Birth order and the Flynn effect

Studies on birth order show that first-born children tend to have IQs that are, on average, 3 points higher than those of their second-born siblings, and second-borns in turn have a point or two advantage on their younger brothers and sisters. The most popular (and most PC) explanation for this is that couples are able to invest all of their parental energy into the first-born before the next child comes along. After that, though, parental attention is split among multiple offspring. But if the explanation is at least partially one of nature (or a product of a woman's reproductive quality declining as the number of times she's given birth accumulates), might there be a causal relationship between declining birth rates and the Flynn effect (realizing that at most this would account for a 1-2 point increase in average IQ and thus constituting only a fraction of the observed effect)?