Resolving Peto's paradox: Modeling the potential effects of size-related metabolic changes, and of the evolution of immune policing and cancer suppression

Revealing endogenous conditions for Peto's paradox via an ordinary differential equation model

Cancer, a disease intimately linked to cellular mutations, is commonly believed to exhibit a positive association with the cell count and lifespan of a species. Despite this assumption, the observed uniformity in cancer rates across species, referred to as the Peto's paradox, presents a conundrum. Recognizing that tumour progression is not solely dependent on cancer cells but involves intricate interactions among various cell types, this study employed a Lotka-Volterra (LV) ordinary differential equation model to analyze the evolution of cancerous cells and the cancer incidence in an immune environment. As a result, this study uncovered the sufficient conditions underlying the absence of correlation in Peto's paradox and provide insights into the reasons for the equitable distribution of cancer incidence across diverse species by applying nondimensionalization and drawing an analogy between the characteristic time interval for the variation of cell populations in the ODE model and that of cell cycles of a species.

The effect of body size and inbreeding on cancer mortality in breeds of the domestic dog: a test of the multi-stage model of carcinogenesis

Cancer is a leading cause of death in domestic dogs. Deaths due to cancer vary widely among breeds, providing an opportunity for testing the multi-stage model of carcinogenesis. This model underpins evolutionary and basic studies of cancer suppression and predicts a linear increase in cancer with breed size, an expectation complicated by bigger breeds having a shorter lifespan (decreasing risk). Using three independent datasets, the weight and lifespan of breeds provided a good fit of lifetime cancer mortality to the multi-stage model, the fit suggesting many canine cancers are initiated by four driver mutations. Of 85 breeds in more than one dataset, only flat-coated retriever showed significantly elevated cancer mortality, with Scottish terrier, Bernese mountain dog and bullmastiff also showing notable risk (greater than 50% over expected). Analysis of breed clades suggested terriers experience elevated cancer mortality. There was no evidence that the lower mass-specific metabolic rate of larger breeds reduced cancer risk. Residuals indicated increased breed inbreeding shortened expected lifespan, but had no overall effect on cancer mortality. The results provide a baseline for identifying increased breed risk for specific cancers and demonstrate that, unless selection promotes increased cancer suppression, the evolution of larger longer-lived animals leads to a predictable increased cancer risk.

Chance, ignorance, and the paradoxes of cancer: Richard Peto on developing preventative strategies under uncertainty

During the early 1980s both cancer biology and epidemiological methods were being transformed. In 1984 the leading cancer epidemiologist Richard Peto - who, in 1981, had published the landmark Causes of Cancer with Richard Doll - wrote a short chapter on "The need for ignorance in cancer research", in which the worlds of epidemiology and speculative Darwinian biology met. His reflections on how evolutionary theory related to cancer have become known as "Peto's paradox", whilst his articulation of "black box epidemiology" provided the logic of subsequent practice in the field. We reprint this sparkling and prescient example of biologically-informed epidemiological theorising at its best in this issue of the European Journal of Epidemiology, together with four commentaries that focus on different aspects of its rich content. Here were provide some contextual background to the 1984 chapter, and our own speculations regarding various paradoxes in cancer epidemiology. We suggest that one reason for the relative lack of progress in indentifying novel modifiable causes of cancer over the last 40 years may reflect such exposures being ubiquitous within environments, and discuss the lessons for epidemiology that would follow from this.

Identifying the Risk Factors for Malignant Mammary Tumors in Dogs: A Retrospective Study

Mammary cancer is one of the main causes of death in female dogs worldwide, considering that many risk factors are involved in its development. This study aimed to elucidate the relationship between epidemiological and clinical risk factors with the histopathological diagnosis of malignant mammary tumors in dogs treated at the Veterinary Hospital of the Federal University of Uberlândia, which has one of the first veterinary oncology services in Brazil. A retrospective matched case-control study was conducted to identify risk factors for the development of malignant mammary tumors in dogs. The variables analyzed were size dog, breed, housing, type of diet, and body score. Potential risk factors were selected by univariate analysis (p < 0.25) before multivariate forward binary logistic regression. The most frequent benign tumor was the benign mixed tumor (35.2%), and the most frequent malignant tumor was the mixed carcinoma (27.4%). Size dog, breed, housing, and overweight are predictors of malignant mammary tumors in dogs. The highest risk of developing malignant mammary tumors is associated with large female dogs, Yorkshire or Poodle breeds, living outside the home, or being overweight.

Wild pedigrees inform mutation rates and historic abundance in baleen whales

Phylogeny-based estimates suggesting a low germline mutation rate (μ) in baleen whales have influenced research ranging from assessments of whaling impacts to evolutionary cancer biology. We estimated μ directly from pedigrees in four baleen whale species for both the mitochondrial control region and nuclear genome. The results suggest values higher than those obtained through phylogeny-based estimates and similar to pedigree-based values for primates and toothed whales. Applying our estimate of μ reduces previous genetic-based estimates of preexploitation whale abundance by 86% and suggests that μ cannot explain low cancer rates in gigantic mammals. Our study shows that it is feasible to estimate μ directly from pedigrees in natural populations, with wide-ranging implications for ecological and evolutionary research.

How size and genetic diversity shape lifespan across breeds of purebred dogs

While the lifespan advantage of small body size and mixed breed status has been documented repeatedly, evidence for an effect of genetic diversity across dog breeds is equivocal. We hypothesized that this might be due to a strong right-censoring bias in available breed-specific lifespan estimates where early-dying dogs from birth cohorts that have not died off completely at the time of data collection are sampled disproportionately, especially in breeds with rapidly growing populations. We took advantage of data on owner reported lifespan and cause of death from a large public database to quantify the effect of size and genetic diversity (heterozygosity) on mortality patterns across 118 breeds based on more than 40,000 dogs. After documenting and removing the right-censoring bias from the breed-specific lifespan estimates by including only completed birth cohorts in our analyses, we show that small size and genetic diversity are both linked to a significant increase in mean lifespan across breeds. To better understand the proximate mechanisms underlying these patterns, we then investigated two major mortality causes in dogs - the cumulative pathophysiologies of old age and cancer. Old age lifespan, as well as the percentage of old age mortality, decreased with increasing body size and increased with increasing genetic diversity. The lifespan of dogs dying of cancer followed the same patterns, but while large size significantly increased proportional cancer mortality, we could not detect a significant signal for lowered cancer mortality with increasing diversity. Our findings suggest that outcross programs will be beneficial for breed health and longevity. They also emphasize the need for high-quality mortality data for veterinary epidemiology as well as for developing the dog as a translational model for human geroscience.

Cell size, body size and Peto's paradox

Carcinogenesis is one of the leading health concerns afflicting presumably every single animal species, including humans. Currently, cancer research expands considerably beyond medicine, becoming a focus in other branches of natural science. Accumulating evidence suggests that a proportional scale of tumor deaths involves domestic and wild animals and poses economical or conservation threats to many species. Therefore, understanding the genetic and physiological mechanisms of cancer initiation and its progression is essential for our future action and contingent prevention. From this perspective, I used an evolutionary-based approach to re-evaluate the baseline for debate around Peto's paradox. First, I review the background of information on which current understanding of Peto's paradox and evolutionary concept of carcinogenesis have been founded. The weak points and limitations of theoretical modeling or indirect reasoning in studies based on intraspecific, comparative studies of carcinogenesis are highlighted. This is then followed by detail discussion of an effect of the body mass in cancer research and the importance of cell size in consideration of body architecture; also, I note to the ambiguity around cell size invariance hypothesis and hard data for variability of cell size across species are provided. Finally, I point to the new research area that is driving concepts to identify exact molecular mechanisms promoting the process of tumorigenesis, which in turn may provide a proximate explanation of Peto's paradox. The novelty of the approach proposed therein lies in intraspecies testing of the effect of differentiation of cell size/number on the probability of carcinogenesis while controlling for the confounding effect of body mass/size.

Cancer suppression and the evolution of multiple retrogene copies of TP53 in elephants: a re‐evaluation

Evolving to become bigger and/or longer lived should increase cancer susceptibility, but this predicted increase is not observed, a contradiction named Peto's paradox. A solution is that cancer suppression evolves to minimize cancer susceptibility, and the discovery of 19 retrogene (RTG) copies of the tumor suppressor gene TP53 in the African elephant (Loxodonta africana) is increasingly cited as a classic example of such adaptive suppression. However, classic examples need rigorous evaluation and an alternative hypothesis is that the RTGs spread by genetic drift. This study shows that before its duplication, the ancestral elephant RTG was already truncated from 390 amino acids to 157 by a frameshift mutation, and that 14 of the 19 copies are now truncated to ≤88 amino acids. There was no compelling evidence of either positive or negative selection acting on these 88 codons, and the pattern of RTG accumulation fits a neutral model with a duplication rate of ~10⁻⁶ per generation. It is concluded that there is no evidence supporting the hypothesis that the 19 elephant RTGs spread to fixation by selection; instead, the evidence indicates that these RTGs accumulated primarily by segmental duplication and drift. It is shown that the evolutionary multistage model of carcinogenesis (EMMC) predicts the recruitment of 1–2 independently acting tumor suppressor genes to suppress the increased cancer risk in elephants, so it is possible that one or a few RTGs may have been favored by selection resulting in the known enhanced sensitivity of elephant cells to DNA damage. However, the analysis does not provide any support for either a direct (via conserved TP53 activity) or indirect (via supporting canonical TP53 function) role of the RTGs sequences, so that the presence of multiple copies of TP53 retrogenes in elephants needs to be further justified before being used as a classic example of tumor suppression in large‐bodied animals.

Increased risk of cancer in dogs and humans: a consequence of recent extension of lifespan beyond evolutionarily-determined limitations?

Cancer is among the most common causes of death for dogs (and cats) and humans in the developed world, even though it is uncommon in wildlife and other domestic animals. We provide a rationale for this observation based on recent advances in our understanding of the evolutionary basis of cancer. Over the course of evolutionary time, species have acquired and fine-tuned adaptive cancer protective mechanisms that are intrinsically related to their energy demands, reproductive strategies, and expected lifespan. These cancer protective mechanisms are general across species and/or specific to each species and their niche, and they do not seem to be limited in diversity. The evolutionarily acquired cancer-free longevity that defines a species' life history can explain why the relative cancer risk, rate, and incidence are largely similar across most species in the animal kingdom despite differences in body size and life expectancy. The molecular, cellular, and metabolic events that promote malignant transformation and cancerous growth can overcome these adaptive, species-specific protective mechanisms in a small proportion of individuals, while independently, some individuals in the population might achieve exceptional longevity. In dogs and humans, recent dramatic alterations in healthcare and social structures have allowed increasing numbers of individuals in both species to far exceed their species-adapted longevities (by 2-4 times) without allowing the time necessary for compensatory natural selection. In other words, the cancer protective mechanisms that restrain risk at comparable levels to other species for their adapted lifespan are incapable of providing cancer protection over this recent, drastic and widespread increase in longevity.

Determining cancer risk: the evolutionary multistage model or total stem cell divisions?

A recent hypothesis proposed that the total number of stem cell divisions in a tissue (TSCD model) determine its intrinsic cancer risk; however, a different model-the multistage model-has long been used to understand how cancer originates. Identifying the correct model has important implications for interpreting the frequency of cancers. Using worldwide cancer incidence data, we applied three tests to the TSCD model and an evolutionary multistage model of carcinogenesis (EMMC), a model in which cancer suppression is recognized as an evolving trait, with natural selection acting to suppress cancers causing a significant mean loss of Darwinian fitness. Each test supported the EMMC but contradicted the TSCD model. This outcome undermines results based on the TSCD model quantifying the relative importance of 'bad luck' (the random accumulation of somatic mutations) versus environmental and genetic factors in determining cancer incidence. Our testing supported the EMMC prediction that cancers of large rapidly dividing tissues predominate late in life. Another important prediction is that an indicator of recent oncogenic environmental change is an unusually high mean fitness loss due to cancer, rather than a high lifetime incidence. The evolutionary model also predicts that large and/or long-lived animals have evolved mechanisms of cancer suppression that may be of value in preventing or controlling human cancers.