 ± 0.1 **	−0.144 ± 0.065 *	2.202 ± 0.149 **
φ(Po)	−0.005 ± 0.026	−2.005 ± 0.436 **	−0.672 ± 0.18 **	−0.156 ± 0.116	1.343 ± 0.27 **
ψ(Eo)	0.007 ± 0.02	−0.888 ± 0.33 **	−0.368 ± 0.136 **	−0.199 ± 0.088 **	0.52 ± 0.204 **
ABS/CSo	0.167 ± 1.959	−285.223 ± 32.94 **	−104.223 ± 13.566 **	−12.112 ± 8.757	189.112 ± 20.349 **
DIo/CSo	0.085 ± 0.43	−73.47 ± 7.22 **	−26.539 ± 2.974 **	−4.626 ± 1.92 **	48.603 ± 4.461
TRo/CSo	−0.607 ± 1.667	−41.748 ± 28.036	−14.79 ± 11.547	−2.208 ± 7.453	29.484 ± 17.32
ETo/CSo	−0.416 ± 0.785	−196.95 ± 13.206 **	−70.455 ± 5.439 **	−11.624 ± 3.511 **	131.481 ± 8.158 **
ABS/CSm	−7.473 ± 20.951	−796.25 ± 352.443 *	−285.556 ± 145.15*	−55.723 ± 93.694	590.167 ± 217.725 **
DIo/CSm	0.223 ± 2.006	−262.38 ± 33.741 **	−97.683 ± 13.896 **	−8.905 ± 8.97	173.143 ± 20.844 **

*, **: significant at 5% and 1% probability levels, respectively.

. Significant additive × additive interaction [i] was detected for all traits requiring the six-parameter model in both crosses, with the exception of TRo/CSo in Kohdasht × Ehsan. The opposite signs of [i] and [d] observed for Fo, TRo/RC, REo/RC, φ(Po), ABS/CSo, TRo/CSo, ABS/CSm, and DIo/CSm indicate that additive × additive interactions partially counteract the main additive effects at these loci, a pattern associated with complex polygenic control [31,32].

Significant additive × dominance interaction [j] was detected for Fo, ABS/CSo, DIo/CSo, and TRo/CSo in N-92-9 × Ehsan, and for Fv, ABS/RC, TRo/RC, ETo/RC, REo/RC, ψ(Eo), DIo/CSo, and ETo/CSo in Kohdasht × Ehsan. The [j] component, which requires simultaneous heterozygosity and allelic divergence between loci, cannot be fixed by inbreeding and is expected to diminish progressively as generations advance toward homozygosity.

Significant dominance × dominance interaction [l] was detected for all traits in both crosses except TRo/CSo and DIo/CSo in Kohdasht × Ehsan. Critically, [h] and [l] exhibited opposite signs for all traits where both components were significant, indicating the prevalence of duplicate epistasis [33]. Under duplicate epistasis, at least one dominant allele at either of two interacting loci is sufficient to produce the phenotypic effect, resulting in a 15:1 segregation ratio. This type of interaction tends to reduce the variance among homozygous genotypes relative to what would be expected under independent gene action, thereby retarding the rate of genetic gain under simple selection [34].

3.6. Variance Components: D, H, and F

3.6.1. Relationship Between [h] and H

Despite the consistent predominance of the net dominance effect [h] over [d] in generation mean analysis, the additive variance component (D) exceeded the dominance variance component (H) for the majority of traits in both crosses. In the N-92-9 × Ehsan cross, H exceeded D only for ψ(Eo) and ABS/CSm. In the Kohdasht × Ehsan cross, H exceeded D only for Fo, Fm, φ(Po), ψ(Eo), and TRo/CSo (

Table 4. Genetic parameters and components of variation for chlorophyll fluorescence parameters.

	(F)		(H)		(D)		(D × H1/2/F)		(D1/2/H)
Traits	C1	C2	C1	C2	C1	C2	C1	C2	C1	C2
Fo	83.125	−29.861	295.324	385.612	742.158	317.694	0.0004	−0.0003	0.159	1.474
Fm	−472.130	−5584.900	16,915.22	42,125.19	54,801.89	32,601.96	−5.094	−4.067	0.096	1.67
Fv	−11,559.310	6703.01	26,300.96	21,738.78	48,410.90	42,362.11	−9.079	7.279	0.296	0.264
Fv/Fm	0.045	0.001	0.124	0.019	0.153	0.033	2.388	1.632	0.655	0.333
ABS/RC	0.029	−0.036	0.092	0.046	0.848	0.457	0.372	−1.713	0.012	0.011
TRo/RC	0.024	0	0.104	0.002	0.466	0.039	0.496	0	0.05	0.003
ETo/RC	−0.007	−0.002	0.032	0.074	0.082	0.034	−2.668	−0.819	0.153	4.804
REo/RC	0.001	0	0.004	0.011	0.046	0.013	5.435	0	0.008	0.626
φ(Po)	0.021	0.006	0.044	0.088	0.147	0.034	3.325	2.006	0.087	6.699
psi(Eo)	0.01	−0.002	0.6	0.028	0.077	0.024	0.62	−2.977	62.184	1.362
ABS/CSo	165.967	−22.77	378.236	166.824	630.606	272.588	0.0007	−0.0006	0.36	0.375
DIo/CSo	17.366	1.518	30.258	13.978	40.845	11.281	0.015	0.01	0.549	1.536
TRo/CSo	120.144	3.166	311.708	412.28	365.618	98.366	0.002	7.807	0.727	17.567
ETo/CSo	149.539	−17.924	198.016	12.436	592.12	78.76	0.002	−0.019	0.112	0.025
ABS/CSm	−5546.27	3128.21	30,567.22	25,204.52	27,272.39	37,131.24	−6.654	3.33	1.257	0.461
DIo/CSm	−106.545	55.876	163.848	108.844	842.966	303.126	−0.0008	0.002	0.037	0.129

C1 and C2 present N-92-9 × Ehsan and Kohdasht × Ehsan, respectively.

and Figure 4).

This apparent divergence between the relative magnitudes of [h] vs. [d] and H vs. D is not a methodological inconsistency. It reflects a fundamental statistical distinction between the two frameworks: [h] is a signed algebraic quantity in which dominance deviations at individual loci may cancel one another, while H is a sum of squared deviations that is insensitive to such cancellation. When dominance deviations at individual loci act in opposing directions (as occurs when favorable dominant alleles are dispersed between the two parents rather than concentrated in one) the net [h] may be large while H remains moderate. The present results are therefore consistent with a dispersed distribution of dominant alleles across the two parental lines, a pattern confirmed by the F/√(DH) analysis below.

The larger D relative to H for most traits indicates that, despite the predominance of net dominance expression, additive genetic variance constitutes the larger component of total genetic variance for the majority of traits. This has an important corollary: long-term recurrent selection within advanced inbred generations remains a viable complementary strategy to hybrid breeding for improving these traits.

3.6.2. Direction of Dominance: F Component and F/√(DH) Ratio

The covariance component F, which reflects the association between additive and dominant gene effects across loci, showed negative values in the N-92-9 × Ehsan cross for Fm, Fv, TRo/RC, ETo/RC, REo/RC, φ(Po), TRo/CSo, ETo/CSo, ABS/CSm, and DIo/CSm. Negative F values indicate that at these loci, the parent carrying more increasing alleles tends to carry the recessive allele; that is, dominance acts in the direction of trait reduction. In the Kohdasht × Ehsan cross, negative F values were observed for Fo, Fm, Fv/Fm, ABS/RC, ETo/RC, ψ(Eo), ABS/CSo, ETo/CSo, and TRo/CSo.

The ratio F/√(DH), as defined by Mather and Jinks [7], provides a standardized index of the average direction of dominance across all segregating loci. Values approaching +1 indicate concentration of dominant alleles in P₁, values approaching −1 indicate concentration in P₂, and values near zero indicate approximately equal dispersal of dominant alleles between parents. In the N-92-9 × Ehsan cross, F/√(DH) ranged from −9.079 to 5.435, while in the Kohdasht × Ehsan cross, values ranged from −4.067 to 7.807. The wide range and variable signs of this ratio across traits confirm that the direction of dominance is trait-specific and that dominant alleles for different fluorescence parameters are not uniformly concentrated in either parent, consistent with the polygenic and multi-pathway nature of PSII function.

3.6.3. Degree of Dominance: √(H/D)

The degree of dominance, estimated as √(H/D), provides a locus-averaged index of the magnitude of dominance relative to additive variance. Values of √(H/D) < 1 indicate partial dominance, =1 complete dominance, and >1 overdominance or pseudo-overdominance [35]. It must be noted that variance component analysis alone cannot distinguish between true overdominance at a single locus and pseudo-overdominance arising from repulsion-phase linkage between loci with opposing dominance, a distinction that requires molecular marker analysis [35].

Evidence for overdominance or pseudo-overdominance (√(H/D) > 1) was detected for ψ(Eo) (√(H/D) = 2.790) and ABS/CSm (1.059) in N-92-9 × Ehsan, and for Fo (1.101), Fm (1.136), ETo/RC (1.474), φ(Po) (1.608), ψ(Eo) (1.080), DIo/CSo (1.114), and TRo/CSo (2.047) in Kohdasht × Ehsan. For all remaining traits, √(H/D) < 1, indicating partial dominance as the prevailing mode of gene action at the locus-averaged level.

3.7. Broad-Sense and Narrow-Sense Heritability

Heritability estimates for all traits in both crosses are presented in Table 4. Broad-sense heritability (H²bs) ranged from moderate to high across traits and crosses. The highest H²bs was recorded for Fv/Fm in N-92-9 × Ehsan (0.991), indicating that nearly all phenotypic variation in this parameter is genetic in origin under the conditions of this experiment. In the Kohdasht × Ehsan cross, the highest H²bs was 0.697 for ABS/CSm, reflecting a substantial but more moderate genetic component.

Narrow-sense heritability (H²ns) values were consistently lower than their broad-sense counterparts across all traits and both crosses, confirming that a substantial proportion of total genetic variance is non-additive. The disparity between H²bs and H²ns was particularly pronounced for traits where H exceeded D in the variance component analysis, consistent with the expectation that a larger dominance component reduces narrow-sense relative to broad-sense heritability.

These heritability patterns have direct implications for breeding strategy: the high H²bs values indicate that phenotypic selection can effectively discriminate among genotypes on a genetic basis, but the lower H²ns values indicate that much of the selectable genetic variation is non-additive and therefore cannot be fixed by inbreeding, a pattern that favors hybrid breeding over pedigree or bulk selection for most traits.

3.8. Estimation of Effective Gene Number

The minimum number of effective gene factors (N) controlling each trait, estimated using the six formulae of Lande [29], is presented in

Table 5. Heritability estimates and model-dependent effective-factor estimates for the evaluated fluorescence parameters.

	Average of Gene Number		h2b		h2n
	C1	C2	C1	C2	C1	C2
Fo	0.036	0.185	0.795	0.716	0.629	0.338
Fm	58.293	11.303	0.868	0.911	0.734	0.519
Fv	7.06	0.015	0.858	0.879	0.644	0.675
Fv/Fm	2.2	1.462	0.991	0.939	0.701	0.715
ABS/RC	2.867	−1.968	0.620	0.503	0.168	0.267
TRo/RC	3.576	0.000	0.526	0.725	0.425	0.700
ETo/RC	2.122	−0.024	0.837	0.923	0.674	0.400
REo/RC	0.00	0.000	0.667	0.506	0.625	0.223
φ(Po)	2.056	2.381	0.974	0.975	0.846	0.411
psi(Eo)	0.000	1.185	0.979	0.579	0.181	0.211
ABS/CSo	0.020	0.568	0.829	0.623	0.599	0.389
DIo/CSo	0.0003	−1.27	0.914	0.841	0.644	0.459
TRo/CSo	0.003	0.027	0.943	0.957	0.644	0.280
ETo/CSo	−0.0004	0.042	0.855	0.708	0.711	0.794
ABS/CSm	1.649	0.356	0.634	0.409	0.275	0.806
DIo/CSm	0.892	0.044	0.715	0.635	0.627	0.304

C1 and C2 present N-92-9 × Ehsan and Kohdasht × Ehsan, respectively. Effective-factor estimates are conditional on assumptions of no epistasis, no linkage, equal allelic effects, and parental allelic divergence. Negative or near-zero estimates are non-informative and should not be interpreted as biological locus counts.

. These estimates carry several important caveats: the formulae assume absence of epistasis, absence of linkage, equal gene effects, and complete allelic divergence between parents (one parent carrying all positive alleles, the other all negative alleles). Violations of any of these assumptions, which are common in polyploid crops such as hexaploid wheat, lead to underestimation of the true gene number [36,37].

In the N-92-9 × Ehsan cross, gene number estimates ranged from approximately 1 to 7.06 (highest for Fv), suggesting that between one and seven loci contribute detectable segregating effects under the model assumptions. In the Kohdasht × Ehsan cross, estimates ranged from non-estimable (negative values for ABS/RC; N = −1.968) to 11.303 (highest for Fm). Negative estimates are biologically impossible and arise as mathematical artefacts when the denominator becomes negative due to epistasis, dominance, or repulsion-phase linkage; such values are considered non-informative and excluded from interpretation [36]. Near-zero estimates reflect minimal parental divergence in mean relative to the segregating variance rather than genuine single-gene control.

The effective-factor estimates varied widely among traits and crosses and included negative, near-zero, and unusually large values. Negative values are biologically inadmissible and indicate failure of the denominator or violation of the underlying assumptions; they were therefore classified as non-estimable. Near-zero values likewise should not be interpreted as evidence of monogenic inheritance. For traits showing significant epistasis, the estimates are presented only for completeness and are not interpreted as precise locus numbers.

4. Discussion

4.1. Genetic Variation Among Generations as a Prerequisite for Analysis

The significant differences among generations detected by ANOVA for most chlorophyll fluorescence parameters in both crosses confirm that the six-generation design employed in this study was appropriate for generation mean analysis. The cross-specific pattern of significance (whereby ψ(Eo) was non-significant in N-92-9 × Ehsan while four parameters were non-significant in Kohdasht × Ehsan) reflects differential parental divergence between crosses rather than a limitation of the analytical approach. This cross-specificity is consistent with the general observation that the outcome of generation mean analysis is sensitive to the genetic distance between parental lines [7,25], and underscores the importance of selecting genetically divergent parents when designing generation mean experiments.

The moderate-to-high CV values observed, particularly in the N-92-9 × Ehsan cross, are expected consequences of genetic segregation in F₂ and backcross generations, and do not indicate unacceptable experimental error. The elevated phenotypic variance in F₂ relative to parental and F₁ generations is consistent with classical quantitative genetic theory and provides the necessary statistical power for partitioning genetic variance into additive and dominance components.

4.2. Predominance of Non-Additive Gene Action

The consistent predominance of the net dominance effect [h] over the additive effect [d] for all traits except TRo/CSo in Kohdasht × Ehsan is one of the central findings of this study. This pattern indicates that non-additive gene action is the primary driver of phenotypic expression in PSII-related fluorescence parameters in wheat flag leaves under the parental combinations studied. Non-additive genetic control of chlorophyll fluorescence traits is biologically plausible given the structural and regulatory complexity of the photosynthetic apparatus: PSII function is determined by the coordinated assembly and interaction of more than twenty protein subunits, multiple chlorophyll-binding complexes, and a suite of regulatory proteins involved in photoprotection, repair, and state transitions [16,17]. The expression of phenotypes arising from such multicomponent systems is inherently susceptible to dominance and epistatic effects at the molecular level.

The predominance of dominance effects in controlling quantitative traits in wheat has been reported previously for grain yield [9,37], yield components [5,8], and stress-related physiological traits. The present study extends this finding to OJIP fluorescence parameters, demonstrating that the same genetic pattern characterizes PSII function at the molecular level. This generality suggests that the dominance architecture of wheat quantitative traits may reflect fundamental properties of the hexaploid wheat genome (including the buffering effects of allopolyploidy and the expression of heterosis across multiple homeologous loci (rather than trait-specific phenomena.

The single exception (TRo/CSo in Kohdasht × Ehsan, where [d] exceeded [h]) indicates that the phenomenological trapping flux per excited cross-section is under predominantly additive genetic control in this parental combination. TRo/CSo is a measure of the total energy trapped at PSII reaction centers per unit leaf cross-section and is therefore sensitive to both the intrinsic efficiency of individual reaction centers and their numerical density in the leaf. The additive control of this parameter suggests that alleles affecting reaction center density or trapping probability at individual loci contribute independently and cumulatively to phenotypic expression, without strong dominance interactions. This result has practical breeding implications: additive control implies that TRo/CSo can be effectively improved through phenotypic selection in segregating populations, with expected genetic gain proportional to narrow-sense heritability [35].

4.3. Nature and Implications of Epistatic Interactions

The detection of significant epistasis for a substantial proportion of fluorescence parameters in both crosses extends the complexity of the genetic architecture beyond the simple additive–dominance framework. The requirement for the full six-parameter model for Fo, ABS/CSo, DIo/CSo, and TRo/CSo in N-92-9 × Ehsan, and for Fv, ABS/RC, TRo/RC, ETo/RC, REo/RC, ψ(Eo), DIo/CSo, and ETo/CSo in Kohdasht × Ehsan, indicates that inter-locus gene interactions contribute significantly to the phenotypic expression of these parameters. The cross-specific pattern of epistasis (with different sets of traits requiring the full model in each cross) further underscores that the nature of gene interaction is contingent on the specific allelic composition of the parental lines rather than being a universal property of the traits themselves.

The classification of epistasis as predominantly duplicate in type (evidenced by opposite signs of [h] and [l] for all epistatic traits) has important implications for understanding the genetic architecture of PSII function. Duplicate epistasis arises when dominant alleles at two or more interacting loci produce qualitatively similar phenotypic effects, so that the presence of at least one dominant allele at any of the interacting loci is sufficient to produce the dominant phenotype [34]. This type of interaction tends to reduce phenotypic variance among homozygous genotypes relative to heterozygous ones, because fixation of either dominant allele at the relevant loci achieves a similar phenotypic outcome. As a consequence, duplicate epistasis retards breeding progress under simple truncation selection: the effective number of favorable genotypic classes is reduced, and favorable allele combinations disrupted by recombination in F₂ may not be efficiently recovered in subsequent generations The presence of significant additive × additive interaction [i] for most traits implies that the additive value of alleles at one locus depends on the genotypic state at other loci, a form of context-dependence that complicates the prediction of breeding values from single-generation phenotypic data. However, the [i] component, unlike [h] and [l], can in principle be fixed by inbreeding, since it is fully expressed in homozygous genotypes. This means that advanced inbred lines may capture the favorable [i] contributions after sufficient generations of selfing, provided that the appropriate allele combinations are brought together through the initial cross [7].

The involvement of epistatic effects in controlling chlorophyll fluorescence parameters is consistent with findings reported for yield-related traits in wheat and other cereals. Epistatic effects have been documented for grain yield in maize [37], for grain yield per spike, thousand-grain weight, and harvest index in wheat [38,39], and for stress-tolerance traits in various crop species [25]. The present findings extend this literature to photosynthetic efficiency parameters, suggesting that the complex multi-locus genetic architecture of quantitative trait inheritance in cereals applies equally to traits directly reflecting the molecular performance of PSII.

4.4. Variance Components and Their Biological Interpretation

The finding that the additive variance component (D) exceeded the dominance component (H) for most traits (despite the consistent predominance of the net dominance effect [h] over [d] in generation mean analysis) requires careful interpretation, as it may appear paradoxical at first glance. As explained in the Results Section, this divergence reflects a fundamental statistical property of the two analytical frameworks rather than a biological contradiction. The key distinction is that [h] is directional (it can be positive or negative and is sensitive to cancellation of opposing contributions across loci), while H is non-directional (it accumulates squared deviations regardless of sign and is therefore insensitive to cancellation). When favorable and unfavorable dominant alleles are dispersed between the two parents (as indicated by the near-zero or variable F/√(DH) ratios observed in this study) [h] may be attenuated by cancellation while H reflects the true dispersion of dominance deviations across loci.

The practical implication of D > H for most traits is that, despite the expression of heterosis in F₁ hybrids, the majority of the genetic variance that can be exploited over multiple selection cycles resides in the additive component. This finding is consistent with the long-term success of pedigree-based selection in wheat improvement, even for traits that show clear dominance in early generations. It does not, however, diminish the value of hybrid breeding for immediate exploitation of heterosis: the large net [h] observed in this study indicates that F₁ hybrids will consistently outperform inbred parental lines for most fluorescence traits, even if the underlying variance structure is predominantly additive [35].

The variable and often extreme values of F/√(DH), ranging from −9.079 to 5.435 in N-92-9 × Ehsan and from −4.067 to 7.807 in Kohdasht × Ehsan, indicate that the dominant alleles controlling different fluorescence parameters are not uniformly distributed between the two parents. For traits with large positive F/√(DH), dominant alleles tend to be concentrated in P₁, while for traits with large negative values, they tend to be concentrated in P₂. This dispersed distribution of dominant alleles has an important implication for hybrid breeding: it suggests that neither parent is universally superior as a donor of dominant favorable alleles, and that the complementarity between the two parents in terms of allele dominance may itself be a source of heterosis in F₁ hybrids.

4.5. Heritability and Breeding Strategy

The high broad-sense heritability values observed for most traits (reaching 0.991 for Fv/Fm in N-92-9 × Ehsan) confirm that phenotypic measurements of chlorophyll fluorescence parameters under the conditions of this experiment are reliable reflections of the underlying genotypic differences. This is consistent with the known stability of OJIP fluorescence parameters under controlled measurement conditions and their high repeatability across replications [16,18]. The somewhat lower H²bs values in the Kohdasht × Ehsan cross (maximum 0.697 for ABS/CSm) likely reflect greater environmental sensitivity of the traits in this genetic background, possibly related to differences in the phenological characteristics and stress responsiveness of Kohdasht and Ehsan.

The consistently lower narrow-sense heritability values have important implications for the design of selection programs aimed at improving photosynthetic efficiency in wheat. Low H²ns indicates that a smaller fraction of the total phenotypic variance is attributable to additive genetic causes that can be transmitted reliably to offspring through selfing. Consequently, the expected response to mass selection (which is proportional to H²ns) will be relatively modest for most traits. This finding reinforces the conclusion from gene effect analysis that hybrid breeding, which captures both additive and dominance variance in a single generation, is the more effective strategy for most fluorescence parameters [40,41,42].

The exception (TRo/CSo in Kohdasht × Ehsan, where additive effects predominated) is likely to show more favorable response to selection, particularly given that its H²ns may be relatively higher than other traits. For this parameter, pedigree selection or bulk advancement in early segregating generations would be expected to yield satisfactory genetic gains, especially if selection intensity is maintained across multiple generations.

It should be emphasized that heritability estimates obtained in this study are specific to the parental combinations, generation structure, and environmental conditions employed. Extrapolation to other populations or environments should be undertaken with caution [7,35].

4.6. Degree of Dominance and Evidence for Overdominance

The evidence for overdominance or pseudo-overdominance (√(H/D) > 1) for several traits (particularly φ(Po) in Kohdasht × Ehsan (1.608) and ψ(Eo) in N-92-9 × Ehsan (2.790)) merits careful consideration. True overdominance, in which the heterozygote at a single locus genuinely exceeds both homozygotes, is theoretically possible but relatively rare in polyploid species [35]. More commonly, apparent overdominance detected by variance component analysis reflects pseudo-overdominance: the statistical consequence of repulsion-phase linkage (Ab/aB configuration) between two or more loci, where the dominant favorable allele at each locus is contributed by a different parent, such that the double heterozygote (AaBb) outperforms both parental homozygotes (AABB and aabb) and their alternative combinations [35].

Given the complexity of the hexaploid wheat genome (with its three constituent sub-genomes (A, B, D), extensive homeologous relationships, and documented occurrence of inter-genomic epistasis [11]) pseudo-overdominance is a biologically plausible explanation for the √(H/D) > 1 values observed in this study. The presence of significant dominance × dominance epistasis ([l]) for most traits where overdominance was detected is consistent with this interpretation, as inter-locus interactions of this type would contribute to the apparent elevation of √(H/D) beyond unity. Resolution of this question would require linkage mapping or QTL analysis in a large F₂ or recombinant inbred line population derived from these crosses.

Regardless of the mechanistic basis of the observed overdominance, the practical breeding implication is the same: heterozygous F₁ genotypes outperform their homozygous inbred counterparts for these traits, and this advantage cannot be recovered by conventional selfing. For φ(Po) and ψ(Eo) (which directly reflect the primary photochemical quantum efficiency of PSII and the probability of electron transport beyond QA, respectively) this finding suggests that hybrid wheat varieties could achieve genuinely superior photosynthetic performance relative to inbred cultivars. This is particularly relevant in the context of the expanding commercial hybrid wheat sector, where photosynthetic efficiency is increasingly recognized as a key target trait for yield improvement [14,20].

4.7. Limitations of the Effective-Factor Estimates and Implications for Future Genetic Mapping

The effective-factor estimates varied among traits and crosses, with positive finite estimates generally falling between 1 and 11. Under the restrictive assumptions of the Lande [29] estimators, such values may be interpreted as estimates of the minimum number of effective segregating factors. However, these assumptions include the absence of epistasis and linkage, approximately equal allelic effects, and sufficient allelic divergence between the parents. Because epistasis was detected for several traits and linkage could not be evaluated in the present populations, these assumptions are not fully satisfied.

Consequently, the reported values should not be interpreted as literal counts of causal loci or as evidence that the underlying loci have individually detectable effects. They provide no direct information about genomic position, allele frequency, linkage phase, or the distribution of individual locus effect sizes. Moreover, where the assumptions of the estimator are substantially violated, even interpretation as a strict lower bound becomes uncertain. The negative estimate obtained for ABS/RC in Kohdasht × Ehsan is biologically inadmissible and was therefore treated as non-estimable; it indicates instability of the estimator or violation of its assumptions rather than a meaningful number of genetic factors.

Accordingly, these estimates do not, by themselves, demonstrate the feasibility of marker-assisted selection or the presence of major-effect QTL. Determining the number, genomic positions, linkage relationships, and effect sizes of loci influencing the fluorescence parameters will require QTL mapping, genome-wide marker analysis, or genomic prediction in larger populations with complete genotype- and phenotype-level records. The effective-factor estimates reported here should therefore be regarded only as descriptive, cross-specific, and model-dependent quantitative-genetic indices. The moderate field population sizes and limited fluorescence subsampling constitute important constraints. Sampling error may disproportionately affect F₂ and backcross variance estimates because these generations contain greater segregation and may include rare recombinant phenotypes. As a result, estimates of D, H, F, heritability, and effective gene number should be interpreted as approximate and cross-specific rather than as highly precise population parameters. Future studies should use larger segregating populations, preferably 200 or more F₂ and backcross individuals where feasible, and should retain complete plant- and leaf-level identifiers.

5. Conclusions

This study provides a comprehensive, cross-specific generation mean analysis of OJIP-derived chlorophyll fluorescence parameters in two bread wheat crosses evaluated under a single field environment using the classical six-generation design. Significant variation among generations was detected for the majority of the evaluated parameters, although the patterns differed between the two parental combinations. These results indicate that the relative contributions of additive, dominance, and epistatic effects to PSII-related fluorescence traits depend on both the parameter and the genetic background of the cross. Accordingly, the findings should be interpreted as conditional on the parental combinations and environmental conditions examined rather than as a universal description of the inheritance of chlorophyll fluorescence traits in wheat.

The net dominance effect [h] exceeded the additive effect [d] for all traits in both crosses except TRo/CSo in Kohdasht × Ehsan, establishing non-additive gene action as the primary determinant of phenotypic expression for PSII-related fluorescence parameters in wheat. This finding has direct implications for breeding strategy selection.

For traits requiring the full six-parameter model, the opposite signs of [h] and [l] confirmed duplicate epistasis as the prevailing type of non-allelic interaction. Duplicate epistasis retards breeding progress under simple selection and necessitates multiple crossing cycles with delayed selection to maximize accumulation of favorable alleles from both parents.

Despite the predominance of [h] over [d] in generation means, the additive variance component (D) exceeded the dominance component (H) for most traits in both crosses, reflecting cancellation of opposing dominance deviations at individual loci. This result indicates that long-term recurrent selection in advanced inbred generations remains a viable complementary approach to hybrid breeding.

Broad-sense heritability reached 0.991 for Fv/Fm (N-92-9 × Ehsan) and 0.697 for ABS/CSm (Kohdasht × Ehsan), confirming a strong genetic basis for phenotypic variation. The consistently lower narrow-sense heritability estimates confirm that non-additive genetic variance predominates, supporting hybrid breeding as the primary strategy for exploiting the genetic potential of these traits. The single exception (TRo/CSo in Kohdasht × Ehsan, where additive effects predominated) is amenable to improvement through pedigree or bulk selection.

Evidence for overdominance or pseudo-overdominance was detected for φ(Po) and ψ(Eo) in at least one cross, suggesting that heterozygous F₁ genotypes can achieve photosynthetic efficiency that exceeds either parental inbred line. This finding provides a genetic rationale for the inclusion of photosynthetic efficiency parameters as selection criteria in hybrid wheat breeding programs, where the commercial production of F₁ hybrids is now technically and economically feasible in several major wheat-producing countries [42].

The results of this study provide a quantitative genetic framework for improving PSII photosynthetic efficiency in wheat, but several important questions remain open. First, the distinction between true overdominance and pseudo-overdominance at loci controlling φ(Po) and ψ(Eo) requires resolution through QTL mapping or genomic analysis in large segregating populations. Second, the cross-specific nature of epistasis suggests that the favorable epistatic interactions identified here may not be generalizable across all parental combinations, and evaluation of additional crosses is warranted to identify parental combinations that consistently express favorable non-additive interactions. Third, validation of these heritability and gene action estimates under multiple environments and seasons is essential before deploying them in applied breeding programs, given the known sensitivity of heritability to environmental conditions. Finally, integration of OJIP fluorescence parameters as early-generation selection indices in hybrid wheat programs (particularly Fv/Fm, φ(Po), and TRo/CSo) should be explored as a means of accelerating genetic gain for photosynthetic efficiency alongside the conventional yield and adaptation traits that currently dominate selection criteria.

OJIP-derived parameters are physiologically responsive and can be affected by temperature, light intensity, water status, nutrient availability, leaf age, developmental stage, and measurement time. Although measurements in this study were standardized with respect to leaf position, dark adaptation, instrument settings, and developmental stage, genotype × environment interaction could not be quantified in a single-season experiment. The reported genetic parameters should therefore be regarded as conditional on the environment in which the generations were evaluated.

The present inferences are based on two biparental crosses evaluated at one location during one growing season. Chlorophyll fluorescence parameters are sensitive to developmental stage, irradiance, temperature, plant water status, nutrient availability, and measurement timing. Consequently, the magnitude and even the relative importance of additive, dominance, and epistatic effects may vary across environments and parental combinations. Multi-year, multi-location experiments with larger populations and complete observation-level records are required before broad conclusions can be drawn for wheat breeding.