Using a computational model, we explored a possible solution to the paradox of the evolution of metastasis identified by Bernards and Weinberg
. We propose that resource heterogeneity selects for cell motility, which leads to emigration from the primary tumor. Our model captures the fitness disadvantage associated with cell migration in that emigrating cells are removed from the model. Intriguingly, we observed that these same “disadvantageous” clones were favored in conditions predicted by dispersal theory in ecology. Namely, we have shown that spatial and temporal resource heterogeneity selects for cell migration within a neoplasm, and as a by-product, emigration from a neoplasm. Specifically, the migration propensity, the maximum migration distance within a neoplasm, and the resulting number of emigrating cells, were maximized when there were only a few blood vessels in the model and when the location of those resource rich patches changed frequently (, , ) as is thought to occur in neoplasms
. Oxygen levels can fluctuate in neoplasms over a period of 10′s of minutes, in a spatially heterogeneous manner, the details of which vary between neoplasms 
. Transient hypoxia has been observed to occur over periods of minutes to hours 
and chronic hypoxia over longer time scales 
. Thus, our simulation results confirm that selection for migration within a neoplasm under resource heterogeneity can result in increased levels of cell emigration from the neoplasm, providing support for the resource heterogeneity solution to the paradox of the evolution of metastasis.
The resource heterogeneity solution to the paradox of metastasis is consistent with a variety of experimental observations, including spatial and temporal patterns of tumor invasion, patterns of gene expression in the primary tumor that predict metastasis, and the metastatic effects of hypoxia on neoplasms. Our model is consistent with observations of rapid metastasis once a neoplasm becomes malignant 
, because we predict that there has been selection for cell migration prior to invasion. In gene expression studies, primary neoplasms often exhibit an expression signature of metastasis 
. Since expression arrays measure the most common clones in the neoplasm, this has been interpreted as evidence that a metastatic phenotype often evolves early in neoplastic progression 
. These gene expression profiles may actually be a signature of resource heterogeneity or of migratory clones. For example, cell motility and stress response genes were enriched in primary neoplasms associated with recurrence 
. Hypoxia has also been associated with increased risk of metastasis 
. The resource heterogeneity hypothesis predicts that temporal variation in hypoxia should select for increased emigration, and this is consistent with observations in mouse models 
. Intriguingly, a molecular mechanism connects hypoxic stress and migration through HIF1-α 
, suggesting that natural selection could co-opt and optimize the (epi)genetics of cells under hypoxic stress to increase cell migration.
The paradox of the evolution of metastasis depends on the observation that emigration is a competitive disadvantage for clones in the primary tumor, and so natural selection should suppress cell emigration. The following steps in metastasis (e.g., survival in the blood, invasion and establishment in a new location, etc. 
) are all selectively advantageous for the emigrating clone, and so are not paradoxical. We have focused here on the evolution of the first step of metastasis: migration of cells within the neoplasm, which leads to emigration from the neoplasm, or invasion in our model. The paradox of metastasis hinges on this first step.
The possible resolutions to the paradox of metastasis are distinct in our model, including that metastatic mutations may also increase fitness, the mutation rate is high enough to generate the metastatic cells de novo
, and microenvironmental changes “activate” a previously neutral mutation late in progression. In our model, mutations only affect the propensity or speed of migration, and do not directly affect apoptosis or proliferation. De novo
migratory mutations cannot explain the evolution of high rates of migration observed in our models. That being said, the other solutions to the puzzle of metastasis are not mutually exclusive with each other or our proposal. There is evidence that some mutations that facilitate metastasis may also increase the fitness of the mutant clone 
Our model is clearly a simplification of intra-tumor dynamics. In a real neoplasm, cells are likely to emigrate through lymphatic and blood vessels, not just by leaving the borders of the neoplasm. Incorporating those details into our model would likely increase the number of emigrating cells, consistent with the behavior of our current model.
One of the weaknesses of models of metastasis is the lack of experimental data on cell migration and hypoxia, particularly at the single cell level in vivo
. Thus, we have used a quantitative model to explore the puzzle of metastasis and develop a hypothesis that can explain current data and be used to guide future experiments. Our model supports previous predictions 
that assays of spatial and/or temporal heterogeneity of available resources in a neoplasm 
should predict the risk of metastasis. Spatial statistics of patchiness could be applied to assays of hypoxia, glucose or other limiting resources in tissue sections 
. We also predict that direct measures of cell migration in the primary tumor, perhaps through measures of genes expression and proteins in cell migration pathways, should be good biomarkers for the risk of metastasis.
There are a number of additional experimentally testable predictions from our model. First, our model suggests that we should find greater expression of migration related proteins in neoplasms with regions of hypoxia compared to neoplasms with uniform oxygenation. If the half-lives of hypoxia inducible markers are significantly longer than the rate of cell movement, migratory cells with those markers might be detected as recent arrivals in normoxic regions. With a fast enough molecular clock, perhaps through methylation of CpG sites 
, one may be able to show more mixing of cell lineages due to migration in a neoplasm with resource heterogeneity compared to neoplasms with uniform resources which should contain contiguous regions of closely related cells.
Interestingly, results from our model of resource heterogeneity suggest a potential strategy for preventing or delaying cancer: normalizing the resources available to a neoplasm, over space or time, should tend to reduce the risk of metastasis. In fact, it has recently been shown that restoration of neoplasm oxygenation suppresses metastasis 
. Our model also predicts that cycles of anti-angiogenic drugs applied to a pre-malignant neoplasm may select for a metastatic clone and so we should be cautious in the application of such drugs for cancer prevention 
. It has recently been shown that a decrease in tumor vascularity is correlated with tumor invasion in gliobalstoma patients treated with anti-angiogenesis therapy 
. These results are consistent with our model results that migration increases when the vessel density is decreased. Nevertheless, there is both theoretical and experimental support for anti-angiogenic therapy in malignant neoplasms 
. In fact, constant, low doses of anti-angiogenic drugs have been shown normalize the vascular networks within neoplasms 
. Thus, the chronic application of such drugs may be a route to normalizing the spatial and temporal resources of a neoplasm, thus preventing selection for cell migration and metastasis.
In a related model, Bearer et al. studied the effects of resource heterogeneity and competition between a low- and high-grade clone on tumor morphology and came to a similar conclusion
. This model represented physical and chemical constraints, along with cell adhesion dynamics to predict how the interface between tumor and normal tissue changes over time. In this model, cell migration was a cellular response to hypoxia and did not evolve. In contrast, our model does not represent the boundary between tumor and normal tissue, and instead focuses on the selective effects of resource heterogeneity on cell migration within the primary tumor. They found that resource heterogeneity was amplified by cellular proliferation and migration, leading to invasive tumor morphologies. From this complementary approach, they also concluded that normalization of resources should help suppress invasion. In their case, because resource homogeneity leads to physical constraints on tumor shape whereas in our case, resource homogeneity suppresses natural selection for cell motility.
We have provided a quantitative model for the evolution of cell migration and emigration from neoplasms that provides a solution to the puzzle of metastasis. Results from the model are consistent with both expression signatures of metastasis in primary neoplasms 
and the observed association between hypoxia and metastasis 
. We propose that cell emigration from a neoplasm is a side effect of selection for migration within a neoplasm. The results of our model do not rely upon the exact details of the model. Regardless of the precise parameters chosen, the result still holds that resource heterogeneity in space and time select for cell migration (see Figures S2
). The predictions of our model are supported by in vivo
and clinical results 
. We hope that an understanding of the evolutionary forces that select for metastasis will be useful for the future prevention of metastasis.