## 1 Introduction  
Headspace solid-phase microextraction (HS-SPME) is widely employed to isolate and pre-concentrate volatiles prior to gas chromatography-mass spectrometry (GC-MS) analysis [1; 2; 3; 4]. SPME has several advantages over other sample preparation techniques (e.g., solid-phase extraction or liquid-liquid extraction), including its avoidance of solvents, ease of automation, and small sample size requirements [5]. These features make SPME particularly well suited for studies that require analysis of a large number of samples, e.g., when evaluating plant populations used by breeders in investigating the genetic underpinnings of traits [6; 7]. Mapping of genes or quantitative trait loci (QTLs) controllingvolatiles--including those associated with aroma--has been reported in several plant species, including tomatoes [2], melons [8; 9], apples [10; 11], and grapes [12; 13; 14]. Plant volatile phenotyping is usually performed by GC-MS, for both targeted analyses of a small number of volatiles [15; 16] and broader profiling of a large number of targeted or nontargeted volatiles (\"metabolomics\") [1; 2; 8; 9; 10; 17]. A challenge associated with SPME, however, is its high susceptibility to matrix effects, including plant matrixes [18; 19]. For example, for a range of volatiles, SPME-GC-MS responses were reported to decrease by 2- to 12-fold in a tomato matrix [15]. This decrease could arise from either competition on the SPME fiber or decreases in analyte volatility. Matrix effects could be compensated for through appropriate calibration, most commonly through the use of well-matched and equilibrated internal standards. When available, the preferred choice for an internal standard is a stable isotope-labeled analogue of the target analyte, i.e., stable isotope dilution analysis (SIDA) [20]. This technique has been employed in grape mapping populations to identify candidate genes associated with monoterpene production (\"muscat\" aroma) [12] following a solid-phase extraction, and in basmati rice grains for phenotype 2-acetyl-1-pyrroline (\"nutty\" aroma) following SPME [21]. SIDA, however, is not employed in most volatile phenotyping studies of breeding populations, including those using SPME, likely due to the high cost or commercial unavailability of isotopically labeled standards [20]. The impracticality of SIDA is particularly severe for nontargeted studies, which may involve measurement of dozens of volatiles whose identity is unknown prior to analysis. Instead, it is common for SPME-based volatile phenotyping studies to use a single surrogate standard or to normalize responses to the total ion count. In this approach, it is assumed that the relative matrix effects on any given compound (analyte or standard) are consistent among individuals, i.e., relative differences in analyte concentrations are preserved. Knowledge of relative ratios of volatiles is still potentially useful, e.g., in QTL analyses to identify associated genetic markers for breeding purposes or identify likely metabolic networks. However, the assumption that matrix effects do not show Compound \(\times\) Individual interactions in ostensibly similar samples is not always valid. For example, the relative response for an \(n\)-decane surrogate in soybean oil changed by up to 8-fold as compared to \({}^{13}\)C-labeled internal standards following thermal oxidation of the oil matrix [22]. Similarly, modest variations in ethanol content of model wines caused Compound \(\times\) Individual matrix effects across a range of volatiles [23]. These effects would not allow for accurate relative quantification based on a single surrogate standard. Although the occurrence of Compound \(\times\) Individual matrix effects during SPME analysis of plant populations can be assumed, the extent of such interactions has not been quantitated and routine approaches to their determination have not been described.