  A fundamental question of human society is the evolution of cooperation. Many
previous studies explored this question via setting spatial background, where
players obtain their payoffs by playing game with their nearest neighbors.
Another undoubted fact is that environment plays an important role in the
individual development. Inspired by these phenomena, we reconsider the
definition of individual fitness which integrates the environment, denoted by
the average payoff of all individual neighbors, with the traditional individual
payoffs by introducing a selection parameter $u$. Tuning $u$ equal to zero
returns the traditional version, while increasing $u$ bears the influence of
environment. We find that considering the environment, i.e. integrating
neighborhoods in the evaluation of fitness, promotes cooperation. If we enhance
the value of $u$, the invasion of defection could be resisted better. We also
provide quantitative explanations and complete phase diagrams presenting the
influence of environment on the evolution of cooperation. Finally, the
universality of this mechanism is testified for different neighborhood sizes,
different topology structures and different game models. Our work may shed a
light on the emergence and persistence of cooperation in our life.
