Are the Fibonacci numbers' prevalence in nature due to confirmation bias? The Fibonacci numbers are frequently found in nature, such as in the petals of flowers or the shape of pinecones.
But are the numbers actually any more prevalent than other numbers? Could it all be because of confirmation bias?
Is there any research that shows that the Fibonacci numbers occur in nature to a statistically significant extent?
 A: As stated, your hypothesis is too vague. In order to make inferences, you need to know what population you are analyzing. Is it the population of all enumerable phenomena? How would one even design a sampling strategy? Such things cannot be done for questions like this unless you know how to measure such a thing. I seriously doubt that you will find a paper to decide your question one way or another.
As for confirmation bias: The world is filled with numbers. However, as humans we are pattern seekers, so we find interest and novelty in phenomena that satisfy our aesthetic sense of order and pattern. The Fibonacci numbers are such a case. We take notice when such a sequence is present in nature, but ignore the vast (I'd say essentially infinite) number of occurrences when such patterns are a absent, because they are uninteresting.
So yes, our preoccupation with noticing interesting patterns in "unstructured" nature is definitely a case of confirmation bias, just like when you run into a friend in a random city and then ask "what are the odds of that?"
