- This event has passed.

# Applied Math Seminar: Linh Huynh (University of Utah)

## March 27 @ 4:15 pm - 5:15 pm

**Title:**Inferring birth and death rates from population size time series data

**Abstract:**

Models of population dynamics are usually formulated and analyzed with net growth rates. However, separately identifying birth and death rates is significant in various biological applications such as disambiguating (1) exploitation vs. interference competition in ecology, (2) bacteriostatic vs. bactericidal antibiotics in clinical treatments, and (3) enhanced-fecundity vs. reduced-mortality mechanisms in drug resistance. In each of these three contexts, the mechanisms are different, but could be manifest in the same mean-field population size.

In this talk, I will discuss a nonparametric method that utilizes stochastic fluctuations to extract birth and death rates from population size time series data. I will demonstrate the method on logistic growth to study density dependence, but the method can be applied to general birth-death processes and does not require a priori assumptions on the rates. I will also discuss how to implement the theory on sample data and our estimation error analysis. This is based on published work joint with Peter Thomas (Case Western Reserve University) and Jacob Scott (Cleveland Clinic) and can be found here: Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes.