They say less than 5% of elephants die from cancer vs up to 25% of human.
Scientists are saying it is because each elephant has more TP53 genes than we do. An elephant has 20 TP53 genes from its father and 20 TP53 genes from it mother, in total 40 TP53 genes. A human has one p53 gene from dad and one TP53 gene from mom, in total 2 TP53 genes.
Each TP53 gene will produce one TP53 protein. TP53 is the most important tumor suppressor protein. TP53 protein's function is to suppress tumor from happening by repairing DNA if something became wrong in DNA and lead cell to death if DNA cannot be fixed.
Cancer is caused by accumulation o multiple gene mutations. Mutated gene produces protein which does not function as it is supposed.
If TP53 gene is mutated, TP53 protein cannot function well as tumor suppression protein. Human has only two copies of TP53, so if one TP53 gene is mutated, we have only one property working TP53 tumor suppressor protein, which makes cell to be vulnerable to become cancer. On the other hand, elephants have 40 TP53 tumor suppressor genes, so even if 3 TP53 genes are mutated, there are still 37 TP53 genes which will produce 37 TP53 tumor suppressor proteins. This is one of main reasons why less than 5% of elephants die from cancer, so the author of the paper published in Scientific America says. Unfortunately, however we try to grow our body size to like elephant by eating much or by training hard, human can produce only 2 TP53 genes.
Incidentally, according The Cancer Genome Atlas project (2015), 50% of muscle invasive bladder cancer had TP53 gene mutations.
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www.scientificamerican.com/article/why-elephants-don-rsquo-t-get-cancer/
www.scientificamerican.com/article/how-evolution-helps-us-understand-cancer-and-control-it/
www.nature.com/articles/nature12965 
