The green lizards lived on lower branches and did not really need to have really sticky feet. But when there cousins the brown lizards invaded there was more of a challenge down on the low branches so they decided to move to the upper level branches the problem was that their feet were not sticky enough. So they had to adapt and have sticker feet which enabled them to swing an get in different places.
The peppered moth had to change its color because during the pollution the trees started getting darker. At first the moths were the lighter color and they blended in really well with the trees but then when the pollution started happening they did not blend in anymore and they had to change that. So they started to slowly over time the moths started turning black to match the trees. When they did this they would match the tree and would not get killed by another living thing
They originate in deserts in parts of Mexico and the United States. For example in Mexico's Valley of Fire the landscape goes from being sandy to dried up lava. In this situation when this started to happen the original pocket mice where a tan color and this was good on the sand but on the dried up lava it was horrible. They stood out and owls could easily see them and eat them. So the rock pocket mice went through natural selection and they started to become dark grey and black. These mice survived better in the dried up lava. The were still in danger when they went out onto the sand. Also since they are only going to be seen from above there stomachs are white.