Kateřina Staňková

• Dr.
• Professor (Associate) at Delft University of Technology

In mathematical models of eco-evolutionary dynamics with a quantitative trait, two species with different strategies can coexist only if they are separated by a valley or peak of the adaptive landscape. A community is ecologically and evolutionarily stable if each species’ trait sits on global, equal fitness peaks, forming a saturated ESS community...

Evolutionary cancer therapy (ECT) delays or forestalls the progression of metastatic cancer by adjusting treatment based on individual patient and disease characteristics. Clinical implementation of ECT can improve patient outcomes but faces technical and cultural challenges. To address those, we propose a systems approach incorporating systems mod...

We analyze the stability of a game-theoretic model of a polymorphic eco-evolutionary system in the presence of human intervention. The goal is to understand how the intensity of this human intervention and competition within the system impact its stability, with cancer treatment as a case study. In this case study, the physician applies anti-cancer...

Personalized cancer treatment is revolutionizing oncology by leveraging precision medicine and advanced computational techniques to tailor therapies to individual patients. Despite its transformative potential, challenges such as limited generalizability, interpretability, and reproducibility of predictive models hinder its integration into clinica...

Mathematical modeling plays an important role in our understanding and targeting therapy resistance mechanisms in cancer. The polymorphic Gompertzian model, analyzed theoretically and numerically by Viossat and Noble to demonstrate the benefits of adaptive therapy in metastatic cancer, describes a heterogeneous cancer population consisting of thera...

In mathematical models of eco-evolutionary dynamics with a quantitative trait, two species with different strategies can coexist only if they are separated by a valley or peak of the adaptive landscape. A community is ecologically and evolutionarily stable if each species’ trait sits on global, equal fitness peaks, forming a saturated ESS community...

Adaptive therapy, which anticipates and counters the evolution of resistance in cancer cells, has gained significant traction, especially following the success of the Zhang et al.’s protocol in treating metastatic castrate-resistant prostate cancer. While several adaptive therapies have now advanced to clinical trials, none currently incorporates m...

We present a game-theoretic model of a polymorphic cancer cell population where the treatment-induced resistance is a quantitative evolving trait. When stabilization of the tumor burden is possible, we expand the model into a Stackelberg evolutionary game, where the physician is the leader and the cancer cells are followers. The physician chooses a...

Prostate-specific antigen (PSA) is the most commonly used serum marker for prostate cancer. It plays a role in cancer detection, treatment monitoring, and more recently, in guiding adaptive therapy protocols, where treatment is alternated based on PSA levels. However, the relationship between PSA levels and tumor volume remains poorly understood. E...

Nature exhibits rapid evolution in response to human activities. When using natural resources for their own profit, humans should account for such responses. Stackelberg evolutionary games (SEG) offer a method for modeling interactions between a rational leader (humans) and evolutionary followers (nature). The followers evolve according to the prin...

We consider two-player zero-sum differential games of fixed duration, where the running payoff and the dynamics are both linear in the controls of the players. Such games have a value, which is determined by the unique viscosity solution of a Hamilton–Jacobi-type partial differential equation. Approximation schemes for computing the viscosity solut...

Mathematical modeling plays an important role in our understanding of ther- apy resistance mechanisms in cancer. The polymorphic Gompertzian model, analyzed theoretically by Viossat and Noble, describes a heterogeneous can- cer population consisting of therapy sensitive and resistant cells. This theo- retically promising model has not previously be...

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control...

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume...

Game theory is a powerful theory to model strategic decision-making, but also complex biological systems, such as cancer. In the past decades, game-theoretical models have helped to understand cancer, its response to various treatments, and to design better therapies. However, to fully utilize the potential of game-theoretical modelling in designin...

We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner’s Dilemma and public goods games. Coordination games, by their more obscure and less...

In this paper, a large dataset of 590 Non-Small Cell Lung Patients treated with either chemotherapy or immunotherapy was used to determine whether a game-theoretic model including both evolution of therapy resistance and cost of resistance provides a better fit than classical mathematical models of population growth (exponential, logistic, classic...

Here we analyze Darwinian dynamics of cancer introduced in [1], extended by including a competition matrix, and evaluate (i) when the eco-evolutionary equilibrium is positive and (ii) when the eco-evolutionary equilibrium is asymptotically stable.

We extend a two-step lottery model of Craft et al. to test the hypothesis that oak trees pursue a form of within-flower female choice to increase the diversity of fathers. Oak trees produce six ovules per flower while maturing just one acorn. When assuming a random ovule selection - which is a natural assumption in the absence of other hypotheses -...

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume...

Prostate-specific antigen (PSA) is the most common serum marker for prostate cancer. It is used to detect prostate cancer, to assess responses to treatment and recently even to determine when to switch treatment on and off in adaptive therapy protocols. However, the correlation between PSA and tumor volume is poorly understood. Moreover, even thoug...

Membrane binding and unbinding dynamics play a crucial role in the biological activity of several non-integral membrane proteins, which have to be recruited to the membrane in order to perform their functions. By localizing to the membrane, these proteins are able to induce downstream signal amplification in their respective signaling pathways. Her...

Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one’s fitness not only depends on one’s own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it is co...

Rapid evolution is ubiquitous in nature. We briefly review some of this quite broadly, particularly in the context of response to anthropogenic disturbances. Nowhere is this more evident, replicated and accessible to study than in cancer. Curiously cancer has been late - relative to fisheries, antibiotic resistance, pest management and evolution in...

We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner's Dilemma and public goods games. Coordination games, by their more obscure and less...

The application of evolutionary and ecological principles to cancer prevention and treatment, as well as recognising cancer as a selection force in nature, has gained impetus over the last 50 years. Following the initial theoretical approaches that combined knowledge from interdisciplinary fields, it became clear that using the eco‐evolutionary fra...

Fish populations subject to heavy exploitation are expected to evolve over time smaller average body sizes. We introduce Stackelberg evolutionary game theory to show how fisheries management should be adjusted to mitigate the potential negative effects of such evolutionary changes. We present the game of a fisheries manager versus a fish population...

Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one’s fitness not only depends on one’s own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather, inherit their traits. Cancer can be framed as such an evolutionary game, as it is c...

In the absence of curative therapies, treatment of metastatic castrate-resistant prostate cancer (mCRPC) using currently available drugs can be improved by integrating evolutionary principles that govern proliferation of resistant subpopulations into current treatment protocols. Here we develop what is coined as an ‘evolutionary stable therapy’, wi...

The concept of the evolutionary stable strategy (ESS) has been fundamental to the development of evolutionary game theory. It represents an equilibrial evolutionary state in which no rare invader can grow in population size. With additional work, the ESS concept has been formalized and united with other stability concepts such as convergent stabili...

For cancer, we develop a 2-D agent-based continuous-space game-theoretical model that considers cancer cells’ proximity to a blood vessel. Based on castrate resistant metastatic prostate cancer (mCRPC), the model considers the density and frequency (eco-evolutionary) dynamics of three cancer cell types: those that require exogenous testosterone (T+...

A game theory study supported by in vitro experimental data shows that drug treatment of non-small-cell lung cancer cells causes the cells to switch between evolutionary games they play among each other. Moreover, the work calls into question standard assumptions on the fitness costs of drug resistance to cancer cells.

In metastatic castrate resistant prostate cancer (mCRPC), abiraterone is conventionally administered continuously at maximal tolerated dose until treatment failure. The majority of patients initially respond well to abiraterone but the cancer cells evolve resistance and the cancer progresses within a median time of 16 months. Incorporating techniqu...

Importance: While systemic therapy for disseminated cancer is often initially successful, malignant cells, using diverse adaptive strategies encoded in the human genome, almost invariably evolve resistance, leading to treatment failure. Thus, the Darwinian dynamics of resistance are formidable barriers to all forms of systemic cancer treatment but...

Metastatic prostate cancer is initially treated with androgen deprivation therapy (ADT). However, resistance typically develops in about 1 year - a clinical condition termed metastatic castrate-resistant prostate cancer (mCRPC). We develop and investigate a spatial game (agent based continuous space) of mCRPC that considers three distinct cancer ce...

This paper deals with integration of energy storage systems into electricity markets. We explain why the energy storage systems increase flexibility of both power systems and energy markets and why such flexibility is desirable, particularly when variable renewable energy sources are being used in existing power systems. As opposed to the existing...

In this paper we put forward a simple game-theoretical model of pollution control, where each country is in control of its own pollution, while the environmental effects of policies do not stop at country borders. In our noncooperative differential game, countries as players minimize the present value of their own costs defined as a linear combinat...

For over 100 years it has been recognized that insect pests evolve resistance to chemical pesticides. More recently, managers have advocated restrained use of pesticides, crop rotation, the use of multiple pesticides, and pesticide-free sanctuaries as resistance management practices. Game theory provides a conceptual framework for combining the res...

Huge numbers of microbes coexist in almost all habitats of our planet. Their interactions are governed by complex mechanisms, where both competition for resources and toxin production play important roles. Our goal is to understand key mechanisms that lead to coexistence. In this chapter we study many possible scenarios of microbial interactions an...

This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (...

This paper deals with integrating energy storage systems (ESS) into existing electricity markets. We explain why ESS increase flexibility of power systems and energy markets and why more flexible systems and markets are desirable, particularly in a context of high integration of variable renewable energy sources (RES). The Dutch electricity markets...

Optimal toll design deals with the problem of determining toll which improves performance of a road traffic system. Noncooperative game theory is an excellent tool to investigate possible strategies to analyze such a problem, in which one has to take drivers’ reaction to toll and consequent changes in the traffic flow into account. Depending on the...

Apart from interacting, prey and predators may also avoid each other by moving into refuges where they lack food, yet survive by switching to an energy-saving physiological state. Lotka –Volterra models of predator – prey interactions ignore this option. Therefore, we have modelled this game of 'joining versus opting out' by extending Lotka–Volterr...

We propose a game-theoretical model to describe intra-seasonal predator–prey interactions between predatory mites (Acari: Phytoseiidae) and prey mites (also called fruit-tree red spider mites) (Acari: Tetranychidae) that feed on leaves of apple trees. Its parameters have been instantiated based on laboratory and field studies. The continuous-time d...

Diversity and inequality are essences of our real world. Ant colonies are comprised of hundreds of in-dividuals, with no two of them being exactly identical. A flock of birds contains individuals with slight variations in size, speed and vision. Looking at human societies such diversity can be seen among individ-uals differing in body shape and in...

The Lloyd algorithm is a key concept in multi-robot Voronoi coverage applications. Its advantages are its simplicity of implementation and asymptotic convergence to the robots' optimal position. However, the speed of this convergence cannot be guaranteed and therefore reaching the optimal position may be very slow. Moreover, in order to ensure the...

We propose an optimal control framework to describe intra-seasonal predator-prey interactions, which are characterized by a continuous-time dynamical model comprising predator and prey density, as well as the energy budget of the prey over the length of a season. The model includes a time-dependent decision variable for the prey, representing the p...

the dominant institutional approach to nuclear weapons (and other Wmds), has been “containment.” during the cold War, nuclear technology was kept classified in the hopes that other states would not develop nuclear weapons, while the two superpowers amassed enormous stores of weapons. in the 1970s, a non-proliferation treaty promised to cut the stor...

In this paper we define the European electricity market liberalization problem as a game with electricity producers as players, while the consumers’ electricity demand is exogenous. The model is based on real data. The producers maximize their profit by investing and choosing how much electricity they will produce by available means of electricity...

This work deals with the formulation of a distributed model predictive control scheme as a decision problem in which the decisions of each subsystem affect the decisions of the other subsystems and the performance of the whole system. This decision problem is formulated as a bargaining game. This formulation allows each subsystem to decide whether...

We consider a two-person discrete-time dynamic game with the prespecified fixed duration. Each player maximizes her profit over the game horizon, taking decisions of the other player into account. Our goal is to find the Stackelberg equilibria for such a game. The solution approach differs with respect to the information available to individual pla...

We consider a two-person discrete-time dynamic game with a prespecified fixed duration. Each player maximizes her profit over the game horizon, taking decisions of the other player into account. Our goal is to find the Stackelberg equilibria for such a game. After having discussed deterministic Stackelberg games in the companion paper (Stackelberg...

We consider the special type of Stackelberg games known as inverse (or reverse) Stackelberg games and their application to the problem of bi-level optimal toll design in road traffic systems. On a given strongly connected network we assume a noncooperative game with two levels of players: the road authority as a leader and travelers as followers. W...

In this paper we deal with the European electricity market liberalization problem, formulated as a game with electricity producers as players, while the consumers’ electricity demand is exogenous. The producers maximize their profit by choosing how much electricity they will produce individually by means of electricity production available to them....

This paper deals with problem of the real-time freeway traffic density estimation/prediction for a jump Markov linear model based on Daganzo's cell transmission variant of the Lighthill-Whitham-Richards continuous macroscopic freeway model. To solve the problem we propose a particle-filtering-based estimation/prediction method. Its performance is i...

The subject of this paper is a one-leader-one-follower dynamic inverse Stackelberg game with a fixed duration between a bank acting as the leader and an investor acting as the follower. The investor makes her transaction decisions with the bank as intermediary and the bank charges her transaction costs that are dependent on the investor's transacti...

In this paper, the dynamic optimal toll design problem is considered as a one leader-many followers hierarchical non-cooperative game. On a given network the road authority as the leader tolls some links in order to reach its objective, while travelers as followers minimize their perceived travel costs. So far toll has always been considered either...

In this paper the dynamic optimal toll design problem as a game of the Stackelberg type is investigated, with the road authority as leader and drivers on the road network as followers. The road authority sets dynamic traffic-flow dependent tolls on some links in order to minimize its objective function, while the drivers choose their routes and dep...

Inverse (or reverse) Stackelberg games have become the subject of recent game theory research, as a special type or as an extension of Stackelberg games. So far, only very little theory about inverse Stackelberg games is available and the available theory is still in its infancy. In this thesis we focus on theoretically solving such problems and we...

In this paper, the dynamic optimal toll design problem is considered as a one-leadermore-followers hierarchical non-cooperative game. On a given network the road authority as the leader tolls some links in the network to minimize the total travel time of the system, while travelers as followers are assumed to be driven by the dynamic route choice e...

In this paper, the dynamic optimal toll design problem is considered as a one-leadermore-followers hierarchical non-cooperative game. On a given network the road authority as the leader tolls some links in the network to minimize the total travel time of the system, while travelers as followers are assumed to be driven by the dynamic route choice e...