Adrian Gonzalez Casanova
-
Office 639, Wexler Hall Tempe,, AZ 85281
-
Mail code: 1804Campus: Tempe
-
Adrian Gonzalez Casanova is interested in probability theory and its applications in theoretical biology, including modelling, simulation and data-driven approaches.
His research primarily focuses on studying interacting particle systems, stochastic duality, coalescent processes, seed-bank models (stochastic delay differential equations), and the modeling of experimental evolution.
Currently, he is exploring various areas, including:
- Biological Latency and how it shapes the fate of competing populations
- Stochastic Duality and its relationship to Exchangeability and Intertwining
- Lookdown Representations and the propagation of exchangeability
- Griffiths representations of the generators of a Levy Diffusion
- Continuous State Branching Processes and generalised Coalescent Processes.
- Experimental Evolution: from Data-Driven Mathematical Modeling to experimental design
- Antibiotic Resistance: Through the Lens of Population Genetics
- Game Theory: Bridging Economics and Evolution
- Public Health: Utilizing Individual-Based Models to Assess Policy Impact, such as the Risk of Cardiac Failure in Individuals with HIV
- Interacting Particle Systems: including the Simple Exclusion Process and the Contact Process
- Branching Fractional Brownian Process: Constructed via the Seed Bank Random Graph approach
Gonzalez Casanova completed a postdoctoral fellowship at the Weierstrass Institute and was later an assistant and associate professor at UNAM, and a Neyman Visiting Assistant Professor at University of California, Berkeley. His work won the Itô Prize in 2017 and the Feldman Prize in 2022. He is a member of the Latin American Academy of Sciences.
He is a member of the long-term scientific committee of the Seminar on Stochastic Processes
and an Associate Editor at ALEA
PhD Technische Universität Berlin, Germany
I work at the interface of Probability Theory and Theoretical Biology, combining modeling, stochastic processes, and data-driven approaches to understand complex biological systems. My research is grounded in the study of Stochastic Processes, particularly:
- Interacting Particle Systems
- Sampling Duality and Moment Duality
- Seed-Bank Models and Stochastic Delay Differential Equations
- Coalescent and Lookdown Processes
- Branching Processes (including Continuous-State Branching Processes and te Fractional Brownian Motion)
- Mathematical models of Experimental Evolution
My current research directions include:
- Biological Latency: Its role in shaping the fate of competing populations
- Stochastic Duality: With a focus on exchangeability, intertwining, and sampling duality
- Lookdown Representations: And the propagation of exchangeability
- Griffiths Representations: For generators of Lévy diffusions
- Continuous-State Branching Processes and Generalised Coalescents
- Experimental Evolution: From stochastic modeling to experimental design
- Antibiotic Resistance: Studied through the lens of population genetics
- Game Theory: Connecting evolutionary biology and economic theory
- Public Health Modeling: Including individual-based simulations (e.g., cardiac failure risk in HIV patients)
- Interacting Particle Systems: Including exclusion and contact processes
- Branching Fractional Brownian Motion: Via the Seed Bank Random Graph approach
Current
Postdocs
Johny Yang (Sep 2025–)
Esteban Vargas (2025–)
PhD Students
Jose Chacon (2024–)
Imanol Nuñez (2022–, co-advised with Jose Luis Perez, CIMAT)
Former
Postdoc
Veronica Miro Pina (2018–2020, co-advised with Arno Siri Jegousse)
PhD Students
Lizbeth Peñaloza (2018–2022, co-advised with Arno Siri Jegousse)
Nils Hansen (2019–2023, co-advised with Maite Wilke Berenguer)
Coauthors
Mexico
- Airam Blancas (ITAM)
- Eneas Aguirre-von-Wobeser (CIAD)
- María Emilia Caballero (UNAM)
- Guadalupe Espín (UNAM)
- Maria Clara Fittipaldi (UNAM)
- Juan Carlos Pardo (CIMAT)
- José Luis Pérez (CIMAT)
- Lizbeth Peñaloza (Universidad del Mar)
- Rafael Peña-Miller (UNAM)
- Sandra Palau (UNAM)
- Arno Siri-Jégousse (UNAM)
- Gloria Soberon (UNAM)
USA
- Inés González-Casanova (University of Indiana)
- Etienne Nzabarushimana (Harvard)
- Jason Schweinsberg (UC San Diego)
- Sebastian Hummel (UC Berkeley)
Europe
- Ellen Baake (Bielefeld, Germany)
- Fernando Cordero (Vienna)
- Jochen Blath (Frankfurt, Germany)
- Florin Boenkost (Vienna, Austria)
- Eugenio Buzzoni
- Simone Floreani
- Felix Hermann (Frankfurt, Germany)
- Jan Lukas Igelbrink (Frankfurt, Germany)
- Noemi Kurt (Frankfurt, Germany)
- Cornelia Pokalyuk (Lübeck, Germany)
- Charline Smadi (Grenoble, France)
- Dario Spano (University of Warwick, England)
- Daniel Valesin (University of Warwick, England)
- Anton Wakolbinger (Frankfurt, Germany)
- Maite Wilke-Berenguer (Humboldt University, Berlin, Germany)
- Linglong Yuan (University of Liverpool, England)
- András Tóbiás (Budapest, Hungary)
Selected papers in Probability
The effective strength of selection in random environment. A. Gonzalez Casanova, D. Spano, M. Wilke-Berenguer. arXiv:1903.12121 (Annals of Applied Probability 2025)
The ratio of two general continuous-state branching processes with immigration, and its relation to coalescent theory M. E. Caballero, A. Gonzalez Casanova, J.L. Perez. arXiv:2010.00742 (Annals of Applied Probability 2024)
Scaling limit of an adaptive contact process, A. Gonzalez Casanova, A. Tobias, D. Valesin. arXiv:2207.03455 (Annals of Probability 2024)
Quasi-equilibria and click times for a variant of Muller’s ratchet. A. Gonzalez Casanova, C. L. Smadi, A. Wakolbinger. arXiv:2211.13109 (Electronic Journal of Probability 2023)
The Symmetric Coalescent and Wright-Fisher models with bottlenecks, A. Gonzalez Casanova, V. Miro Pina, A. Siri-Jegousse. (Annals of Applied Probability 2022).
Particle systems with coordination. A. Gonzalez Casanova. N. Kurt, A. Tobias. (ALEA 2021)
Duality and Fixation in Xi-Wright-Fisher processes with frequency-dependent selection. A. Gonzalez Casanova, D. Spano. (The Annals of Applied Probability 2018)
An individual based Model for the Lenski experiment, and the deceleration of the relative fitness. A. Gonzalez Casanova, N. Kurt, A. Wakolbinger and L.Yuan. (Stochastic Processes and their Applications 2016) Winner of the Ito Prize 2017.
A new coalescent for seed-bank models. J. Blath, A. Gonzalez Casanova, N. Kurt and M. Wilke-Berenguer. (The Annals of Applied Probability 2016)
Selected papers in Applied Mathematics (modeling, simulation and data-driven projects)
Plasmid stability in fluctuating environments: population genetics of multi-copy plasmids. J. Carlos R. Hernandez-Beltran, Veronica Miro Pina, Arno Siri-Jegousse, Sandra Palau, Rafael Peña-Miller, A. Gonzalez Casanova. (Ecology and Evolution 2023)
The role of connectivity on COVID-19 preventive approaches. V. Miro Pina, J. Nava-Trejo, A. Tobias, E. Nzabarushimana, A. Gonzalez Casanova, I. Gonzalez-Casanova. 17(9). (PLOS ONE 2022)
The Wright-Fisher model with efficiency. A. Gonzalez Casanova, V. Miro Pina, J. C. Pardo. (Theoretical Population Biology 2020)
Modelling and simulating Lenski's long-term evolution experiment. E, Baake, A. Gonzalez Casanova, S. Probst, A. Wakolbinger. (Theoretical Population Biology 2019) Winner of the Feldman Prize 2022.
Genetic variability under the seed-bank coalescent. J. Blath, B. Eldon, A. Gonzalez Casanova, N. Kurt and M. Wilke-Berenguer. (Genetics 2015)
Publications
2025
- The effective strength of selection in random environment. A. Gonzalez Casanova, D. Spano, M. Wilke-Berenguer. Annals of Applied Probability, accepted. arXiv:1903.12121
2024
2. Scaling limit of an adaptive contact process. A. Gonzalez Casanova, A. Tobias, D. Valesin. Annals of Probability, 52(1), pp. 296–349.
3. Lookdown construction for a Moran seed-bank model. M.C. Fittipaldi, A. Gonzalez Casanova, J.E. Nava-Trejo. Electronic Communications in Probability, 29, pp. 1–14.
4. Muller’s ratchet in a near-critical regime: tournament versus fitness proportional selection. J.L. Igelbrink, A. Gonzalez Casanova, C.L. Smadi, A. Wakolbinger. Theoretical Population Biology, 158, pp. 121–138.
5. The ancestral selection graph for a Λ-asymmetric Moran model. A. Gonzalez Casanova, N. Kurt, J.L. Perez. Theoretical Population Biology, 159, pp. 91–107.
6. Asymptotics of the frequency spectrum for general Dirichlet Ξ-coalescents. A. Gonzalez Casanova, V. Miro Pina, E. Schertzer, A. Siri-Jegousse. Electronic Journal of Probability, 29, pp. 1–35.
7. The relative frequency between two continuous-state branching processes with immigration and their genealogy. M.E. Caballero, A. Gonzalez Casanova, J.L. Perez. Annals of Applied Probability, 34(1B), pp. 1271–1318.
8. Alpha-stable branching and beta-frequency processes, beyond the IID assumption. A. Gonzalez Casanova, I. Nunez, J.L. Perez. Electronic Communications in Probability, 29, pp. 1–12.
9. Quasi-equilibria and click times for a variant of Muller’s ratchet. A. Gonzalez Casanova, C.L. Smadi, A. Wakolbinger. Electronic Journal of Probability, 2024. arXiv:2211.13109.
2023
10. Seed bank Cannings graphs: How dormancy smooths random genetic drift. A. Gonzalez Casanova, L. Penaloza, A. Siri-Jegousse. ALEA, 2023. arXiv:2210.05819.
11. Plasmid stability in fluctuating environments: population genetics of multi-copy plasmids. J.C.R. Hernandez-Beltran, V. Miro Pina, A. Siri-Jegousse, S. Palau, R. Pena-Miller, A. Gonzalez Casanova. Ecology and Evolution, 2023.
2022
12. The role of connectivity on COVID-19 preventive approaches. V. Miro Pina, J. Nava-Trejo, A. Tobias, E. Nzabarushimana, A. Gonzalez Casanova, I. Gonzalez-Casanova. PLOS ONE, 17(9), 2022.
13. Λ-coalescents arising in populations with dormancy. F. Cordero, A. Gonzalez Casanova, J. Schweinsberg, M. Wilke-Berenguer. Electronic Journal of Probability, 2022.
14. The symmetric coalescent and Wright-Fisher models with bottlenecks. A. Gonzalez Casanova, V. Miro Pina, A. Siri-Jegousse. Annals of Applied Probability, 2022.
15. The shape of a seed bank tree. A. Gonzalez Casanova, L. Penaloza, A. Siri-Jegousse. Journal of Applied Probability, 2022.
2021
16. Haldane’s formula in Cannings models: The case of moderately strong selection. F. Boenkost, A. Gonzalez Casanova, C. Pokalyuk, A. Wakolbinger. Journal of Mathematical Biology, 2021.
17. Particle systems with coordination. A. Gonzalez Casanova, N. Kurt, A. Tobias. ALEA, 2021.
18. Separation of time-scales for the seed bank diffusion and its jump-diffusion limit. J. Blath, E. Buzzoni, A. Gonzalez Casanova, M. Wilke-Berenguer. Journal of Mathematical Biology, 2021.
19. Branching processes with interactions: The subcritical cooperative regime. A. Gonzalez Casanova, J.C. Pardo, J.L. Perez. Advances in Applied Probability, 2021.
20. Haldane’s formula in Cannings models: The case of moderately weak selection. F. Boenkost, A. Gonzalez Casanova, C. Pokalyuk, A. Wakolbinger. Electronic Journal of Probability, 2021.
2020–2013
21. Multidimensional Λ-Wright-Fisher processes with general frequency-dependent selection. A. Gonzalez Casanova, C. Smadi. Journal of Applied Probability, 2020.
22. The Wright-Fisher model with efficiency. A. Gonzalez Casanova, V. Miro Pina, J.C. Pardo. Theoretical Population Biology, 2020.
23. The seed bank coalescent with simultaneous switching. J. Blath, A. Gonzalez Casanova, N. Kurt, M. Wilke-Berenguer. Electronic Journal of Probability, 2020.
24. Structural properties of the seed bank and the two-island diffusion. J. Blath, E. Buzzoni, A. Gonzalez Casanova, M. Wilke-Berenguer. Journal of Mathematical Biology, 2019.
25. Modelling and simulating Lenski’s long-term evolution experiment. E. Baake, A. Gonzalez Casanova, S. Probst, A. Wakolbinger. Theoretical Population Biology, 2019. (Feldman Prize 2022)
26. Duality and fixation in Ξ-Wright-Fisher processes with frequency-dependent selection. A. Gonzalez Casanova, D. Spano. Annals of Applied Probability, 2018.
27. An individual-based model for the Lenski experiment, and the deceleration of the relative fitness. A. Gonzalez Casanova, N. Kurt, A. Wakolbinger, L. Yuan. Stochastic Processes and their Applications, 2016. (Ito Prize 2017)
28. A new coalescent for seed-bank models. J. Blath, A. Gonzalez Casanova, N. Kurt, M. Wilke-Berenguer. Annals of Applied Probability, 2016.
29. Genetic variability under the seed-bank coalescent. J. Blath, B. Eldon, A. Gonzalez Casanova, N. Kurt, M. Wilke-Berenguer. Genetics, 2015.
30. Genealogy of a Wright-Fisher model with strong seed-bank component. J. Blath, B. Eldon, A. Gonzalez Casanova, N. Kurt. Birkhäuser Progress in Probability, 2014.
31. Strong seed-bank effects in bacterial evolution. A. Gonzalez Casanova, E. Aguirre, G. Espin, L. Servin-Gonzalez, N. Kurt, D. Spano, J. Blath, G. Soberon-Chavez. Journal of Theoretical Biology, 2014.
32. The ancestral process of long-range seed-bank models. J. Blath, A. Gonzalez Casanova, N. Kurt, D. Spano. Journal of Applied Probability, 2013.
Articles in Press
- Seed balancing selection: Coexistence in seedbank models. A. Gonzalez Casanova, J.L. Perez Garmendia, M.E. Caballero. Advances in Applied Probability, accepted. arXiv:2109.07645
Submitted
- Multitype Λ-coalescents and continuous-state branching processes. A. Gonzalez Casanova, N. Kurt, I. Nunez Morales, J.L. Perez. arXiv:2501.00329
- Two waves of adaptation: speciation induced by dormancy in a model with a changing environment. F. Cordero, A. Gonzalez Casanova, J. Schweinsberg. arXiv:2410.10890
- From clonal interference to Poissonian interacting trajectories. F. Hermann, A. Gonzalez Casanova, R.S. Santos, A. Tobias, A. Wakolbinger. arXiv:2407.00793
- Absorption and stationary times for the Λ-Wright-Fisher process. A. Blancas, A. Gonzalez Casanova, S. Palau, S. Hummel. arXiv:2308.09218
- Non-equilibrium steady state of the symmetric exclusion process. S. Floriani, A. Gonzalez Casanova. arXiv:2307.02481
I'm interested in Probability Theory and its applications in Theoretical Biology, including modelling, simulation and data-driven approaches.
My research primarily focuses on studying Interacting Particle Systems, Stochastic Duality, Coalescent Processes, Seed-Bank Models (Stochastic Delay Differential Equations), and the modeling of Experimental Evolution.
Currently, I'm exploring various areas, including:
- Biological Latency and how it shapes the fate of competing populations
- Stochastic Duality and its relationship to Exchangeability and Intertwining
- Lookdown Representations and the propagation of exchangeability
- Griffiths representations of the generators of a Levy Diffusion
- Continuous State Branching Processes and generalised Coalescent Processes.
- Experimental Evolution: from Data-Driven Mathematical Modeling to experimental design
- Antibiotic Resistance: Through the Lens of Population Genetics
- Game Theory: Bridging Economics and Evolution
- Public Health: Utilizing Individual-Based Models to Assess Policy Impact, such as the Risk of Cardiac Failure in Individuals with HIV
- Interacting Particle Systems: including the Simple Exclusion Process and the Contact Process
- Branching Fractional Brownian Process: Constructed via the Seed Bank Random Graph approach
Courses
2025 Fall
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| MAT 343 | Applied Linear Algebra |
2025 Spring
| Course Number | Course Title |
|---|---|
| MAT 494 | Special Topics |
| APM 598 | Special Topics |
2024 Fall
| Course Number | Course Title |
|---|---|
| MAT 343 | Applied Linear Algebra |
Associate Editor at ALEA