- Mathematical: density-dependent population processes, branching processes, Fleming-Viot processes, coalescent theory, and large deviations.
- Biological: demographic stochasticity, community genetics, robustness & adaptability, molecular evolution, and phylogenetics.

- Day, T.,
**Parsons, T. L.**, Lambert, A., and Gandon, S. (2020) The Price equation and evolutionary epidemiology*Philos. Trans. Royal Soc. B*375: 20190357. - Billaud, O., Moen, D. S.,
**Parsons, T. L.**, and Morlon, H. (2020) Estimating diversity through time using molecular phylogenies: old and species-poor frog families are the remnants of a diverse past.*Syst. Biol.*. 69 (2): 363-383. **Parsons, T. L.**, Lambert, A., Day, T., and Gandon, S. (2018) Pathogen evolution in finite populations: slow and steady spreads the best.*J. Royal Soc. Interface*. 15 (147): 20180135. Supplementary material.**Parsons, T. L.**(2018) Invasion probabilities, hitting times, and some fluctuation theory for the stochastic logistic process.*J. Math. Biol.*77 (4): 1193-1231.**Parsons, T. L.**and Rogers, T. (2017) Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology.*J. Phys. A: Math. Theor.*50 (41): 415601- Harris, K.,
**Parsons, T. L.**, Ijaz, U. Z., Lahti, L., Holmes, I., and Quince, C. (2017) Linking statistical and ecological theory: Hubbell's unified neutral theory of biodiversity as a hierarchical Dirichlet process.*Proc. IEEE*105 (3): 516-529. Supplementary material - Stewart, A. J.,
**Parsons, T. L.**, and Plotkin, J. B. (2016) Evolutionary consequences of behavioral diversity.*Proc. Natl. Acad. Sci. USA*113 (45): E7003-E7009. Supplementary material. - Stewart, A. J.,
**Parsons, T. L.**, and Plotkin, J. B. (2012) Environmental robustness and the evolvability of populations.*Evolution*66 (5): 1598-1612. Supplementary material. - Morlon, H.,
**Parsons, T. L.**, and Plotkin, J. B. (2011) Reconciling molecular phylogenies with the fossil record.*Proc. Natl. Acad. Sci. USA*108 (39): 16327-16332. Supplementary material. - Draghi, J. A.,
**Parsons, T. L.**,and Plotkin, J. B. (2011) Epistasis increases the rate of conditionally neutral substitution in an adapting population.*Genetics*187 (4): 1139-1152. **Parsons, T. L.**, Quince, C., and Plotkin, J. B. (2010) Some consequences of demographic stochasticity in population genetics.*Genetics*185 (4): 1345-1354.- Draghi, J. A.,
**Parsons, T. L.**, Wagner, G. P., and Plotkin, J. B. (2010) Mutational robustness can facilitate adaptation.*Nature*463 (7279): 353-355. Supplementary material. **Parsons, T. L.**, Quince, C., and Plotkin, J. B. (2008) Absorption and fixation times for neutral and quasi-neutral populations with density dependence.*Theor. Pop. Biol.*74 (4): 302-310.**Parsons, T. L.**and Quince, C. (2007) Fixation in haploid populations exhibiting density dependence II: The quasi-neutral case.*Theor. Pop. Biol.*72 (4): 468-479.**Parsons, T. L.**and Quince, C. (2007) Fixation in haploid populations exhibiting density dependence I: The non-neutral case.*Theor. Pop. Biol.*72 (1): 121-135.

- Bowen, E. J.,
**Parsons, T. L.**, Curtis, T. P., Plotkin, J. B. and Quince, C. Integrating theory and experiment to explain the breakdown of population synchrony in a complex microbial community.

- Genes, Chinese Restaurants & Textual Analysis, Eureka 64.
- Endowed with an Extra Sense : Mathematics and Evolution, historical talk given to the Cambridge University Mathematics Society in October, 2014.
- Bifurcation, Hysteresis, Catastrophe, a sculpture installation with with artists Jebney Lewis and K. R. Wood. Covered by
*The Scientist*as Catastrophic art.

- Ph.D.: Asymptotic Analysis of Some Stochastic Models from Population Dynamics and Population Genetics.