Effects on different genders
Dr. Simpson explains that the Simpson gene is on the Y chromosome, and so mainly affects males (the only known exception being Homer's half-sister Abbey), meaning Lisa and Maggie Simpson are unaffected. This was proven further in the comics when, during a reunion, several of them where sharing stories about their successful lives.
Despite her intelligence, Lisa has shown some of Homer's traits like saying "D'oh!" and "Woo-hoo!", indicating she is influenced by the Simpson gene to a small extent; she has also inherited her father's chubby fingers.
Degree of effects on male Simpsons
While the Simpson gene affects all male Simpsons, it is not always to the same degree. Homer's half-brother Herbert Powell was able to graduate from Harvard and start a successful company. However, he was still affected in small bursts of idiocy and recklessness, like when he trusted his half-brother Homer to design a new car. Although Bart is mischievous, the Simpson gene never had a large impact on his faculties as he plans his pranks in advance and was able to discover that Robert Terwilliger framed Krusty the Clown and later planned to kill his aunt Selma Bouvier for money. In "Bart's Comet", Homer theorized that Springfield's polluted atmosphere would prove beneficial as it burned up an incoming comet upon entry. After Lisa remarked that Homer was indeed correct, he claimed to be scared by his prediction. Abraham Simpson II was able to enter the U.S. Army and allegedly fight in both World Wars, though the Simpson gene seemed to have finally caught up with him sometime after Homer and Marge Simpson married.
Homer and Bart have also displayed high levels of intelligence, ability and accuracy in specified areas, which could be seen as having savant syndrome.
Homer Simpson Syndrome
Homer has an unusual condition — dubbed Homer Simpson Syndrome — where his brain is cushioned by an especially thick layer of fluid acting as a helmet of sorts. It is unknown whether the Simpson gene causes this, though the males in the Simpson family seem to have a thing for putting pots and pans on their heads and then headbutting, suggesting a connection.
Other reasons for Homer's stupidity
In "Whacking Day", Homer claims a battle between good and evil rages inside everyone, including himself. We then see a gravestone that reads "RIP Good Homer", and a devil version of Homer dancing on it, saying "I am evil Homer! I am evil Homer!", while shaking maracas.
In "HOMЯ", another reason for Homer's stupidity is that a crayon was lodged in his brain since he was 6 years old. His IQ without the crayon was 105, placing him in the "average" bracket of about 90 to 110.
Homer's drinking may also be a factor. As Homer says in "Treehouse of Horror IV", "Oh, Lisa. You and your stories. Bart is a vampire, beer kills brain cells. Now lets go back to that... building... thingy, where our beds and TV... is." However, that was a Treehouse of Horror series episode and therefore non-canon.
In "Itchy & Scratchy: The Movie", he tells Bart about how he wanted a bike when he was a kid but his dad wouldn't let him have one, so he held his breath until he passed out. He mentioned the doctors told him he had brain damage.
In "Marge on the Lam", he once went to a military camp for experimental testing to avoid one of Selma and Patty Bouvier's visits. The doctors warned him that injections would result in hair loss and lower intelligence.
He may have also become challenged due to low self-esteem from his father putting him down despite suffering from the Simpson gene as well. This is reinforced by Homer's statement in "Grampa vs. Sexual Inadequacy" that if Abe hadn't put him down, he might've had more of a chance at success.
In "We're on the Road to D'oh-where", Homer tells Bart that "Serious Homer" has "Fun Homer" locked up until Bart gets to discipline camp. We then peer into Homer's mind where we see Serious Homer threatening to kill Fun Homer just like he killed "Intellectual Homer", pointing to a Homer corpse lying in a pool of blood wearing a tweed jacket, mortarboard and half-frame glasses while clutching a diploma.
Homer has also sustained many injuries throughout the series, most of which were repeated blows to the head. Therefore, he could suffer from severe brain damage due to cranial trauma.
Homer has the defective Simpson gene located on the Y-chromosome. The "Simpson gene" is actually an allelic anomaly that exerts phenotypic dominance over its counterpart locus on the X-chromosome donated by his mother, regardless of the fact they are non-homologous. Because it is a dominant allele in this hemizygous condition, the exceptional intelligence that would result from the expression of the allele on the X chromosome is repressed. This allows for the expression of the Simpson gene, causing mental inertia to begin at approximately age eight and increase until it plateaus in adulthood. Therefore, Homer's intelligence is naturally below-average due to his genetic condition, but years of working at the Springfield Nuclear Power Plant have mutated his Y-chromosome and rendered his Simpson allele inactive. This grants him both normal and exceptional intelligence facilitated by the unblocked allele locus on his X-chromosome. This, however, is unexpressed because of a crayon lodged in the frontal lobe of his forebrain (a key area of regulation for cognition and behavior) since he was a child. It was once removed, revealing this extraordinary intelligence but he later insisted it be re-lodged to restore his original status.