Interference length reveals regularity of crossover placement across species

Defining interference length as a measure for crossover interferenceCrossover (CO) interference is quantified based on the observed CO count per chromosome, N, and the associated CO positions xi along each chromosome. One central quantity is the mean number of COs per bivalent, 〈N〉, which is typically reduced when CO interference is strong. However, 〈N〉 does not contain any information about CO positions, so it cannot capture the fact that it is unlikely to find COs in close proximity. To capture such positional information, the main idea of the interference length Lint is to measures the increase of distances between all (not just adjacent) CO pairs due to CO interference. This increase can be expressed by the difference$${L}_{{\rm{int}}}={d}_{{\rm{int}}}-{d}_{{\rm{noInt}}}\,,$$
(1)
where dint quantifies observed distances, with a correction for variations in the distribution of the CO count N, which we introduce in detail below. In contrast, dnoInt quantifies the distance in the null hypothesis without interference. Motivated by the zyp1-mutant in A. thaliana12,45, we choose a null hypothesis where COs are placed independently along the chromosomes, sampling from all observed CO positions. In this null hypothesis, the CO count N per chromosome follows a Poisson distribution with the same mean 〈N〉 as the observed data42. We define the associated distance dnoInt as the average distance between any two COs chosen from the pool of all samples for a given chromosome. This definition of dnoInt preserves the CO density along the chromosome.To quantify the observed distances and define dint, we could have simply used the average distance dobs of all observed CO pairs. However, this naive choice would only take into account chromosomes with at least two COs, and completely ignore those with one or zero COs. These samples without any CO pairs can represent a large portion of the observation, e.g., in A. arenosa46 and C. elegans5,7,47 or in genetic data from A. thaliana12,48. In such cases, the naive choice would then only consider data from the small subset with two or more COs, which would dominate the quantity. More importantly, if most samples only carried the obligate CO, strong interference would be likely, which our quantity should capture. These arguments show that the distribution of the observed CO count N per chromosome needs to be considered for defining dint. The observed distribution of CO counts N in case of interference is generally narrower than the Poisson distribution of the null hypothesis of no interference; see Fig. 2A. This deviation, even if it is small, can have a significant impact on the number of observed pairs, because there are \(\frac{1}{2}N(N-1)\) pairs for a chromosome with N COs. To see this, imagine observed data of three chromosomes with two COs each, resulting in three distinct pairs; see Fig. 2B. In contrast, without interference, we might have one, two, and three COs on these chromosomes since the distribution of N is broader. This would lead to a total of four possible CO pairs, thus providing more pairs than in the observed data, despite identical 〈N〉. This example illustrates that the narrower observed distribution of CO counts N leads to fewer CO pairs than the null hypothesis without interference. To account for these missing pairs, we compare the average number of observed pairs, \({\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}\), to the average number of pairs in the null hypothesis, \({\bar{N}}_{{\rm{noInt}}}^{{\rm{pair}}}=\frac{1}{2}{\langle N\rangle }^{2}\), which follows from the assumed Poisson distribution; see section 2A of the Supplementary Information. The difference quantifies the average number of missing pairs, \({\bar{N}}_{{\rm{mis}}}^{{\rm{pair}}}={\bar{N}}_{{\rm{noInt}}}^{{\rm{pair}}}-{\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}\). A larger value of \({\bar{N}}_{{\rm{mis}}}^{{\rm{pair}}}\) indicates stronger interference, which should be reflected in our measure via a suitable definition of dint.Fig. 2: Crossover interference reduces the number of CO pairs.A Comparison of the observed distribution (green) of the number N of COs per chromosome to the reference without interference (gray) for the same genetic data as in Fig. 1. The corresponding number of CO pairs, \({N}^{{\rm{pair}}}=\frac{1}{2}N(N-1)\), are indicated with respective means. B Schematic CO placements on three chromosomes highlighting the effect of interference. The upper panel shows chromosomes with one, two, and three COs, consistent with the broad Poisson distribution in the case without interference. In contrast, interference typically leads to a narrower distribution (bottom panel), where each chromosome has two COs. While both cases have the same mean CO count, 〈N〉 = 2, the thin gray lines indicate that we have a total of three CO pairs with interference (\({\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}=1\)), and thus less than in absence of interference (\({\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}=\frac{4}{3}\)), suggesting interference reduces \({\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}\).The distance dint quantifies the distance of CO pairs in case of interference, which should capture the actually observed distances as well as the fact that interference is stronger when there are more missing CO pairs. We thus define dint using a weighted average of observed and missing pairs,$${d}_{{\rm{int}}}=\frac{{\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}{d}_{{\rm{obs}}}+{\bar{N}}_{{\rm{mis}}}^{{\rm{pair}}}{d}_{{\rm{mis}}}}{{\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}+{\bar{N}}_{{\rm{mis}}}^{{\rm{pair}}}},$$
(2)
where dobs is the mean distance between all (not just adjacent) CO pairs on the same chromosome. In contrast, dmis quantifies the distance associated with missing pairs. For simplicity, we assume that dmis is a constant, and in particular does not depend on the distribution of CO positions. The value of dmis cannot be larger than the chromosome length L since such distances can principally not be observed. We thus choose the largest possible value, dmis = L, as the most natural length scale; For cytological data, we for simplicity use the average SC length of the respective chromosome, neglecting variations (c.f. ref. 49). We will discuss below how this choice is related to the maximal interference length that can realistically be observed. Taken together, the interference length can be expressed as$${L}_{{\rm{int}}}=\phi ({d}_{{\rm{obs}}}-{d}_{{\rm{noInt}}})+(1-\phi )(L-{d}_{{\rm{noInt}}}),$$
(3)
where \(\phi={\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}/{\bar{N}}_{{\rm{noInt}}}^{{\rm{pair}}}=2{\bar{N}}_{{\rm{obs}}}^{{\rm{pair}}}/{\langle N\rangle }^{2}\) denotes the ratio of observed to expected CO pairs, which is small in case of strong interference; compare Fig. 3A. Eq. (3) highlights that the interference length Lint combines information of (i) the distribution of CO positions via dnoInt, (ii) the distribution of the observed distances of CO pairs via dobs, and (iii) the distribution of observed CO counts via ϕ.Fig. 3: Visualizations of interference length Lint.Shown is data for the first chromosome of male meiosis of A. thaliana12,48. A Comparison of the observed (green) and expected (gray) distribution of distances of all CO pairs for wild-type data. The last, cyan bin accounts for missing pairs, which contribute with a length of dmis = L where L = 30.4 Mb is the measured chromosome length. The interference length Lint is the distance between the mean values of these distributions (denoted by vertical dashed lines). B Cumulative distributions visualizing the same data as in panel A. Since the cumulative distribution is an integrated measure, binning is not required and Lint corresponds to the blue area. The dashed gray line indicates the theoretical distribution for uniform CO distributions. C Coefficient of coincidence curves of four different genotypes of chromosome 1 of male A. thaliana12,48. Vertical bands mark associated interference lengths Lint (blue) and interference distances dCoC (orange) with respective standard error of the mean.Figure 3A shows a graphical interpretation of the interference length Lint based on the histogram of the distances between all CO pairs per sample. In contrast to Fig. 1A, we account for missing CO pairs, which contribute with the maximal distance L (cyan region). Consequently, the mean distance of the observed data shifts to larger values (compare dashed green lines in Fig. 1A and Fig. 3A), capturing that missing CO pairs indicate strong interference. Figure 3B visualizes the same idea using cumulative distribution functions. Here, Lint corresponds to the blue area between the gray curve representing the null hypothesis and the green curve for observed data with interference, which is scaled by ϕ to account for missing CO pairs. The cumulative distribution function highlights that Lint can be determined without binning, abolishing this step that could degrade data quality.The interference length Lint has multiple properties that make it a suitable measure of CO interference: (i) Lint is a scalar quantity of dimension length. Consequently, Lint is reported in units of μm for cytological data (SC space), and units of megabases (Mb) for genetic data (DNA space). (ii) We show in section 2B of the Supplementary Information that Lint is invariant to random sub-sampling (similar to CoC curves), which facilitates the comparison of cytological and genetic data. (iii) Lint uses all empirical data on CO positions and does not use any binning or parametrization. On the one hand, all observed CO pairs contribute equally to dobs and thus Lint; see Eqs. (2)–(3). On the other hand, the definition also accounts for chromosomes without COs or only one CO via the average number of missing pairs, \({\bar{N}}_{{\rm{mis}}}^{{\rm{pair}}}\). (iv) The quantity dnoInt is based on the observed distribution of CO positions along the chromosome, so that variations of CO density, e.g., due to suppression in centromeric regions, are incorporated in Lint. (v) Lint allows for uncertainty estimations (section 2C of the Supplementary Information) and significance testing (section 2D of the Supplementary Information). We provide a reference implementation of Lint with the Supporting Material.Large interference lengths indicate strong interferenceTo see how well the interference length Lint captures CO interference, we start by comparing it to the more traditional CoC curves. Figure 3C shows four representative CoC curves for various strains of A. thaliana, known to exhibit very different CO interference. In all cases, Lint (blue bands) qualitatively captures the distance at which the CoC curve approaches 1, indicating the point at which distances between COs are as frequent as in the null hypothesis without interference. In particular, Lint is larger for cases known to exhibit strong interference (e.g., the HEI10het mutant), and it correlates (cf. Supplementary Fig. 3C) with the interference distance dCoC (orange band; where the CoC curves exceeds 0.5). However, Lint can be calculated more precisely (indicated by the smaller standard error of the mean; see Supplementary Fig. 1B), and it can also be determined for cases without interference (e.g., the zyp1 mutant) and when few CO pairs are observed. This first analysis thus indicates that Lint captures essential aspects of CoC curves and CO interference.The only crucial parameter in the definition of Lint is the distance dmis associated with missing pairs. Our choice of dmis = L implies that Lint assumes values on the order of the chromosome length L in cases of strong interference. Since there are multiple cases that could be called “strong interference”, we next evaluate Lint for four theoretical scenarios: (i) When all chromosomes exhibit exactly one CO per chromosome, we have ϕ = 0 and thus Lint = L − dnoInt. In this scenario of complete interference, we obtain \({L}_{{\rm{int}}}=\frac{2}{3}L\) when COs are distributed uniformly along the chromosome; see section 2E of the Supplementary Information. These results persist if some chromosomes have no CO instead of one. (ii) We also find \({L}_{{\rm{int}}}=\frac{2}{3}L\) when all chromosomes have exactly two COs at opposite ends of the chromosome. (iii) The maximal-interference model of Lint for a given average CO count N yields \({L}_{{\rm{int}}}=\frac{4}{3}L{N}^{-1}\) (limited to Lint = L for N = 1 when COs always occur at the same position); see section 2F of the Supplementary Information. (iv) Finally, we consider the case where exactly N COs are placed at fixed distance L/N, and the first CO is located uniformly between 0 and L/N, so the overall CO frequency is uniform along the chromosome. This regular-placement model predicts \({L}_{{\rm{int}}}=L[{N}^{-1}-\frac{1}{3}{N}^{-2}]\); see section 2G of the Supplementary Information. Taken together, these theoretical scenarios suggest two limiting behaviors of Lint in case of strong interference: For few COs, 〈N〉 ≈ 1, the first two scenarios suggest \({L}_{{\rm{int}}}\approx \frac{2}{3}L\). Conversely, for many COs, 〈N〉 ≫ 1, the last two scenarios suggest the scaling Lint ~ L/〈N〉. We expect that intermediate values of 〈N〉 interpolate between these two extremes. In the contrasting case without interference, when the CO count N follows a Poisson distribution and COs are placed independently (but not necessarily uniformly) along the chromosome, we have ϕ = 1, dobs = dnoInt, and hence Lint = 0, corresponding to the null hypothesis without interference. This indicates that larger values of Lint are associated with stronger interference, and that the precise value depends on L and 〈N〉. We next test these predictions for experimental data.Interference length recovers sex differences and mutant behaviorWe start by using the interference length Lint to query known properties of CO interference across different chromosomes, genotypes, and species. Since Lint is invariant to sub-sampling, cytological and genetic data can be compared directly, assuming that non-interfering class II COs are negligible and that chromosomes are compacted uniformly. To test this, we took advantage of published data where both genetic and cytological data where available. This includes human male50,51, as well as A. thaliana wild type and mutants with variations in the expression levels of HEI109,12,45,48,52; see details of data handling in section 3 of the Supplementary Information. Figure 4A shows that the average CO count 〈N〉 of the cytological data is approximately twice that of the genetic data. This is consistent with expected sub-sampling since a CO detected in cytology affects only two of the four chromatids, and is thus detected in only half the gametes28,29,30. The data also suggests that non-interfering class II COs are negligible, consistent with the low fraction of class II COs in A. thaliana, which is estimated at maximally 15%53,54.Fig. 4: Interference length retrieves known results.A Comparison of the average CO count 〈N〉 for male meiosis in A. thaliana for various genotypes based on genetic12,48,52 and cytological data9,45, and male human wild type based on genetic51 and cytological data50 for individual chromosomes. The black line indicates the expectation that 〈N〉 is twice as large for cytology compared to genetic data. B Comparison of the interference length Lint normalized to the chromosome length L for the same data as in (A). C Comparison of Lint for male and female meiosis for various genotypes based on genetic data of A. thaliana12,48,52 and wild-type, as well as cytological data for human50 scaled with the respective DNA lengths according to55 and thus measured in DNA space [Mb]. D Comparison of Lint of the same data as in C; A. thaliana data is scaled with respective SC lengths12,50 and thus measured in SC space [μm]. A–D Error bars indicate standard error of the mean. Data handling is detailed in section 3 of the Supplementary Information. Source data are provided as a Source Data file.We next compare the interference lengths Lint/L determined for the genetic and cytological data normalized with the chromosome length and the SC length, respectively. Figure 4B shows that cytological and genetic data lead to very similar values of Lint/L. In particular, the null hypothesis that the values agree is not rejected for A. thaliana wild type (p = 0.95, significance test described in section 2D of the Supplementary Information), HEI10oe (p = 0.49), HEI10het (p = 0.85), and zyp1 (p = 0.68), as well as human (p = 0.10).Another important feature of CO interference are sex differences, where CO rates differ between female and male. In A. thaliana, female meiosis generally features fewer COs and stronger CO interference according to coefficient of coincidence (CoC) analysis9,12,21,27. Figure 4C shows that genetic data12,48,52 of females indeed exhibit larger interference lengths Lint in DNA space than males. This difference is significant in wild type (p = 10−4), but not in HEI10oe (p = 0.06) and in HEI10het (p = 0.32). It is generally accepted that interference propagates in the μm space of the SC6,21. Indeed, when we convert the genetic data from DNA space to SC space using the chromosome and SC lengths reported in ref. 12 and then calculate Lint, the difference between female and male is less significant for A. thaliana wild type (p = 0.02) and is absent for HEI10het (p = 0.09) as well as HEI10oe (p = 0.83) see Fig. 4D. Taken together, this supports a common process in male and female governing CO interference in SC space, whereas sex differences are a consequence of different chromosome organisation, consistent with literature6,21.To corroborate this, we also investigated sex differences for human data from cytological imaging of MLH1 foci50, where CoC analysis in SC space suggest no significant sex difference, thus implying weaker interference for females if measured in DNA space due to lower DNA compaction in female meiosis50. Instead, we find a weakly significant difference for Lint for the cytological data (Fig. 4D, p = 0.03), whereas converting cytological data from SC space to DNA space using chromosome lengths reported in ref. 55 results in significantly smaller Lint for females (Fig. 4C, p = 10−6). Our analysis again suggests that sex differences are predominately caused by different chromosome compaction, whereas female and male exhibit similar CO interference in SC space.Finally, we test whether Lint recovers the behavior of A. thaliana mutants. Increasing HEI10 levels (HEI10oe line) decreases Lint for both male (p = 10−3) as well as female (p = 4 ⋅ 10−4) in genetic data12 and for male cytological data (p = 2 ⋅ 10−4)46; see Fig. 4B–D. Lowering HEI10 levels (HEI10het line) increases Lint for male genetic data (p = 0.04)12 and cytological data (p = 0.045)46, but Lint remains unchanged for female genetic data (p = 0.15), suggesting that CO interference is already almost maximal (Lint/L = 0.52…0.67). For mutants where the SC is absent12,27,45,56, Lint is consistent with absent interference in female zyp1 mutant12 (p = 0.60), the male zyp1 mutant (cytology)45 (p = 0.23) and the double mutant zyp1 HEI10oe12 (male p = 0.56, female p = 0.78), whereas male zyp1 mutants (genetic)12 might exhibit some residual interference (absent with p = 0.04). We thus showed that the interference length Lint recovers known behavior of CO interference in A. thaliana mutants.Interference length facilitates comparison across multiple speciesWe established that the interference length Lint tends to be larger when CO interference is stronger and that this correlation recovers many aspects of CO interference. However, we so far have not interpreted the numeral value of Lint in detail, particularly when comparing different genotypes or even different species. Since Lint is a single number, such a comparison is easily feasible and can shed light onto the mechanism of CO interference in different species.To compare measured interference lengths Lint of different species, we show Lint obtained from cytological data, and thus only interfering class I COs, as a function of the SC length L in Fig. 5A. Evidently, Lint can vary widely across species, even when SC lengths are comparable. For instance, for L ≈ 40 μm, A. arenosa exhibits Lint ≈ 20 μm, whereas A. thaliana, maize, and human exhibit progressively smaller values down to Lint ≈ 5 μm, suggesting reduced CO interference. However, we also find that Lint is correlated with L: Multiple species (A. arenosa46, C. elegans47, mouse57, and tomato18) exhibit data very close to the line \({L}_{{\rm{int}}}\approx \frac{2}{3}L\), which we associate with complete interference motivated by the theoretical scenarios studied above. Whereas these species exhibit an almost proportional relationship between Lint and L, other species (maize58, A. thaliana9, and human50) exhibit a weaker dependence. The associated values of Lint are smaller than \(\frac{2}{3}L\), indicating incomplete interference. However, all observed wild-type values are significantly larger than zero, suggesting that they all exhibit CO interference. Taken together, this initial comparison suggests that species either exhibit strong interference close to maximal values (\({L}_{{\rm{int}}}\approx \frac{2}{3}L\)) or they exhibit smaller values and weaker L-dependence.Fig. 5: Interference length allows for simple comparison across species and genotypes.A Interference length Lint as a function of SC length L for cytological data of wild-type data of A. arenosa46, A. thaliana9, C. elegans47, human50, maize58, mouse57, and tomato18. B Interference length Lint as a function of SC length L for cytological data of indicated genotypes for A. thaliana9,45, C. elegans47, and tomato18. For tomato, we present the interference length of class I COs, of all observed foci (class I and class II CO), as well as pairs with one class I and one class II CO (cf. section 2I of the Supplementary Information). A–B Error bars indicate standard error of the mean. Data handling is detailed in section 3 of the Supplementary Information. Source data are provided as a Source Data file. An analogous representation of the genetic data of A. thaliana12,48,52, human51, and S. cerevisiae59 is given in the Supplementary Fig. 4.We next investigate how mutations change Lint for a few species. Figure 5B. shows that the C. elegans ie29 strain (green triangle) has the same value of Lint as the wild type (p = 0.68), suggesting that this strain does not exhibit altered CO interference. In contrast, Lint is strongly reduced for C. elegans syp-4 mutants (green circle47), consistent with the idea that an intact SC is required for CO interference. We observe a similarly strong reduction of Lint in A. thaliana zyp1 mutants (orange circles), consistent with the described abolished interference9,45. In A. thaliana, Lint can also be reduced by over-expressing HEI10 (orange triangles pointing up), whereas interference is increased when HEI10 levels are reduced in the HEI10het strain (orange triangles pointing down), consistent with the analysis of the genetic data shown above and literature9,12,45.A challenge in interpreting CO interference experimentally is that some methods (e.g., based on labeling MLH1 in cytology) only observe class I COs, whereas others (e.g., based on electron microscopy or genetics) cannot distinguish class I COs from class II COs7,11,13. A study in tomato18 used correlative microscopy to identify MLH1-positive recombination nodules (class I CO) and MLH1-negative nodules (class II CO) in the same cells. We analyzed these data and determined Lint for various combinations of the two classes of COs; see Fig. 5B. The resulting Lint is largest when it is determined only for class I COs (pink disks), which are known to exhibit interference. The value reduces significantly (p ≈ 10−4) when Lint is calculated based on all foci (pink circles), and this reduction is consistent (p = 0.29) with an approximate correction of Lint taking class II COs (6% to 19%) into account; see section 2H of the Supplementary Information. We also quantify how class II COs interfere with the positioning of class I COs by evaluating Lint associated with pairs comprising a class I CO and a class II CO (pink squares); see section 2I of the Supplementary Information. These mixed pairs exhibit a positive (p = 0.01), weaker interference (p = 10−4, compared with Lint of all foci), but we have no evidence that class II COs interfere with each other (p = 0.58, Lint not shown in figure) or exhibit different interference than the mixed pairs (p = 0.51), consistent with literature18.Taken together, these data show that the interference length Lint recovers central observations about CO interference. In particular, values of Lint tend to vary between small values (indicating absence of interference) and large values \({L}_{{\rm{int}}}\approx \frac{2}{3}L\) (indicating strong interference). While we briefly explored the dependence on the chromosome length L, we expect from our theoretical analysis that Lint also depends on the mean CO count 〈N〉, which could distort the interpretations we made so far.Crossover interference exhibits similarity across species and mutants with intact SCThe maximal-interference model and the regular-placement model suggest the scaling Lint ~ L/〈N〉, i.e., that Lint is generally larger for longer chromosomes and fewer COs. To test this scaling, we analyze the normalized interference length, \({L}_{{\rm{int}}}^{{\rm{norm}}}={L}_{{\rm{int}}}\langle N\rangle /L\), which would be a constant if the scaling held perfectly. Since L/〈N〉 estimates the expected distance between COs, \({L}_{{\rm{int}}}^{{\rm{norm}}}\) relates to the regularity of COs placement along chromosomes. Note that 〈N〉 is the number of COs per bivalent, implying that we need to double the CO counts measured for individual chromatids in genetic data to account for the sub-sampling. Figure 6A shows that \({L}_{{\rm{int}}}^{{\rm{norm}}}\) clusters around values between  ~0.6 and  ~0.8 for wild types of many species, particularly when they have few COs (〈N〉 ≲ 4). Notable exceptions are C. elegans, which exhibits a skewed distributions of CO positions, and S. cerevisiae, which generally seems to exhibit weaker CO interference than other species we analyzed13,43.Fig. 6: Normalized interference length unveils similarity of mutant behavior across species.A Normalized interference length \({L}_{{\rm{int}}}^{{\rm{norm}}}={L}_{{\rm{int}}}\langle N\rangle /L\) as a function of the mean CO count 〈N〉 for wild-type data of A. arenosa46, A. thaliana9,12,48, C. elegans47, human50,51, maize58, mouse57, tomato18, and S. cerevisiae59 using both cytological and genetic data. B \({L}_{{\rm{int}}}^{{\rm{norm}}}\) as a function of 〈N〉 for the same wild-type data as in Panel A (violet), mutations with altered HEI10 levels in A. thaliana (magenta,9,12,52), mutations that affect the SC in A. thaliana and C. elegans (orange,12,45,47) and the msh4 mutant for S. cerevisiae (gold,59,60). A–B The dashed line marks the prediction of the regular-placement model corresponding to strong interference (see section 2G of the Supplementary Information), whereas the black line corresponds to the coarsening model for A. thaliana12. Error bars indicate standard error of the mean. Data handling is detailed in section 3 of the Supplementary Information. Source data are provided as a Source Data file.To explain the observed narrow band of \({L}_{{\rm{int}}}^{{\rm{norm}}}\), we compare the data to two theoretical predictions. First, we investigate the regular-placement model (dashed lines in Fig. 6), where 〈N〉 COs are placed uniformly with separation L/〈N〉. This model overestimates Lint for larger values of 〈N〉, likely because CO placement is not as regular in reality. Interestingly, the model underestimates Lint for small 〈N〉, which is a consequence of its uniform CO placement along the chromosome, whereas the observed distributions are often highly non-uniform. Second, we study the recently proposed coarsening model of CO interference8,9,12 for parameters obtained for A. thaliana12. While the model (black lines in Fig. 6) captures the general trend better than the regular-placement model, there are significant deviations: The model overestimates \({L}_{{\rm{int}}}^{{\rm{norm}}}\) for most species, except A. arenosa46, most likely because of very localized CO positions. The discrepancies between data and model revealed by \({L}_{{\rm{int}}}^{{\rm{norm}}}\) could guide future model refinements.Our analysis of the normalized interference length \({L}_{{\rm{int}}}^{{\rm{norm}}}\) for simple models and wild-type data suggests that systems with strong interference exhibit similar values of \({L}_{{\rm{int}}}^{{\rm{norm}}}\), which depend only weakly on L and 〈N〉. In particular, the normalized interference length removes the dependency on L and 〈N〉 that dominated in Fig. 5A: On the one hand, the species obeying the scaling \({L}_{{\rm{int}}} \sim \frac{2}{3}L\) all exhibit 〈N〉 ≈ 1, implying that the associated \({L}_{{\rm{int}}}^{{\rm{norm}}}\) is roughly 0.7. On the other hand, the cases in Fig. 5A that deviated from this scaling all exhibit more COs, explaining the reduced values of Lint. Consequently, all the cases shown in Fig. 5A (except human female chromosome 1 with 〈N〉 ≈ 6) exhibit values of \({L}_{{\rm{int}}}^{{\rm{norm}}}\) between  ~ 0.6 and  ~ 0.8. This similarity in \({L}_{{\rm{int}}}^{{\rm{norm}}}\) in all analyzed species (except S. cerevisiae, which exhibits larger CO counts and lower Lint) indicates a similar regularity in CO placement, which could originate from a similar mechanism that governs CO interference in these different species.We next test the hypothesis that the normalized interference length \({L}_{{\rm{int}}}^{{\rm{norm}}}\) captures an essential aspect of the CO interference process by comparing wild-type data with mutants known to affect CO interference. Figure 6B shows that mutants affecting the SC (orange and gold symbols) exhibit lower values of \({L}_{{\rm{int}}}^{{\rm{norm}}}\), distributed around \({L}_{{\rm{int}}}^{{\rm{norm}}}=0\). This observation is consistent with the strongly reduced interference described in the literature12,45,47,59,60, which disrupts the regularity of CO placement. In contrast, A. thaliana mutants with altered HEI10 levels (magenta symbols) exhibit values of \({L}_{{\rm{int}}}^{{\rm{norm}}}\) that are consistent with the wild-type results (violet symbols). Apparently, changing HEI10 levels only affects the CO count 〈N〉 but not the CO interference as measured by \({L}_{{\rm{int}}}^{{\rm{norm}}}\). Taken together, we propose that \({L}_{{\rm{int}}}^{{\rm{norm}}}\) quantifies aspects of CO interference that are independent of 〈N〉, which suggests that CO interference is not affected by changing HEI10 levels, but is strongly impaired in mutants affecting the SC. This interpretation is consistent with the coarsening model, where the SC is vital for mediating coarsening between COs on the same chromosome, whereas changing HEI10 levels merely affects the degree of coarsening without disrupting the mechanism.