fortuitously

In a fortuitous manner; in a manner of happening by chance; coincidentally; accidentally.

[…] For the genetic constitution of the individual may determine only a range of possible behaviour. The actual behaviour of each individual is fortuitously dependent on the total environment, and this latter can include the actual group. For example, the tendency of birds to refrain from mating may prevent the group from exhausting its food supply.

In a fortuitous manner; in a manner of happening by a lucky chance; luckily; fortunately.