Quality Trimming read loss - Trimmomatic

[Patrice]

Hello community,

I plan to do a reference assisted genome assembly for a yeast genome.
I have some questions regarding the trimming prior the assembly:

# Setup:
Illumnia MiSeq / Paired end sequencing / coverage around 80x

# Case:
Intended pipeline:
raw reads --> trimming --> Spades or Velvet --> Contiguator

I ran FastQC on the raw reads (see attached files, forward reads shown):
FastQC does not detect adapters.
Since the quality drops in the end of the reads, so I decided to use trimmomatic for quality trimming.

I needed to apply a strict quality cutoff in order to obtain better FastQC results (see attachements). I used following parameters in trimmomatic:

SLIDINGWINDOW:4:30 HEADCROP:11 MINLEN:40

However, I recognized a huge loss of reads after the trimming :

Raw reads: 9322401
trimmed reads: 7320129
-> loss of 21 %

# Questions:
1. Since FastQC did not detect illumina adapters in the raw reads, would you still run a adapter removing step (eg AdapterRemoval or trimmomatic [ILLUMINACLIP])?

2. What would you suggest regarding the quality trimming? Some people suggest not to run any trimming at all. Should I go down with the cutoff values in order to keep more reads?

Best regards