A second view is that it is more fit if it has more offspring. Incidentally, surviving longer helps the animal have more offspring, but if the animal becomes old and infertile, further survival is useless. In fact, further survival is worse than useless, because the animal would be eating food that its fertile offspring could be eating instead, so it is reducing the chances of their reproduction.

But the correct view combines these first two. Fitness is increased by both survival and reproduction, independently.

A more fit animal is one that increases its population. The naive view (actually not naive, just different?) is that "the animal" means the specific individual. The only way to increase the population of a specific individual besides asexual reproduction is by making it live longer-- so its population remains 1 instead of falling to 0. The second view is that "the animal" is really the genes, so population growth consists of having more of those genes, even if they are living in different combinations and in combinations that include genes not in the original animal-- mutations, or genes from mates.

How do we increase the population of genes? The most dramatic way is by reproduction, which can increase a gene's population from 1 to 1 billion very quickly. But survival remains as another way. It still represents keeping a population of 1 instead of 0-- or, if there has been reproduction, at N instead of N-1. But having one more copy of the gene out there is still a contribution to population growth and evolutionary success.

Moreover, the two contributors to fitness interact. The second view recognized that increased survival makes increased reproduction more valuable-- if you die you, immense fertility is just a waste. But it is also true that increased reproduction makes increased survival more valuable. If a gene reproduces and make 100 copies, then each extra year of lifetime increases its population not by 1 but by 100 for that year.

Thus, there is an evolutionary reason for altruism towards aged parents. Imagine two tribes of people in a wilderness where disease, not food, is the limiting input. The Alagala tribe starves their old people; the Baragara tribe keeps them alive. Which tribe will be bigger? --the Baragara tribe. It will not be a huge effect, and the Baragara tribe would not increase so much that it would eliminate the Alagala tribe, but the fact remains that if you heaved a rock into a cave, you would be more likely to hit a Baragaran than an Alagalan.