The intriguing research raises the possibility that doctors could take clinical decisions on how an individual patient's cancer will change, and what treatments should be used, by applying mathematical formulas to tumour biopsies.
Scientists at The Institute of Cancer Research, London, and Queen Mary University of London (QMUL), used a wealth of data - generated from more than 900 tumours of 14 different types - to show that many cancers evolve in particular patterns that can be predicted.
The study, published in Nature Genetics (Monday), was funded by a donation to The Institute of Cancer Research by Chris Rokos and by organisations including the Wellcome Trust, Cancer Research UK and the Medical Research Council.
Many cancer types, such as bowel, stomach and some lung cancers, closely followed a path set out by a theoretical model describing the accumulation and spread of genetic mutations during a single rapid expansion.
The model, created by the research team, predicted that in many tumours, all important cancer genes are already present at the beginning of tumour growth, and new mutations inside the tumour are essentially 'passengers', with no additional effect.
The team showed that these passenger mutations would accumulate following a so-called 1/f power-law distribution. This pattern is found through nature in a variety of physical, chemical and biological systems including the flow of the River Nile and the luminosity of stars - and even helps to govern the financial market.
The model was less good at predicting the path of some other cancers, such as brain and pancreatic tumours, suggesting that in these cases natural selection - driven by pressures on resources and space - might play a greater role in the spread of mutations.
But in the future, the development of these types of cancers could also be predicted using more elaborate mathematical models, the scientists said. The next step in their research is to determine how the new predictive features they can measure - such as the speed of emergence of aggressive or drug-resistant mutations - map to outcomes for patients over time.
This new analysis of cancer data potentially has important clinical implications - providing a new way to distinguish mutations that should be targeted with treatment, versus 'passenger' mutations that may have no effect on cancer cell growth.
Study co-leader Dr Andrea Sottoriva, Chris Rokos Fellow in Evolution and Cancer at The Institute of Cancer Research, London, said: "Our study shows that the spread of mutations through a cancer follows natural laws - and is therefore theoretically predictable, just as we can predict the movement of celestial bodies or the weather.
"This predictability means that the vast amount of genetic data we can generate from tumour biopsies could tell us how a given cancer will develop over time - which mutations will come to drive it into more aggressive disease, when they will emerge, and which drugs are best to treat them. Like in a game of chess, the aim is anticipating the next move of the adversary, to ultimately win the game."
Study co-leader Dr Trevor Graham, head of the Evolution and Cancer laboratory at the Barts Cancer Institute at QMUL, said: "We often think of cancers as being the chaotic and uncontrolled growth of cells within the body. But counter to this intuition, our study shows how cancer evolution is in fact often highly ordered and can even be explained by a straightforward mathematical rule.
"This rule is important because it hugely simplifies our view of how cancers evolve. Now that we know the rule, we can attempt to bend it in our favour to improve patient outcomes."
Dr Kat Arney, Cancer Research UK's Science Information Manager, said: "Research like this is enabling scientists to anticipate how different cancers evolve in the body. If doctors were able to reliably predict how cancers change with time, it could help them choose the most effective treatments for each patient. Advances in DNA sequencing technology mean that we're now able to track how individual tumours change over time at the deepest genetic level."
The Institute of Cancer Research, London, is one of the world's most influential cancer research institutes.
Scientists and clinicians at The Institute of Cancer Research (ICR) are working every day to make a real impact on cancer patients' lives. Through its unique partnership with The Royal Marsden Hospital and 'bench-to-bedside' approach, the ICR is able to create and deliver results in a way that other institutions cannot. Together the two organisations are rated in the top four cancer centres globally.
The ICR has an outstanding record of achievement dating back more than 100 years. It provided the first convincing evidence that DNA damage is the basic cause of cancer, laying the foundation for the now universally accepted idea that cancer is a genetic disease. Today it leads the world at isolating cancer-related genes and discovering new targeted drugs for personalised cancer treatment.
As a college of the University of London, the ICR provides postgraduate higher education of international distinction. It has charitable status and relies on support from partner organisations, charities and the general public.
The ICR's mission is to make the discoveries that defeat cancer.
Queen Mary University of London (QMUL) is one of the UK's leading universities, and one of the largest institutions in the University of London, with 20,260 students from more than 150 countries.
A member of the Russell Group, we work across the humanities and social sciences, medicine and dentistry, and science and engineering, with inspirational teaching directly informed by our research - in the most recent national assessment of the quality of research, we were placed ninth in the UK (REF 2014).
We also offer something no other university can: a stunning self-contained residential campus in London's East End. As well as our home at Mile End, we have campuses at Whitechapel, Charterhouse Square and West Smithfield dedicated to the study of medicine, and a base for legal studies at Lincoln's Inn Fields.
We have a rich history in London with roots in Europe's first public hospital, St Barts; England's first medical school, The London; one of the first colleges to provide higher education to women, Westfield College; and the Victorian philanthropic project, the People's Palace based at Mile End.
QMUL has an annual turnover of £350m, a research income worth £100m, and generates employment and output worth £700m to the UK economy each year.