I am writing to inquire about a problem I keep running into while running DESeq2. After running DESeq2 comparing two samples, I encounter an issue where I get >10000 differentially expressed genes. Furthermore, I have been getting a couple thousand genes that has a padj of 0 or negligibly close to zero (e.g. 2E-320). I've pasted below a PCA plot of the samples. The samples I directly compared were the MII oocyte and secondary follicle oocytes. Comparing them either in vitro or in vivo also resulted in the same problem. I've also attached a volcano plot for reference as well. Lastly, I've pasted my R Session below as well:

library(DESeq2)
> setwd("/Users/anjalimohan/Desktop/Research/Hikabe/")
> list.files()
 [1] "All_TPM_Maths.csv"               "All_TPMs.csv"                    "All_TPMs.xlsx"                   "counts.txt"                     
 [5] "counts.txt.summary"              "countsonly_2ndfol.csv"           "countsonly_copy.csv"             "countsonly_MII.csv"             
 [9] "countsonly_PGCs.csv"             "countsonly_vivo.csv"             "countsonly.csv"                  "GTFs"                           
[13] "Metadata.csv"                    "Metadata1.csv"                   "Mouse_Gene_Reference_GRCm38.csv" "Results_Vitro"                  
[17] "results_vitro_2ndfol_MII_2.csv"  "Results_Vivo"                    "SraRunTable.txt"                 "TPMs_Calc"                      
> somecounts <- read.delim("counts.txt", row.names=NULL, comment.char="#")
> countsonly <- cbind(somecounts[,1], somecounts[,7:29])
> write.csv(countsonly, "countsonly.csv", row.names= F)
> 
> # Change naming scheme in notepad++
> 
> countData <- read.delim("countsonly.csv", row.names = 1, header = TRUE, sep = ",")
> head(countData)
                   SRR3313577.bam SRR3313578.bam SRR3313579.bam SRR3313580.bam SRR3313581.bam SRR3313582.bam SRR3313583.bam SRR3313584.bam SRR3313585.bam
ENSMUSG00000102693              0              0              0              0              0              0              0              0              0
ENSMUSG00000064842              0              0              0              0              0              0              0              0              0
ENSMUSG00000051951              0              0              1             14              0             30             34             22             45
ENSMUSG00000102851              0              0              0              0              0              0              0              0              0
ENSMUSG00000103377              0              0              0              0              0              0              0              0              0
ENSMUSG00000104017              0              0              0              0              0              0              0              0              0
                   SRR3313586.bam SRR3313587.bam SRR3313588.bam SRR3313589.bam SRR3313590.bam SRR3313591.bam SRR3313592.bam SRR3313593.bam SRR3313594.bam
ENSMUSG00000102693              0              0              0              0              0              0              0              0              0
ENSMUSG00000064842              0              0              0              0              0              0              0              0              0
ENSMUSG00000051951             59             48            132             62             93              2             15              7             47
ENSMUSG00000102851              0              0              0              0              0              0              0              0              0
ENSMUSG00000103377              0              0              0              0              0              0              0              0              0
ENSMUSG00000104017              0              0              0              0              0              0              0              0              0
                   SRR3313595.bam SRR3313596.bam SRR3313597.bam SRR3313598.bam SRR3313599.bam
ENSMUSG00000102693              0              0              0              0              0
ENSMUSG00000064842              0              0              0              0              0
ENSMUSG00000051951             40             38             47             35             51
ENSMUSG00000102851              0              0              0              0              0
ENSMUSG00000103377              0              0              0              0              0
ENSMUSG00000104017              0              0              0              0              0
> groups <-read.csv("Metadata1.csv", row.names = NULL, header = T, sep = ",")
> head(groups)
            Name Sample  Type Group
1 SRR3313577.bam    ESC  vivo     A
2 SRR3313578.bam    ESC  vivo     A
3 SRR3313579.bam    ESC  vivo     A
4 SRR3313580.bam  PGCLC vitro     B
5 SRR3313581.bam  PGCLC vitro     B
6 SRR3313582.bam  PGCLC vitro     C
> # Look at characteristics of data:
> str(groups)
'data.frame':   23 obs. of  4 variables:
 $ Name  : chr  "SRR3313577.bam" "SRR3313578.bam" "SRR3313579.bam" "SRR3313580.bam" ...
 $ Sample: chr  "ESC" "ESC" "ESC" "PGCLC" ...
 $ Type  : chr  "vivo" "vivo" "vivo" "vitro" ...
 $ Group : chr  "A" "A" "A" "B" ...
> #Filtering out genes w/ below 10 counts (average):
> keep <- countData[rowMeans(countData) >= 10,]
> #Change characteristics of group to factors instead of numbers:
> groups$Group <- as.factor(groups$Group)
> dds <- DESeqDataSetFromMatrix(countData , colData = groups , design = ~ Group)
> dds <- DESeq(dds)
estimating size factors
estimating dispersions
gene-wise dispersion estimates
mean-dispersion relationship
final dispersion estimates
fitting model and testing
> res <- results(dds, contrast=c("Group","G","H"))
> #Make the res into a data frame:
> resdata<- as.data.frame(res)
> #Convert row names into first column:
> resdata <- cbind(rownames(resdata), data.frame(resdata, row.names=NULL))
> ref <- read.csv("/Users/anjalimohan/Desktop/Research/Hikabe/Mouse_Gene_Reference_GRCm38.csv", row.names=NULL)
> ref$Gene_ID <- sub("\\..*", "", ref$Gene_ID)
> head(ref)
  Chromosome Database ID_Type   Start     End Strand Evidence_Level            Gene_ID            Gene_Type     Gene_Name      MGI_ID
1       chr1   HAVANA    gene 3073253 3074322      +        level 2 ENSMUSG00000102693                  TEC 4933401J01Rik MGI:1918292
2       chr1  ENSEMBL    gene 3102016 3102125      +        level 3 ENSMUSG00000064842                snRNA       Gm26206 MGI:5455983
3       chr1   HAVANA    gene 3205901 3671498      -        level 2 ENSMUSG00000051951       protein_coding          Xkr4 MGI:3528744
4       chr1   HAVANA    gene 3252757 3253236      +        level 1 ENSMUSG00000102851 processed_pseudogene       Gm18956 MGI:5011141
5       chr1   HAVANA    gene 3365731 3368549      -        level 2 ENSMUSG00000103377                  TEC       Gm37180 MGI:5610408
6       chr1   HAVANA    gene 3375556 3377788      -        level 2 ENSMUSG00000104017                  TEC       Gm37363 MGI:5610591
> #Merging resdata and ref:
> merged <- as.data.frame(merge(resdata, ref, by.x = "rownames(resdata)",by.y = "Gene_ID", all.x = T))
> # For mouse:
> merged2 <- merged[, c(8:17, 1:7)]
> colnames(merged2) <- c("Chromosome", "Database", "ID_Type", "Start", "End","Strand","Evidence_Level", "Gene_Type", "Gene_Name", "MGI_ID", "Gene_ID", "baseMean", "log2FoldChange", "lfcSE", "stat", "pvalue", "padj")
> head(merged2)
  Chromosome Database ID_Type     Start       End Strand Evidence_Level      Gene_Type Gene_Name      MGI_ID            Gene_ID     baseMean
1       chr3   HAVANA    gene 108107280 108146146      -        level 2 protein_coding     Gnai3   MGI:95773 ENSMUSG00000000001 10619.044861
2       chrX   HAVANA    gene  77837901  77853623      -        level 2 protein_coding      Pbsn MGI:1860484 ENSMUSG00000000003     0.000000
3      chr16   HAVANA    gene  18780447  18811987      -        level 2 protein_coding     Cdc45 MGI:1338073 ENSMUSG00000000028  3470.071707
4       chr7   HAVANA    gene 142575529 142578143      -        level 2         lncRNA       H19   MGI:95891 ENSMUSG00000000031  1937.134359
5       chrX   HAVANA    gene 161082525 161258213      +        level 1 protein_coding     Scml2 MGI:1340042 ENSMUSG00000000037  8086.321943
6      chr11   HAVANA    gene 108343354 108414396      +        level 2 protein_coding      Apoh   MGI:88058 ENSMUSG00000000049     1.532495
  log2FoldChange      lfcSE         stat        pvalue          padj
1    -3.21292749 0.09630001 -33.36373050 4.605950e-244 3.360769e-242
2             NA         NA           NA            NA            NA
3    -2.89216761 0.19056813 -15.17655427  5.056560e-52  3.811170e-51
4     0.04406129 1.21546762   0.03625048  9.710826e-01  1.000000e+00
5    -4.75648056 0.20690752 -22.98843781 6.083945e-117 1.193078e-115
6     2.71359509 3.12823959   0.86745117  3.856949e-01            NA
> write.csv(merged2,row.names= FALSE, file = "results_vitro_2ndfol_MII_2.csv")
> library(ggplot2)
> library(dplyr)
> 
> # order results table by the smallest adjusted p value:
> ordered <- merged2[order(merged2$padj),]
> 
> results = as.data.frame(dplyr::mutate(as.data.frame(ordered), Significant=ifelse(ordered$padj<0.05, "FDR<0.05", "Non-sig")), row.names=rownames(ordered))
> head(results)
    Chromosome Database ID_Type     Start       End Strand Evidence_Level      Gene_Type Gene_Name      MGI_ID            Gene_ID  baseMean log2FoldChange
55        chr8   HAVANA    gene 106603351 106670246      +        level 2 protein_coding      Cdh1   MGI:88354 ENSMUSG00000000303 19329.150      -4.831978
209       chr6   HAVANA    gene  86691768  86733383      -        level 2 protein_coding     Gmcl1 MGI:1345156 ENSMUSG00000001157  6095.072      -4.412727
421      chr17   HAVANA    gene   5841329   5931954      +        level 2 protein_coding      Snx9 MGI:1913866 ENSMUSG00000002365 18311.996      -4.681864
736       chr5   HAVANA    gene  33634952  33652574      -        level 2 protein_coding      Slbp  MGI:108402 ENSMUSG00000004642 47557.392      -3.760671
750       chr1   HAVANA    gene  33719887  33742564      +        level 1 protein_coding     Rab23   MGI:99833 ENSMUSG00000004768  3498.283      -3.850737
767       chr1   HAVANA    gene 181815335 181843046      -        level 2 protein_coding       Lbr MGI:2138281 ENSMUSG00000004880 23091.828      -4.011269
         lfcSE      stat pvalue padj Significant
55  0.11711838 -41.25722      0    0    FDR<0.05
209 0.09899603 -44.57478      0    0    FDR<0.05
421 0.10533009 -44.44945      0    0    FDR<0.05
736 0.07913969 -47.51941      0    0    FDR<0.05
750 0.09672259 -39.81218      0    0    FDR<0.05
767 0.10478831 -38.27974      0    0    FDR<0.05
> 
> DEgenes_DESeq <- results[which(abs(results$log2FoldChange) > log2(0.5) & results$padj < 0.05),]
> 
> p = ggplot2::ggplot(results, ggplot2::aes(log2FoldChange, -log10(pvalue))) +
+   ggplot2::geom_point(ggplot2::aes(col = Significant)) +
+   theme(legend.text=element_text(size=18)) +
+   ggplot2::scale_color_manual(values = c("red", "black")) +
+   ggplot2::xlim(-7.5,7.5) +
+   ggplot2::ggtitle("Volcano Plot")
> 
> p + ggrepel::geom_text_repel(data=results[1:20, ], ggplot2::aes(label=results[1:20,9]))
Warning message:
Removed 30360 rows containing missing values (geom_point).

The PCA plot shows huge separation between groups. The null hypothesis is trivial to reject. Have you seen the DESeq2 paper discussion on this topic? (You can specify an lfcThreshold. See also the vignette section on this topic.)