Yes. Generation time has a significant effect on how fast a species evolves. Here's an article about the effect on molecular evolution in bacteria (which can evolve even faster than mayflies):
It's a common misconception that a mayfly (Ephemeroptera) only lives one day. They have four phases: Egg, nymph, subimago and imago. Most of their life is spent as a nymph under water. They live for up to a year before they emerge to the surface and "hatch" into an adult subimago. After hanging out for a bit, they molt one last time and become an imago. From there they mate and die - that last part is what lasts a day. For all intents and purposes, they probably evolve at about the same rate as other insects.
Comparing the fossil record of both Ephemeroptera and Homo Sapiens, I could make an argument that factors other than the generational cycle time is driving evolution of the species; some species simply "break out" - perhaps due to an interaction with the environment. It's believed that evolution is not necessarily linear, but is full of fits, starts and breakthroughs. As far as species go, mayflies are rather primitive and are quite similar to their ancestors from 300 Million years ago.
All the answers are focusing on speed of evolution in relation to generation time. No one is mentioning that mayflies live way longer than a day. In some species the adult stage may only last one or a few days, but the juvenile aquatic stage lasts months or even years.
It would be more accurate to say it increases their *potential* to evolve faster.
Rates of evolution depend on a series of factors, most prominently selection pressure, mutation rate, and reproductive rate. Without a strong selective pressure, and mutations that satisfy it, faster reproduction alone will not give rise to faster evolution.
Yes, short reproduction cycles have faster results, but the winged part of the mayfly lifecycle is not the whole lifecycle, like many other insects it is only the final stage, if you want really fast evolution check-out bacteria and virus, they are really fast...
Yes that’s exactly how that works.
That’s we are able to make dogs look a certain way with selective breeding... that’s us driving evolution. The more generations you get in a short amount of time the more chance of there being mutations that help the species... then those individuals get to breed and the species evolves. With humans it takes so long because we live a lot longer.
It's true, but there are some exceptions (also, as others have noted, mayflies don't actually live for a day).
So, to the exceptions:
First, explanation. Evolution comes from two directions, broadly speaking: natural selection, and random drift. Natural selection is the "survival of the fittest" part you are talking about...favorable mutations are selected for and spread through the population. Drift, on the other hand, is random change that spreads through the population just due to chance, rather than because it provides an advantage.
Under natural selection, quickly reproducing things can respond more quickly to changes in their environment because of the increased churn of reproduction. That's the default "faster you reproduce, yeah, the faster you evolve". But in practice, you don't always _see_ faster evolution due to selection. Why? Because the environment isn't always changing. If the environment doesn't change, it can actually select for a well-adapted organism to stay the same...if it ain't broke, there's no need to fix it. In such an environment you may not see a lot of obvious change even in rapidly reproducing species.
Another interesting tidbit is for species involved in symbiotic relationships. In those situations, the situation can vary between mutualistic and parasitic...for example, consider trees with symbiotic nitrogen-fixing bacteria on their roots. If the bacteria take nutrients and give up plenty of nitrogen, then it's mutualistic. If the bacteria mutates to take nutrients but give less nitrogen, it can become parasitic. Turns out, according to some research I've seen, the slower-evolving species actually has the upper hand in these situations precisely because it's slower evolving. You can think of this as being like a negotiation...the slower evolving species can't "move" on its point quickly, which means it actually has the stronger position. The faster-evolving species basically has to accommodate it or see the host die.
Ok, but back to the topic:
The final way things can evolve is through random drift. The thing is, though, that random drift happens faster in small populations. It's easier for a gene to predominate randomly in a small population than in a large one because it has to get "lucky" fewer times.
Why am I talking about this? Because a lot of slow-reproducers have small population sizes, and a lot of fast reproduceres have huge population size. Think of, eg, mice vs elephants. Loads of mice living fast and dying young, a handful of elephants living a long time. In these particular comparisons, you may find the small shortlived species drifts surprisingly slow compared to the big species, because the population size difference outweighs the lifespan difference.