Question

if natural selection operates to select for a specific trait which statement must be true about that trait for evolution to occur

Answer 1

OK so basically it would be passed on genetically to the next generation 

Answer 2

Natural Selection: Requirements

Three conditions must be met for selection to occur in a population:

1. Variation: Individuals in the population must differ with respect to the trait in question. Without this variation, all individuals will have the same trait value and cannot be distinguished with respect to that trait.

2. Heritability: The variation found in the population must (at least partially) be heritable, e.g. transmitted from parent to offspring. If the variation in the trait was due entirely to the environment, for example, changes in the parent population would not affect the characteristics of the offspring population.

3. Differential Mortality: Finally, individuals must have a probability of survival that is a function of the value of the trait in question. If all individuals, regardless of there trait value, had an equal probability of survival and fecundity, no predictable change in the mean value of the population would occur.