Cancer is a numbers game, caused by just the right mutationnuclear DNA constantly: you can't put a bunch of complex molecules in close proximity without frequent breakage, and that's even without considering the fact that portions of a cell are involved in the energetic business of converting nutrients into energy stores, a process that generates reactive molecules as a byproduct, or that cells are frequently stressed by heat or exercise. A great deal of a cell's complexity is in fact due to the panoply of mechanisms required for ongoing detection of damage, recycling of damaged components, and building replacement parts as needed. This is a continual process, always attempting to keep up with the pace of damage. Of course all of those mechanisms are also vulnerable to damage and must therefore be capable of repairing themselves, but no repair process is perfectly efficient. DNA repair machinery is some of the most efficient of all of these mechanisms, but it still lets things through: there are so many cells in the body that even a tiny failure rate leads to unrepaired damage.
Fortunately most of the time this just means that at worst a cell will falter or break. Most cells are temporary parts of their tissue, and will die off within days or weeks to be replaced by others. A mutated cell with a more serious breakage may become senescent, removing itself from the cell cycle of replication, or destroy itself. Even in the situation of a potentially cancerous mutation, the cell will still most likely be destroyed by the immune system or its own defenses. But again, there are a lot of cells in the body. It only takes one to slip through all of the layers of defense to start up a tumor. You can develop cancer at any age - you just have to be very unlucky for it to happen in youth, when there is little damage and all of the repair and defense mechanisms are operating a peak efficiency. Later on is a different story, of course, and cancer is an age-related disease because the odds get progressively worse with increasing tissue damage and a growing failure of repair machinery and immune surveillance.
So as I said, this is a numbers game. Count the cells, multiply by mutation rates, and divide by repair efficiency - and there is the scaling factor for your odds of cancer. Or at least in theory, from a naive point of view. Yet here is an interesting thing: mice are little cancer factories in comparison to humans. Yet we humans have thousands of times as many cells as a mouse. Further, what about whales? They have thousands of times as many cells as we do, and some of them seem capable of living twice as long as we do. Yet they don't seem to have any significantly greater cancer incidence. If you compare across other mammals, it turns out that there really isn't any correlation between body mass and cancer rate. This observation is known as Peto's Paradox, proposed with the idea that there is evidently more to the cancer numbers game than first thought.
The motivation for researchers is to be able to identify the differences that exist in the biochemistry of large mammals to explain why they don't have very high cancer rates. There is presumably some chance that this research could result in therapies for humans, though the odds are unknowable in advance. Any sort of investigation of other species could turn up differences that are near impossible to apply to human biochemistry, or differences that could soon lead to therapies, and it's next to impossible to put real numbers to those odds without further research. Still there has been some progress on the basics in recent years, and this open access paper is an example of present thinking on the topic.
It is an open question why an elephant, with 100× more cells than a human, or a whale with 1000× more cells than a human, has approximately the same (or lower) cancer risk as a human. This is Peto's paradox, and though many potential solutions have been proposed, it remains unsolved. The fact that cancer rates are approximately constant across body sizes and lifespans suggests that there has been selection on the life histories of organisms to prevent cancer in large, long-lived organisms. In order to investigate Peto's paradox, it would be helpful to understand how much evolution would have to change the parameters of somatic evolution to compensate for the evolution of large bodies and long lifespans. For example, we can ask how much the somatic mutation rate must decrease in order for a whale, which has 1000× more cells than a human, to retain the same cancer risk as a human.
There is still much work to be done in the field to obtain more accurate estimates of human somatic mutation rates, as reported values span orders of magnitude. Though the estimates are not perfect, slight differences in mutation rate across species have been observed. For example, one study that derives somatic mutation rates from specific loci across eukaryotes found that the per base mutation rates for human and mouse are a factor of 3.6 apart. This 3.6-fold decrease in mutation rate in human versus mouse is remarkably close to the results of our modelling, which suggest that a two- to threefold decrease in mutation rate can account for a 1000-fold difference in body size between mice and humans. This effective decrease in mutation rate may be accomplished by having better DNA repair in the larger species, more efficient removal of mutated cells, or less endogenous damage as a result of a lower mass-specific basal metabolic rate.
Analysis of previously published models of colorectal cancer suggests that a two- to three-fold decrease in the mutation rate or stem cell division rate is enough to reduce a whale's cancer risk to that of a human. Similarly, the addition of one to two required tumour-suppressor gene mutations would also be sufficient. We surveyed mammalian genomes and did not find a positive correlation of tumour-suppressor genes with increasing body mass and longevity. However, we found evidence of the amplification of TP53 in elephants, FBXO31 in microbats, which might explain Peto's paradox in those species. Exploring parameters that evolution may have fine-tuned in large, long-lived organisms will help guide future experiments to reveal the underlying biology responsible for Peto's paradox and guide cancer prevention in humans.