Final answer:
The Trivers-Willard hypothesis assumes that a mother's condition influences the condition of her offspring, shaping parental investment towards males or females depending on the mother's state.
Step-by-step explanation:
The critical assumption of the Trivers-Willard hypothesis is offspring condition depends on the mother's condition. This hypothesis pertains to parental investment theory in sexual reproduction and relies on the idea that parents will invest differently in offspring depending on their condition and potential future reproductive success. The hypothesis assumes that mothers in good condition are more likely to produce and invest in male offspring, who can potentially father many children, while mothers in poorer condition will produce and invest in female offspring, who are more consistently able to reproduce albeit with fewer progeny.