Question

in a changing environment, which organisms have an advantage-those that reproduce asexualy or those that reproduce sexually? Explain your answer.

Answer 1

Sexual reproduction

it will introduce new variations in DNA by recombination, by combining different gamates.
increased variation leads to better selection . leading to adaptation

Answer 2

it actually isn't that easy.

the core questions are: how fast is the environment changing? how long is the reproduction time of the organism?

more reproduction means more life cycles and therefore more genetical variance. humans reproduce every, say, 18 years (some take much longer). e. coli takes 20 minutes. I postulate that statistically, e. coli achieves greater genetical variance in 18 years than a human, and can therefore survive in a fast-changing environment.

also, there are mechanisms of asexually reproducing organisms called lateral gene transfer (through sex-pili, if you're familiar with that). this works kinda like crossing-over during meiosis, but doesn't interfere with reproduction. thus, adaption can happen even faster.

as you see, your problem can't be broken down to the question asexually vs sexually. in history of earth, there were fast changing times long before humans arose. and many asexually reproducing organisms have survived that. this is your proof. :-)