feature selection method using pearson residuals discrepancies

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What happened?

Hi,

I have performed multiple way to do features selection using pearson residuals and methods return different results.

Method 1 plot:

Method 2 plot:

I dont understand why these 2 methods dont produce the same result.

Based on those graph I think the best is method 2 but would like to understand why these dont produce similar plots.

Thanks in advance for your help

Minimal code sample

### 1st method:
analytic_pearson = sc.experimental.pp.normalize_pearson_residuals(adata, inplace=False)
adata.layers["analytic_pearson_residuals"] = csr_matrix(analytic_pearson["X"])
sc.pp.highly_variable_genes(adata, layer="analytic_pearson_residuals", n_top_genes=4000)
ax = sns.scatterplot(
data=adata.var, x="means", y="dispersions", hue="highly_variable", s=5
)

## 2nd method:

fig, ax = plt.subplots(1, 1, figsize=(10, 5))
sc.experimental.pp.highly_variable_genes(
adata, flavor="pearson_residuals", n_top_genes=4000
)
ax = sns.scatterplot(
data=adata.var, x="means", y="dispersions", hue="highly_variable", s=5
)
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_title("Feature selection using Pearson residuals normalisation (from highly_variable_genes flavor pearson_residuals)")
pdf.savefig(bbox_inches="tight")

Error output

Versions

Start by reproducing the two workflows using normalize_pearson_residuals, highly_variable_genes with the pearson_residuals flavor, and the provided plotting code. Compare the intermediate values and selection criteria, then determine whether the differing plots are expected or indicate a defect; document the explanation or add a regression test if a defect is confirmed.