##### Department of Mathematics,

University of California San Diego

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### Math 218: Seminar on Mathematics for Complex Biological Systems

## Prof. Jason Schweinsberg

#### Math, UCSD

## Using Coalescent Theory to Estimate the Growth Rate of a Tumor

##### Abstract:

Consider a birth and death process in which each individual gives birth at rate $\lambda$ and dies at rate $\mu$, so that the population size grows at rate $r = \lambda - \mu$. Lambert (2018) and Harris, Johnston, and Roberts (2020) came up with methods for describing the exact genealogy of a sample of size $n$ taken from this population after time $T$. We use the construction of Lambert, which is based on the coalescent point process, to obtain asymptotic results for the site frequency spectrum associated with the sample. This allows us to derive point and interval estimates for the growth rate $r$, which are valid when $T$ and $n$ are large. We apply this method to the problem of estimating the growth rate of clones in blood cancer. This is joint work with Kit Curtius, Brian Johnson, and Yubo Shuai.

### February 22, 2024

### 2:00 PM

APM 6402

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