Cells Forget Fitness: How Cancer Hijacks the Epigenetic Landscape

68% of cells settle in one valley not because they’re fitter—but because the landscape guides them there.

That number comes from a simulation of tumor-like cell populations navigating a double-well epigenetic landscape

. The two valleys represent distinct cellular states: drug-sensitive versus resistant, stem-like versus differentiated. A strong fitness gradient pulls cells toward the right-hand state—one that proliferates nearly 20 times faster than its counterpart. Yet when the population reaches carrying capacity, almost seven in ten cells end up in the slower-growing state. Not due to chance. Not due to mutation. But because the terrain of gene regulation—the epigenetic landscape—favors it.

This counterintuitive result isn’t just theoretical. It emerges from a new unifying framework that redefines how we understand cellular identity, cancer evolution, and therapy resistance (Fassoni, 2026). At its core is a radical proposition: in mature, crowded tissues, natural selection stops working. Once space and resources are fully occupied, differences in growth rate become irrelevant. All phenotypes become selectively neutral. What determines long-term survival isn’t who divides fastest—but who switches states most effectively.

And cancer? It doesn’t just mutate. It corrupts the very geometry of cellular possibility.

The Science

Artur C. Fassoni’s paper bridges three levels of biological description: compartmental models of discrete cell types, continuum partial differential equations (PDEs) for continuous phenotypes, and stochastic differential equations (SDEs) tracking individual cells. Starting from a standard n-compartment ODE model:

$$u_i^{\prime }=r_i(t)u_{i}g(U)+\sum _{j\ne i}(k_{ji}{u}_j-k_{ij}{u}_i),$$

where $u_i$ is the abundance of phenotype $i$, $r_i$ its proliferation rate, $g(U)$ a shared density-dependent growth modulation (e.g., logistic), and $k_{ij}$ the transition rate from $i$ to $j$, Fassoni proves a powerful theorem under what he calls uniform competition—the assumption that all cells experience the same environmental constraints regardless of type.

Under four key conditions—(H1) common growth limitation, (H2) stable carrying capacity, (H3) connected plasticity (any state reachable from any other), and (H4) persistent proliferation in at least one lineage—the system converges to a fixed distribution determined entirely by the transition rates $k_{ij}$, encoded in the stationary distribution $\pi$ of the Markov process $\mathbf{u}' = A\mathbf{u}$, where $A$ is the transition rate matrix.

This convergence holds even if some phenotypes have vastly higher intrinsic fitness. Why? Because net growth $r_i g(U)$ vanishes as total population $U \to U^*$, rendering all $r_i$ irrelevant at equilibrium. Selection can only act during transient growth phases. After that, plasticity dominates.

Fassoni then extends this to a continuum limit. By restricting transitions to neighboring states and taking a diffusion approximation, the compartmental model becomes a reaction–advection–diffusion PDE:

$$\frac{\partial u}{\partial t}=r(x)u(1-U)+\frac{\partial }{\partial x}\left(D(x)\frac{\partial u}{\partial x}+v(x)u\right),$$

where diffusion coefficient $D(x)$ and advection velocity $v(x)$ are derived directly from local switching rates. Crucially, the same asymptotic irrelevance of fitness applies: long-term solutions converge to the stationary distribution of the purely advective-diffusive process.

Finally, interpreting $v(x) = -P'(x)$ as the negative gradient of an effective potential $P(x)$ transforms the Fokker–Planck equation into the forward Kolmogorov equation of a Langevin SDE:

$$d{x}_t=-P^{\prime }(x_t)dt+\sqrt{2D}d{W}_t,$$

meaning individual cells perform stochastic gradient descent (SGD) on the epigenetic landscape—a concept borrowed from machine learning, now grounded in biophysics.

Non-local jumps (e.g., mutations) are incorporated via integro-differential terms, yielding a unified model of reaction, gradient flow, diffusion, and discontinuous transitions.

What They Found

The simulations tell the story more vividly than equations.

In

, a population evolves under a tilted double-well potential $P(x)$ that favors the left well (68% occupancy at equilibrium). But the proliferation rate $r(x)$ strongly favors the right. During early growth (Figure 2c), the composition shifts dramatically toward the fitter, faster-dividing right-well phenotype. The L¹ distance between actual composition and the plasticity-determined stationary distribution $\psi \propto e^{-P/D}$ spikes to 1.26 (

Composition Converges to Stationary Distribution Despite Fitness Bias

Label	Value
t = 0	0.02
t = 2	0.85
t = 4	1.26
t = 6	0.95
t = 8	0.6
t = 10	0.35
t = 15	0.15
t = 20	0.05

{{chart:0}} From simulation in Figure 2(e): L¹ distance peaks during expansion then decays at rate \(\lambda_1 \approx 0.066\).

).

Yet once the population saturates (~t=5), this fitness-driven distortion begins to unwind. Switching dynamics take over. Within 15 time units, the composition returns to $\psi$, erasing the memory of selection. The system has forgotten its Darwinian past.

Even more striking is

, where cells start as a narrow peak at the far left of a multi-well landscape—precisely where proliferation is highest ($r(x) = r_0 - mx$). Over time, despite this initial advantage, the population spreads across the landscape and settles into a distribution indistinguishable from $u_{\text{eq}}(x) \propto \exp(-P(x)/D)$ (

Phenotype Distribution in Multi-Well Potential

Label	Value
Left well	0.62 %
Middle well	0.32 %
Right well	0.06 %

{{chart:1}} Data extracted from Figure 3(e): simulated vs predicted densities agree within 2.6×10⁻³ L¹ error.

). No trace remains of the fitness gradient that shaped early dynamics.

The mixing time—the duration over which fitness imprints persist—depends critically on the spectral gap $\lambda$ of the transition operator. When barriers between states are high relative to noise ($\Delta P / D$ large), $\lambda$ becomes tiny, and memory lasts longer (scaling as $e^{\Delta P/D}$ in the Kramers regime). But eventually, it always fades.

Meanwhile,

illustrates how single-cell trajectories realize this SGD dynamics. In flat, linear, harmonic, and rugged landscapes, the final distributions match theoretical predictions: uniform, exponential, Gaussian, heavy-tailed. Critically, when noise itself depends on state—$D(x) = D_0(1+x^2)$—the effective landscape $P(x)/D(x)$ becomes shallower, enhancing exploration. This gives cancer a stealthy path to increased plasticity: it doesn’t need to alter gene regulatory circuits—it can just increase transcriptional noise.

Why This Changes Things

This framework flips several assumptions in cancer biology.

First, intratumor heterogeneity does not require ongoing selection. Traditionally, diverse cell states in a tumor were seen as evidence of clonal competition—each subpopulation maintained by its fitness advantage. But Fassoni’s work shows that once a tumor reaches size, selection halts. Heterogeneity can persist passively, sustained purely by transition rates between states. A drug-resistant clone doesn’t need to outcompete others—it just needs to be reachable.

Second, therapy resistance can arise de novo, not just through selection of rare pre-existing mutants. If treatment kills off sensitive cells rapidly, the population may never return to equilibrium before relapse occurs. But even if it does, resistance can emerge stochastically via plasticity. This aligns with clinical observations of antigen loss in CAR-T therapy and reversible resistance in breast and prostate cancers.

Third, Waddington’s epigenetic landscape—a metaphor since 1957—now has mathematical teeth. It’s no longer just a cartoon. It’s a physical potential whose gradients guide cell fate decisions, and whose curvature shapes transition probabilities. Cells aren’t pushed by selection; they roll downhill, nudged by noise.

And cancer? It doesn’t just climb hills via mutations. It melts the hills themselves. By increasing transcriptional noise—through chromatin dysregulation, metabolic stress, or inflammatory signaling—it flattens barriers between states. The landscape becomes corrupted: valleys shallow, ridges erode, new paths open. Cells drift freely between identities. Differentiation breaks down. And therapies fail—not because resistant clones dominate, but because the system keeps regenerating them.

This reframes therapeutic strategy. Instead of chasing moving targets, we might stabilize the landscape. Reduce noise. Reinforce epigenetic barriers. Lock cells into vulnerable states.

What's Next

The model raises urgent questions.

Can we measure $P(x)$ and $D(x)$ in real tumors? Single-cell RNA-seq data, mapped onto low-dimensional manifolds via dimensionality reduction, may allow inference of pseudopotentials. Trajectory inference tools like RNA velocity already estimate local drift—potentially approximating $-P'(x)$. Coupled with measures of transcriptional noise, we could reconstruct effective landscapes in health and disease.

Do human tumors operate near carrying capacity? In solid tumors, yes—growth is constrained by vasculature, space, immune pressure. But in liquid cancers or metastatic niches, populations may cycle through expansion and bottleneck phases, prolonging the window for selection. The balance between $\lambda$ (mixing rate) and $\tau$ (growth duration) will determine whether fitness leaves a lasting mark.

What happens when competition isn’t uniform? Tumors create microenvironments—hypoxic cores, immune-excluded zones—where resource access differs by location and phenotype. If $g_i(U)$ varies across states, fitness may remain relevant. Extending the framework to structured, spatial settings is essential.

And clinically: can we design “landscape-stabilizing” therapies? HDAC inhibitors, DNMT inhibitors, BET blockers—all modulate epigenetic noise. Could they be dosed not to kill, but to reduce plasticity? To prevent resistance rather than treat it?

One caveat looms: the model assumes reversibility. In strict differentiation hierarchies, de-differentiation is blocked. Stem cells give rise to progenitors, but not vice versa. There, plasticity isn’t connected, and fitness differences may persist indefinitely. Yet in cancer, such barriers often break down. Dedifferentiation, transdifferentiation, lineage infidelity—hallmarks of malignancy—are precisely what reconnect the graph.

Fassoni’s synthesis offers more than a model. It offers a new lens. We’ve spent decades optimizing treatments to out-evolve tumors. Maybe it’s time to stop fighting evolution—and start shaping development.