Earthquake insurance is separate. As mentioned above, homeowners policies may just cover the structure, and nothing inside. If that is the case, then in the event of an earthquake and total loss of your belongings – say the house collapses, you’ll want to protect all your belongings. Since everyone thinks the big one is due, I’d recommend getting it given its a marginal cost per year to add on that rider to your renters insurance.
Also you mentioned having a pool and a family of 5. Assuming you have kids and they might have friends over – another reason to get the renters insurance – you don’t want to get sued because a kid slips and falls by the pool or something even worse happens!