A natural place to look for alleles of large effect are the otherwise conserved (from mouse through chimp) variants that are different in humans. See The Genetics of Humanness and The Essential Difference.
My guess (without checking the paper to see if they report it) is that test-retest correlation for chimps is well below the 0.9--0.95 often found for (human) g. Thus the h2 = 0.5 figure reported below could be significantly higher if corrected for reliability.
Nature News: Smart chimpanzees often have smart offspring, researchers suggest in one of the first analyses of the genetic contribution to intelligence in apes. The findings, published online today in Current Biology1, could shed light on how human intelligence evolved, and might even lead to discoveries of genes associated with mental capacity.
A team led by William Hopkins, a psychologist at Georgia State University in Atlanta, tested the intelligence of 99 chimpanzees aged 9 to 54 years old, most of them descended from the same group of animals housed at the Yerkes National Primate Research Center in Atlanta. The chimps faced cognitive challenges such as remembering where food was hidden in a rotating object, following a human’s gaze and using tools to solve problems.
A subsequent statistical analysis revealed a correlation between the animals' performance on these tests and their relatedness to other chimpanzees participating in the study. About half of the difference in performance between individual apes was genetic, the researchers found.
In humans, about 30% of intelligence in children can be explained by genetics; for adults, who are less vulnerable to environmental influences, that figure rises to 70%. Those numbers are comparable to the new estimate of the heritability of intelligence across a wide age range of chimps, says Danielle Posthuma, a behavioural geneticist at VU University in Amsterdam, who was not involved in the research.
“This study is much overdue,” says Rasmus Nielsen, a computational biologist at the University of California, Berkeley. “There has been enormous focus on understanding heritability of intelligence in humans, but very little on our closest relatives.”