The documentation of estimateDispersions in DESeq2 says

estimateDispersions checks for the case of an analysis with as many samples as the number of coefficients to fit, and will temporarily substitute a design formula ~ 1 for the purposes of dispersion estimation.

However, it appears that the results of estimateDispersions are different depending on the design of the DESeq2 object it receives as input.

As an example for that, the mean of the dispersions resulting from different designs is different, here is sample code :

```{r} suppressPackageStartupMessages(library(DESeq2)) ```

```{r} set.seed(1234) ```



```{r} dds <- makeExampleDESeqDataSet(betaSD = 1) ```

```{r} mycolData <- colData(dds) mycolData$batch <- factor(c(1,1,1,2,2,2,1,1,1,2,2,2)) colData(dds) <- mycolData

colData(dds)

```

DataFrame with 12 rows and 2 columns
         condition    batch
          <factor> <factor>
sample1          A        1
sample2          A        1
sample3          A        1
sample4          A        2
sample5          A        2
...            ...      ...
sample8          B        1
sample9          B        1
sample10         B        2
sample11         B        2
sample12         B        2

```{r}
dds <- estimateSizeFactors(dds)


dds2<- dds
design(dds2) <- ~ 1
dds2 <- estimateDispersions(dds2)

design(dds) <- ~batch  + condition
dds <- estimateDispersions(dds)


print(paste("Mean of dispersions with model ~batch+condition", mean(dispersions(dds),na.rm=T) ) )

print(paste("Mean of dispersions with model ~1", mean(dispersions(dds2),na.rm=T) ) )
```

gene-wise dispersion estimates
mean-dispersion relationship
final dispersion estimates
gene-wise dispersion estimates
mean-dispersion relationship
final dispersion estimates
[1] "Mean of dispersions with model ~batch+condition 0.93962274256627"
[1] "Mean of dispersions with model ~1 0.99071610332295"
```{r}
sessionInfo()
```

R version 3.6.0 (2019-04-26)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 16.04.6 LTS

Matrix products: default
BLAS:   /usr/lib/atlas-base/atlas/libblas.so.3.0
LAPACK: /usr/lib/atlas-base/atlas/liblapack.so.3.0

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
 [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
 [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
[10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   

attached base packages:
[1] parallel  stats4    stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] DESeq2_1.26.0               SummarizedExperiment_1.16.0
 [3] DelayedArray_0.12.0         BiocParallel_1.20.0        
 [5] matrixStats_0.55.0          Biobase_2.46.0             
 [7] GenomicRanges_1.38.0        GenomeInfoDb_1.22.0        
 [9] IRanges_2.20.0              S4Vectors_0.24.0           
[11] BiocGenerics_0.32.0        

loaded via a namespace (and not attached):
 [1] locfit_1.5-9.1         Rcpp_1.0.2             lattice_0.20-38       
 [4] zeallot_0.1.0          digest_0.6.22          backports_1.1.5       
 [7] acepack_1.4.1          RSQLite_2.1.2          ggplot2_3.2.1         
[10] pillar_1.4.2           zlibbioc_1.32.0        rlang_0.4.1           
[13] lazyeval_0.2.2         rstudioapi_0.10        data.table_1.12.6     
[16] annotate_1.64.0        blob_1.2.0             rpart_4.1-15          
[19] Matrix_1.2-17          checkmate_1.9.4        splines_3.6.0         
[22] geneplotter_1.64.0     stringr_1.4.0          foreign_0.8-71        
[25] htmlwidgets_1.5.1      RCurl_1.95-4.12        bit_1.1-14            
[28] munsell_0.5.0          compiler_3.6.0         xfun_0.10             
[31] pkgconfig_2.0.3        base64enc_0.1-3        htmltools_0.4.0       
[34] nnet_7.3-12            tibble_2.1.3           gridExtra_2.3         
[37] htmlTable_1.13.2       GenomeInfoDbData_1.2.2 Hmisc_4.2-0           
[40] XML_3.98-1.20          crayon_1.3.4           bitops_1.0-6          
[43] grid_3.6.0             xtable_1.8-4           gtable_0.3.0          
[46] DBI_1.0.0              magrittr_1.5           scales_1.0.0          
[49] stringi_1.4.3          XVector_0.26.0         genefilter_1.68.0     
[52] latticeExtra_0.6-28    vctrs_0.2.0            Formula_1.2-3         
[55] RColorBrewer_1.1-2     tools_3.6.0            bit64_0.9-7           
[58] survival_2.44-1.1      AnnotationDbi_1.48.0   colorspace_1.4-1      
[61] cluster_2.0.8          memoise_1.1.0          knitr_1.25

Thanks for your post — that sentence in the man page is out of date and needs to be removed, DESeq2 no longer will fit these designs.

As for your second question, yes the design definitely changes the dispersion. This is correct, and desired behavior.