Cell size and cancer: a new solution to Peto's paradox?

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.

Mechanical shear flow regulates the malignancy of colorectal cancer cells

Colorectal cancer (CRC) is notable for its high mortality and high metastatic characteristics. The shear force generated by bloodstream provides mechanical signals regulating multiple responses of cells, including metastatic cancer cells, dispersing in blood vessels. We, therefore, studied the effect of shear flow on circulating CRC cells in the present study. The CRC cell line SW620 was subjected to shear flow of 12.5 dynes/cm2 for 1 and 2 h separately. Resulting elevated caspase-9 and -3 indicated that shear flow initiated the apoptosis of SW620. Enlarged cell size associated with a higher level of cyclin D1 was coincident with the flow cytometric results indicating that the cell cycle was arrested at the G1 phase. An elevated phosphor-eNOSS1177 increased the production of nitric oxide and led to reactive oxygen species-mediated oxidative stress. Shear flow also regulated epithelial-mesenchymal transition (EMT) by increasing E-cadherin and ZO-1 while decreasing Snail and Twist1. The migration and invasion of sheared SW620 were also substantially decreased. Further investigations showed that mitochondrial membrane potential was significantly decreased, whereas mitochondrial mass and ATP production were not changed. In addition to the shear flow of 12.5 dynes/cm2, the expressions of EMT were compared at lower (6.25 dynes/cm2) and at higher (25 dynes/cm2) shear flow. The results showed that lower shear flow increased mesenchymal characteristics and higher shear flow increased epithelial characteristics. Shear flow reduces the malignancy of CRC in their metastatic dispersal that opens up new ways to improve cancer therapies by applying a mechanical shear flow device.

Anthropometric indicators may explain the high incidence of follicular lymphoma in Europeans: Results from a bidirectional two-sample two-step Mendelian randomisation

BACKGROUND

Non-Hodgkin's lymphoma incidence rates vary between European and Asian populations. The reasons remain unclear. This two-sample two-step Mendelian randomisation (MR) study aimed to investigate the causal relationship between anthropometric indicators (AIs) and diffuse large B-cell lymphoma (DLBCL) and follicular lymphoma (FL) and the possible mediating role of basal metabolic rate (BMR) in Europe.

METHODS

We used the following AIs as exposures: body mass index (BMI), whole-body fat mass (WBFM), whole-body fat-free mass (WBFFM), waist circumference(WC), hip circumference(HC), standing height (SH), and weight(Wt). DLBCL and FL represented the outcomes, and BMR was a mediator. A two-sample MR analysis was performed to examine the association between AIs and DLBCL and FL onset. We performed reverse-MR analysis to determine whether DLBCL and FL interfered with the AIs. A two-step MR analysis was performed to determine whether BMR mediated the causality.

FINDINGS

WBFFM and SH had causal relationships with FL. A causal association between AIs and DLBCL was not observed. Reverse-MR analysis indicated the causal relationships were not bidirectional. Two-step MR suggested BMR may mediate the causal effect of WBFFM and SH on FL.

CONCLUSIONS

We observed a causal relationship between WBFFM and SH and the onset of FL in Europeans, Which may explain the high incidence of follicular lymphoma in Europeans.

Genetically predicted thyroid function and risk of colorectal cancer: a bidirectional Mendelian randomization study

BACKGROUND

Observational studies have reported an association between thyroid function and colorectal cancer (CRC), with conflicting results. Elucidating the causal relationship between thyroid function and CRC facilitates the development of new preventive strategies to reduce CRC incidence.

METHOD

We applied a two-sample Mendelian randomization (MR) method to evaluate the causal relationship between five thyroid-related indexes, including hyperthyroidism, hypothyroidism, thyroid stimulating hormone (TSH), free thyroxine (FT4) and basal metabolic rate (BMR), and CRC. Genome-wide association study statistics for thyroid-related phenotypes were obtained from the ThyroidOmics consortium, and summary statistics for genetic associations with CRC were obtained from the FinnGen consortium. We set a series of criteria to screen single nucleotide polymorphisms (SNPs) as instrumental variables and then performed bidirectional MR analysis, stratified analysis and extensive sensitivity analysis. Multiplicative random-effects inverse variance weighted was the primary analysis method, supplemented by weighted median and MR-Egger.

RESULT

We identified 12 SNPs for hyperthyroidism, 10 SNPs for hypothyroidism, 41 SNPs for TSH, 18 SNPs for FT4, and 556 SNPs for BMR. Genetically predicted hyperthyroidism, hypothyroidism, TSH, and FT4 were not associated with CRC risk (all P > 0.05). Sensitivity analysis revealed no heterogeneity or pleiotropy. Genetically predicted BMR was significantly associated with increased CRC risk after removing outlier (OR = 1.30, P = 0.0029). Stratified analysis showed that BMR was significantly associated with colon cancer (OR = 1.33, P = 0.0074) but not rectal cancer. In the reverse analysis, there was no evidence of an effect of CRC on thyroid function (all P > 0.05).

CONCLUSION

Our bidirectional MR analysis provides new insights into the relationship between thyroid function and CRC. CRC prevention may benefit from enhanced screening of high BMR populations.

Insight into the causality between basal metabolic rate and endometrial and ovarian cancers: Analysis utilizing systematic Mendelian randomization and genetic association data from over 331,000 UK biobank participants

BACKGROUND

Observational studies have demonstrated that basal metabolic rate (BMR) is associated with the risk of endometrial cancer (EC) and ovarian cancer (OC). However, it is unclear whether these associations reflect a causal relationship.

OBJECTIVE

To reveal the causality between BMR and EC and OC, we performed the first comprehensive two-sample Mendelian randomization (MR) analyses.

METHODS

Genetic variants were used as proxies of BMR. GWAS summary statistics of BMR, EC and OC were obtained from the UK Biobank Consortium, Endometrial Cancer Association Consortium and Ovarian Cancer Association Consortium respectively. The inverse variance weighted method was employed as the main approach for MR analysis. A series of sensitivity analyses were implemented to validate the robustness and reliability of the results.

RESULTS

BMR was significantly related to an increased risk of EC (OR_SD  = 1.49; 95% CI: 1.29-1.72; p-Value < .001) and OC (OR_SD  = 1.21; 95% CI: 1.08-1.35; p-Value < .001). Furthermore, the stratified analysis indicated that BMR was positively associated with endometrioid endometrial cancer (EEC) (OR_SD  = 1.45; 95% CI, 1.23-1.70; p-Value < .001), clear cell ovarian cancer(CCOC) (OR_SD  = 1.89; 95% CI:1.35-2.64; p-Value < .001) and endometrioid ovarian cancer risk (EOC) (OR_SD  = 1.45; 95% CI: 1.12-1.88; p-Value = .005). However, there were no significant associations of BMR with invasive mucinous ovarian cancer (IMOC), high-grade serous ovarian cancer (HGSOC) and low-grade serous ovarian cancer (LGSOC). The robustness of the above results was further verified in sensitivity analyses.

CONCLUSION

The MR study provided etiological evidence for the positive association of BMR with the risk of EC, EEC, OC, CCOC and EOC. But this study did not provide enough evidence suggesting the causal associations of BMR with IMOC, HGSOC and LGSOC.

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.

A novel perspective suggesting high sustained energy expenditure may be net protective against cancer

Energy expenditure (EE) is generally viewed as tumorigenic, due to production of reactive oxygen species (ROS) that can damage cells and DNA. On this basis, individuals within a species that sustain high EE should be more likely to develop cancer. Here, we argue the opposite, that high EE may be net protective effect against cancer, despite high ROS production. This is possible because individuals that sustain high EE have a greater energetic capacity (=greater energy acquisition, expenditure and ability to up-regulate output), and can therefore allocate energy to multiple cancer-fighting mechanisms with minimal energetic trade-offs. Our review finds that individuals sustaining high EE have greater antioxidant production, lower oxidative stress, greater immune function and lower cancer incidence. Our hypothesis and literature review suggest that EE may indeed be net protective against cancer, and that individual variation in energetic capacity may be a key mechanism to understand the highly individual nature of cancer risk in contemporary human populations and laboratory animals.

Lay summary The process of expending energy generates reactive oxygen species that can lead to oxidative stress, cell and DNA damage, and the accumulation of this damage is thought to be a major contributor to many ageing related diseases that include cancer. Here, we challenge this view, proposing how and why high energy expenditure (EE) may actually be net protective against cancer, and provide literature support for our hypothesis. We find individuals with high sustained EE have greater energetic capacity and thus can invest more in repair to counter oxidative stress, and more in immune function, both of which reduce cancer risk. Our hypothesis provides a novel mechanism to understand the highly individual nature of cancer, why taller individuals are more at risk, why physically active individuals have lower cancer risk, and why regular exercise can reduce cancer risk.

Effect of Basal Metabolic Rate on Cancer: A Mendelian Randomization Study

Background: Basal metabolic rate is associated with cancer, but these observations are open to confounding. Limited evidence from Mendelian randomization studies exists, with inconclusive results. Moreover, whether basal metabolic rate has a similar role in cancer for men and women independent of insulin-like growth factor 1 increasing cancer risk has not been investigated.

Methods: We conducted a two-sample Mendelian randomization study using summary data from the UK Biobank to estimate the causal effect of basal metabolic rate on cancer. Overall and sex-specific analysis and multiple sensitivity analyses were performed including multivariable Mendelian randomization to control for insulin-like growth factor 1.

Results: We obtained 782 genetic variants strongly (p-value < 5 × 10^–8) and independently (r² < 0.01) predicting basal metabolic rate. Genetically predicted higher basal metabolic rate was associated with an increase in cancer risk overall (odds ratio, 1.06; 95% confidence interval, 1.02–1.10) with similar estimates by sex (odds ratio for men, 1.07; 95% confidence interval, 1.002–1.14; odds ratio for women, 1.06; 95% confidence interval, 0.995–1.12). Sensitivity analyses including adjustment for insulin-like growth factor 1 showed directionally consistent results.

Conclusion: Higher basal metabolic rate might increase cancer risk. Basal metabolic rate as a potential modifiable target of cancer prevention warrants further study.

What Animal Cancers teach us about Human Biology

Cancers in animals present a large, underutilized reservoir of biomedical information with critical implication for human oncology and medicine in general. Discussing two distinct areas of tumour biology in non-human hosts, we highlight the importance of these findings for our current understanding of cancer, before proposing a coordinated strategy to harvest biomedical information from non-human resources and translate it into a clinical setting. First, infectious cancers that can be transmitted as allografts between individual hosts, have been identified in four distinct, unrelated groups, dogs, Tasmanian devils, Syrian hamsters and, surprisingly, marine bivalves. These malignancies might hold the key to improving our understanding of the interaction between tumour cell and immune system and, thus, allow us to devise novel treatment strategies that enhance anti-cancer immunosurveillance, as well as suggesting more effective organ and stem cell transplantation strategies. The existence of these malignancies also highlights the need for increased scrutiny when considering the existence of infectious cancers in humans. Second, it has long been understood that no linear relationship exists between the number of cells within an organism and the cancer incidence rate. To resolve what is known as Peto's Paradox, additional anticancer strategies within different species have to be postulated. These naturally occurring idiosyncrasies to avoid carcinogenesis represent novel potential therapeutic strategies.

TERT promoter alterations could provide a solution for Peto's paradox in rodents

Cancer is a genetic disease caused by changes in gene expression resulting from somatic mutations and epigenetic changes. Although the probability of mutations is proportional with cell number and replication cycles, large bodied species do not develop cancer more frequently than smaller ones. This notion is known as Peto's paradox, and assumes stronger tumor suppression in larger animals. One of the possible tumor suppressor mechanisms involved could be replicative senescence caused by telomere shortening in the absence of telomerase activity. We analysed telomerase promoter activity and transcription factor binding in mammals to identify the key element of telomerase gene inactivation. We found that the GABPA transcription factor plays a key role in TERT regulation in somatic cells of small rodents, but its binding site is absent in larger beavers. Protein binding and reporter gene assays verify different use of this site in different species. The presence or absence of the GABPA TF site in TERT promoters of rodents correlates with TERT promoter activity; thus it could determine whether replicative senescence plays a tumor suppressor role in these species, which could be in direct relation with body mass. The GABPA TF binding sites that contribute to TERT activity in somatic cells of rodents are analogous to those mutated in human tumors, which activate telomerase by a non-ALT mechanism.

Interplay between Cellular Metabolism and the DNA Damage Response in Cancer

Metabolism is a fundamental cellular process that can become harmful for cells by leading to DNA damage, for instance by an increase in oxidative stress or through the generation of toxic byproducts. To deal with such insults, cells have evolved sophisticated DNA damage response (DDR) pathways that allow for the maintenance of genome integrity. Recent years have seen remarkable progress in our understanding of the diverse DDR mechanisms, and, through such work, it has emerged that cellular metabolic regulation not only generates DNA damage but also impacts on DNA repair. Cancer cells show an alteration of the DDR coupled with modifications in cellular metabolism, further emphasizing links between these two fundamental processes. Taken together, these compelling findings indicate that metabolic enzymes and metabolites represent a key group of factors within the DDR. Here, we will compile the current knowledge on the dynamic interplay between metabolic factors and the DDR, with a specific focus on cancer. We will also discuss how recently developed high-throughput technologies allow for the identification of novel crosstalk between the DDR and metabolism, which is of crucial importance to better design efficient cancer treatments.

Low basal metabolic rate as a risk factor for development of insulin resistance and type 2 diabetes

INTRODUCTION

Identification of physiological factors influencing susceptibility to insulin resistance and type 2 diabetes (T2D) remains an important challenge for biology and medicine. Numerous studies reported energy expenditures as one of those components directly linked to T2D, with noticeable increase of basal metabolic rate (BMR) associated with the progression of insulin resistance. Conversely, the putative link between genetic, rather than phenotypic, determination of BMR and predisposition to development of T2D remains little studied. In particular, low BMR may constitute a considerable risk factor predisposing to development of T2D.

RESEARCH DESIGN AND METHODS

We analyzed the development of insulin resistance and T2D in 20-week-old male laboratory mice originating from three independent genetic line types. Two of those lines were subjected to divergent, non-replicated selection towards high or low body mass-corrected BMR. The third line type was non-selected and consisted of randomly bred animals serving as an outgroup (reference) to the selected line types. To induce insulin resistance, mice were fed for 8 weeks with a high fat diet; the T2D was induced by injection with a single dose of streptozotocin and further promotion with high fat diet. As markers for insulin resistance and T2D advancement, we followed the changes in body mass, fasting blood glucose, insulin level, lipid profile and mTOR expression.

RESULTS

We found BMR-associated differentiation in standard diabetic indexes between studied metabolic lines. In particular, mice with low BMR were characterized by faster body mass gain, blood glucose gain and deterioration in lipid profile. In contrast, high BMR mice were characterized by markedly higher expression of the mTOR, which may be associated with much slower development of T2D.

CONCLUSIONS

Our study suggests that genetically determined low BMR makeup involves metabolism-specific pathways increasing the risk of development of insulin resistance and T2D.

Functional and structural changes in aorta of mice divergently selected for basal metabolic rate

Cardiovascular diseases (CVD) are one of the most common causes of mortality likely genetically linked to the variation in basal metabolic rate (BMR). A robust test of the significance of such association may be provided by artificial selection experiments on animals selected for diversification of BMR. Here we asked whether genetically determined differences in BMR correlate with anatomical shift in endothelium structure and if so, the relaxation and contraction responses of the aorta in mice from two lines of Swiss-Webster laboratory mice (Mus musculus) divergently selected for high or low BMR (HBMR and LBMR lines, respectively). Functional and structural study of aorta showed that a selection for divergent BMR resulted in the between-line difference in diastolic aortic capacity. The relaxation was stronger in aorta of the HBMR mice, which may stem from greater flexibility of aorta mediated by higher activity of Ca²⁺-activated K⁺ channels. Structural examination also indicated that HBMR mice had significantly thicker aorta's middle layer compared to LBMR animals. Such changes may promote arterial stiffness predisposing to cardiovascular diseases. BMR-related differences in the structure and relaxation ability of aortas in studied animals may be reminiscent of potential risk factors in the development of CVD in humans.

A Zombie LIF Gene in Elephants Is Upregulated by TP53 to Induce Apoptosis in Response to DNA Damage

Large-bodied organisms have more cells that can potentially turn cancerous than small-bodied organisms, imposing an increased risk of developing cancer. This expectation predicts a positive correlation between body size and cancer risk; however, there is no correlation between body size and cancer risk across species ("Peto's paradox"). Here, we show that elephants and their extinct relatives (proboscideans) may have resolved Peto's paradox in part through refunctionalizing a leukemia inhibitory factor pseudogene (LIF6) with pro-apoptotic functions. LIF6 is transcriptionally upregulated by TP53 in response to DNA damage and translocates to the mitochondria where it induces apoptosis. Phylogenetic analyses of living and extinct proboscidean LIF6 genes indicates that its TP53 response element evolved coincident with the evolution of large body sizes in the proboscidean stem lineage. These results suggest that refunctionalizing of a pro-apoptotic LIF pseudogene may have been permissive (although not sufficient) for the evolution of large body sizes in proboscideans.

A mathematical solution to Peto's paradox using Polya's urn model: implications for the aetiology of cancer in general

Ageing is the leading risk factor for the emergence of cancer in humans. Accumulation of pro-carcinogenic events throughout life is believed to explain this observation; however, the lack of direct correlation between the number of cells in an organism and cancer incidence, known as Peto's Paradox, is at odds with this assumption. Finding the events responsible for this discrepancy can unveil mechanisms with potential uses in prevention and treatment of cancer in humans. On the other hand, the immune system is important in preventing the development of clinically relevant tumours by maintaining a fine equilibrium between reactive and suppressive lymphocyte clones. It is suggested here that the loss of this equilibrium is what ultimately leads to increased risk of cancer and to propose a mechanism for the changes in clonal proportions based on decreased proliferative capacity of lymphocyte clones as a natural phenomenon of ageing. This mechanism, being a function of the number of cells, provides an explanation for Peto's Paradox.

Time to change your mind? Modelling transient properties of cortex formation highlights the importance of evolving cell division strategies

The successful development of the mammalian cerebral neocortex is linked to numerous cognitive functions such as language, voluntary movement, and episodic memory. Neocortex development occurs when neural progenitor cells divide and produce neurons. Critically, although the progenitor cells are able to self-renew they do not reproduce themselves endlessly. Hence, to fully understand the development of the neocortex we are faced with the challenge of understanding temporal changes in cell division strategy. Our approach to modelling neuronal production uses non-autonomous ordinary differential equations and allows us to use a ternary coordinate system in order to define a strategy space, through which we can visualise evolving cell division strategies. Using this strategy space, we fit the known data and use approximate Bayesian computation to predict the founding progenitor population sizes, currently unavailable in the experimental literature. Counter-intuitively, we show that humans can generate a larger number of neurons than a macaque's even when starting with a smaller number of progenitor cells. Accompanying the article is a self-contained piece of software, which provides the reader with immediate simulated results that will aid their intuition. The software can be found at www.dpag.ox.ac.uk/team/noemi-picco.

From humans to hydra: patterns of cancer across the tree of life

Cancer is a disease of multicellularity; it originates when cells become dysregulated due to mutations and grow out of control, invading other tissues and provoking discomfort, disability, and eventually death. Human life expectancy has greatly increased in the last two centuries, and consequently so has the incidence of cancer. However, how cancer patterns in humans compare to those of other species remains largely unknown. In this review, we search for clues about cancer and its evolutionary underpinnings across the tree of life. We discuss data from a wide range of species, drawing comparisons with humans when adequate, and interpret our findings from an evolutionary perspective. We conclude that certain cancers are uniquely common in humans, such as lung, prostate, and testicular cancer; while others are common across many species. Lymphomas appear in almost every animal analysed, including in young animals, which may be related to pathogens imposing selection on the immune system. Cancers unique to humans may be due to our modern environment or may be evolutionary accidents: random events in the evolution of our species. Finally, we find that cancer‐resistant animals such as whales and mole‐rats have evolved cellular mechanisms that help them avoid neoplasia, and we argue that there are multiple natural routes to cancer resistance.

Aging, Metabolism, and Cancer Development: from Peto's Paradox to the Warburg Effect

Medical advances made over the last century have increased our lifespan, but age-related diseases are a fundamental health burden worldwide. Aging is therefore a major risk factor for cardiovascular disease, cancer, diabetes, obesity, and neurodegenerative diseases, all increasing in prevalence. However, huge inter-individual variations in aging and disease risk exist, which cannot be explained by chronological age, but rather physiological age decline initiated even at young age due to lifestyle. At the heart of this lies the metabolic system and how this is regulated in each individual. Metabolic turnover of food to energy leads to accumulation of co-factors, byproducts, and certain proteins, which all influence gene expression through epigenetic regulation. How these epigenetic markers accumulate over time is now being investigated as the possible link between aging and many diseases, such as cancer. The relationship between metabolism and cancer was described as early as the late 1950s by Dr. Otto Warburg, before the identification of DNA and much earlier than our knowledge of epigenetics. However, when the stepwise gene mutation theory of cancer was presented, Warburg's theories garnered little attention. Only in the last decade, with epigenetic discoveries, have Warburg's data on the metabolic shift in cancers been brought back to life. The stepwise gene mutation theory fails to explain why large animals with more cells, do not have a greater cancer incidence than humans, known as Peto's paradox. The resurgence of research into the Warburg effect has given us insight to what may explain Peto's paradox. In this review, we discuss these connections and how age-related changes in metabolism are tightly linked to cancer development, which is further affected by lifestyle choices modulating the risk of aging and cancer through epigenetic control.

Changing the Paradigm of Cancer Screening, Prevention, and Treatment

The war on cancer has been fought during the past several decades primarily based on the somatic mutation model of cancer. This has resulted in the emphasis on cancer screening and elimination of any detected cancerous/precancerous cells as the primary method of cancer prevention. This approach has reduced mortality from some cancers, but age-adjusted cancer mortality rates continue to be high. The lack of significant progress in reducing cancer mortality rates may be indicative of a fundamental flaw in the cancer model used. An alternative model of cancer is the immune suppression model of cancer based on the tremendous increase in cancers when the immune system is suppressed. According to this model, the key carcinogenic event is the suppression of the immune system which enables the already existing covert cancers to grow uncontrollably, causing cancer. Hence, cancer screening would consist of identifying those with weak immune system response. The primary mode of cancer prevention and treatment would be boosting of the immune system, for example, through exercise, infection, and low-dose radiation, as they are all known to enhance immune system response and reduce cancers. There is sufficient evidence to justify clinical trials of this approach for cancer screening, prevention, and treatment.

The multiple facets of Peto's paradox: a life-history model for the evolution of cancer suppression

Large animals should have higher lifetime probabilities of cancer than small animals because each cell division carries an attendant risk of mutating towards a tumour lineage. However, this is not observed--a (Peto's) paradox that suggests large and/or long-lived species have evolved effective cancer suppression mechanisms. Using the Euler-Lotka population model, we demonstrate the evolutionary value of cancer suppression as determined by the 'cost' (decreased fecundity) of suppression verses the 'cost' of cancer (reduced survivorship). Body size per se will not select for sufficient cancer suppression to explain the paradox. Rather, cancer suppression should be most extreme when the probability of non-cancer death decreases with age (e.g. alligators), maturation is delayed, fecundity rates are low and fecundity increases with age. Thus, the value of cancer suppression is predicted to be lowest in the vole (short lifespan, high fecundity) and highest in the naked mole rat (long lived with late female sexual maturity). The life history of pre-industrial humans likely selected for quite low levels of cancer suppression. In modern humans that live much longer, this level results in unusually high lifetime cancer risks. The model predicts a lifetime risk of 49% compared with the current empirical value of 43%.

Can Peto's paradox be used as the null hypothesis to identify the role of evolution in natural resistance to cancer? A critical review

BACKGROUND

Carcinogenesis affects not only humans but almost all metazoan species. Understanding the rules driving the occurrence of cancers in the wild is currently expected to provide crucial insights into identifying how some species may have evolved efficient cancer resistance mechanisms. Recently the absence of correlation across species between cancer prevalence and body size (coined as Peto's paradox) has attracted a lot of attention. Indeed, the disparity between this null hypothesis, where every cell is assumed to have an identical probability to undergo malignant transformation, and empirical observations is particularly important to understand, due to the fact that it could facilitate the identification of animal species that are more resistant to carcinogenesis than expected. Moreover it would open up ways to identify the selective pressures that may be involved in cancer resistance. However, Peto's paradox relies on several questionable assumptions, complicating the interpretation of the divergence between expected and observed cancer incidences.

DISCUSSIONS

Here we review and challenge the different hypotheses on which this paradox relies on with the aim of identifying how this null hypothesis could be better estimated in order to provide a standard protocol to study the deviation between theoretical/theoretically predicted and observed cancer incidence. We show that due to the disproportion and restricted nature of available data on animal cancers, applying Peto's hypotheses at species level could result in erroneous conclusions, and actually assume the existence of a paradox. Instead of using species level comparisons, we propose an organ level approach to be a more accurate test of Peto's assumptions.

SUMMARY

The accuracy of Peto's paradox assumptions are rarely valid and/or quantifiable, suggesting the need to reconsider the use of Peto's paradox as a null hypothesis in identifying the influence of natural selection on cancer resistance mechanisms.