The extinction of some species such as Bison does have an effect on the ecosystem as it is said to reduce biodiversity.
When there is reduction in biodiversity, it is said to affect the resilience of an ecosystem. Biologically is said to a lot of communities that has species that brings about resilience to that ecosystem and thus a reduction will also reduce the chance of species having traits that helps them to adapt to a changing environment.
Note that as species is said to go into extinct, they are therefore not part of the food chain and as such Animals that had eaten the newly-extinct species will have to look for new food sources or starve and dies.
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