Part of the input for Gene Set Enrichment Analysis with fgseaMultilevel is a list of GO terms and genes assigned to it. E.g.:

library(fgsea)

data(examplePathways)
examplePathways[1:3]
$`1221633_Meiotic_Synapsis`
 [1] "12189"     "13006"     "15077"     "15078"...

$`1368092_Rora_activates_gene_expression`
[1] "11865"  "12753"  "12894"  "18143"  "19017"  "19883"  "20787"  "217166" "328572"

$`1368110_Bmal1:Clock,Npas2_activates_circadian_gene_expression`
 [1] "11865"  "11998"  "12753"  "12952"  "12953"...

My question is: Am I right that if a gene is annotated with a specific GO term, then all the ancestors of that GO term should also be assigned to that gene? (This is because if you are annotated with a specific term then you are autamtically annotated also with the less specific terms, right?)

Assuming I'm correct, ensembl/biomart often assigns a specific GO term to a gene but it doesn't assign all of the ancestor terms. This means that data retrieved from biomart is not immediately usable for fgsea. Here's an example:

At first impression it would appear that no human gene is annotated with term GO:0044815:

library(biomaRt)
library(GO.db)

ensembl <- useEnsembl(biomart = 'genes',
  dataset = 'hsapiens_gene_ensembl',
  version = 105)

getBM(filters=c('go'), attributes=c('ensembl_gene_id'), values=list('GO:0044815'), mart=ensembl)
[1] ensembl_gene_id
<0 rows> (or 0-length row.names)

However, several genes are annotated with the offspring of GO:0044815:

offspring <- as.list(GOCCOFFSPRING['GO:0044815'])
offspring
$`GO:0044815`
[1] "GO:0000786" "GO:0000796" "GO:0043505" "GO:0140573"

getBM(filters=c('go'), attributes=c('ensembl_gene_id'), values=list(offspring[[1]]), mart=ensembl)
    ensembl_gene_id
1   ENSG00000281813
2   ENSG00000285435
3   ENSG00000284841
4   ENSG00000285449
...
122 ENSG00000113810
123 ENSG00000151503

This means that if you prepare the data for fgsea straight from ensembl/biomart, the term GO:0044815 is not tested at all even if there are many genes effectively annotated with it. So, the data from biomart should be "augmented" to add to each gene the ancestors of each GO term assigned to that gene. This augmentation is not too difficult (I think) but I haven't seen it mentioned anywhere so I am wondering if I'm misunderstanding something here.

sessionInfo()
R version 4.1.1 (2021-08-10)
Platform: x86_64-conda-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)

Matrix products: default
BLAS/LAPACK: /export/III-data/wcmp_bioinformatics/db291g/miniconda3/envs/20220405_chris_cerebral_malaria/lib/libopenblasp-r0.3.18.so

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

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

other attached packages:
[1] fgsea_1.20.0         GO.db_3.14.0         AnnotationDbi_1.56.1 IRanges_2.28.0       S4Vectors_0.32.3     Biobase_2.54.0       BiocGenerics_0.40.0  biomaRt_2.50.0      

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.8.3           lattice_0.20-45        prettyunits_1.1.1      png_0.1-7              Biostrings_2.62.0      assertthat_0.2.1       digest_0.6.29          utf8_1.2.2             BiocFileCache_2.2.0    R6_2.5.1               GenomeInfoDb_1.30.0   
[12] RSQLite_2.2.8          httr_1.4.2             ggplot2_3.3.3          pillar_1.7.0           zlibbioc_1.40.0        rlang_1.0.2            progress_1.2.2         curl_4.3.2             data.table_1.14.0      blob_1.2.2             Matrix_1.4-1          
[23] BiocParallel_1.28.3    stringr_1.4.1          RCurl_1.98-1.6         bit_4.0.4              munsell_0.5.0          compiler_4.1.1         pkgconfig_2.0.3        tidyselect_1.1.2       KEGGREST_1.34.0        gridExtra_2.3          tibble_3.1.6          
[34] GenomeInfoDbData_1.2.7 XML_3.99-0.9           fansi_1.0.3            crayon_1.5.1           dplyr_1.0.9            dbplyr_2.2.1           bitops_1.0-7           rappdirs_0.3.3         grid_4.1.1             gtable_0.3.0           lifecycle_1.0.1       
[45] DBI_1.1.2              magrittr_2.0.3         scales_1.1.1           cli_3.3.0              stringi_1.7.6          cachem_1.0.6           XVector_0.34.0         xml2_1.3.3             ellipsis_0.3.2         filelock_1.0.2         generics_0.1.3        
[56] vctrs_0.4.1            fastmatch_1.1-3        tools_4.1.1            bit64_4.0.5            glue_1.6.2             purrr_0.3.4            hms_1.1.2              parallel_4.1.1         fastmap_1.1.0          colorspace_2.0-3       memoise_2.0.1

You should include the filter as an attribute. I would also reverse the query, asking instead for the GO terms for each gene. But anyway.

> mart <- useEnsembl("ensembl","hsapiens_gene_ensembl")
> z <- getBM(filters=c('go'), attributes=c('go_id','ensembl_gene_id'), values=list('GO:0044815'), mart=mart)
> z
        go_id ensembl_gene_id
1  GO:0000781 ENSG00000146047
2  GO:0005634 ENSG00000146047
3  GO:0003677 ENSG00000146047
4  GO:0030527 ENSG00000146047
5  GO:0046982 ENSG00000146047
6  GO:0006334 ENSG00000146047
7  GO:0000786 ENSG00000146047
8  GO:0005694 ENSG00000146047
9  GO:0005654 ENSG00000146047
10 GO:0003674 ENSG00000146047
11 GO:0035093 ENSG00000146047
12 GO:0006337 ENSG00000146047
13 GO:0042393 ENSG00000146047
14 GO:0006325 ENSG00000146047
15 GO:0006954 ENSG00000146047
16 GO:0031639 ENSG00000146047
17 GO:0051099 ENSG00000146047
18 GO:0051276 ENSG00000146047
19 GO:0071674 ENSG00000146047
20 GO:0001674 ENSG00000146047
21 GO:0019897 ENSG00000146047
22 GO:0044815 ENSG00000146047

> gos <- getBM(c("go_id","ensembl_gene_id"), "ensembl_gene_id", "ENSG00000281813", mart)
> gos
        go_id ensembl_gene_id
1             ENSG00000281813
2  GO:0005634 ENSG00000281813
3  GO:0046872 ENSG00000281813
4  GO:0016740 ENSG00000281813
5  GO:0006355 ENSG00000281813
6  GO:0003677 ENSG00000281813
7  GO:0006325 ENSG00000281813
8  GO:0016746 ENSG00000281813
9  GO:0006334 ENSG00000281813
10 GO:0000786 ENSG00000281813
11 GO:0043966 ENSG00000281813
12 GO:0000123 ENSG00000281813
13 GO:0045893 ENSG00000281813
14 GO:0004402 ENSG00000281813
15 GO:0016573 ENSG00000281813
16 GO:0005515 ENSG00000281813
17 GO:0042393 ENSG00000281813
18 GO:0045892 ENSG00000281813
19 GO:0061629 ENSG00000281813
20 GO:0005654 ENSG00000281813
21 GO:0045944 ENSG00000281813
22 GO:0003712 ENSG00000281813
23 GO:0070776 ENSG00000281813
24 GO:0050793 ENSG00000281813
25 GO:1903706 ENSG00000281813
26 GO:0016407 ENSG00000281813

This is based on the current version, not 105.