Demographic Inference

Workshop

Ekaterina (Katya) Noskova

17-19 November 2025

Demographic History

Visualization

drawn by demes [Gower et al. 2022]

Why Reconstruct

Demographic History

?

Understand population history

Why Reconstruct

Demographic History

?

Conservation biology studies

Starting Tutorial

You can view all the materials online:

Link

You can download the repository to your local system (optional):

$ git clone https://github.com/noscode/GADMA_workshops.git
Materials are located in: GADMA_workshops/2025-11-Demographic_Inference_Worshop/tutorials

Remember to activate your conda environment:

$ conda activate gadma_workshop_env

Demes Tutoral

Go to the directory: 1_demes_tutorial

Notebook: 1_demes_tutorial.ipynb

Online link

Data Checks Tutoral

Go to the directory: 2_data_checks_tutorial

Notebook: 2_data_checks_tutorial.ipynb

Online link

Data:

Alelle Frequency Spectrum

Allele Frequency Spectrum

Derived allele is a new allele formed by mutation.

Allele frequency spectrum (AFS) of P populations is the joint distribution of the derived allele frequencies of a given set of loci (SNP’s) across P populations.

Allele Frequency Spectrum Example

Reference:	ATACGTC
	1 population	2 population
1 individual	ATCCGAC	ACACTTC
2 individual	ACACGTC	ACACGTT
3 individual	GCACGTC

Position	1	2	3	4	5	6	7
Der. allele	G	C	C	-	T	A	T
Freq. in 1 pop.	1	2	1	-	0	1	0
Freq. in 2 pop.	0	2	0	-	1	0	1

$$ A = \begin{matrix} \scriptsize 3 \\ \scriptsize 2 \\ \scriptsize 1 \\ \scriptsize 0 \\ \\ \end{matrix} \begin{matrix} \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \\ \begin{matrix} \scriptsize 0 & \scriptsize 1 & \scriptsize 2 \end{matrix} \\ \end{matrix} $$ $$ A = \begin{matrix} \scriptsize 3 \\ \scriptsize 2 \\ \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=3}{1} \\ \scriptsize 0 \\ \\ \end{matrix} \begin{matrix} \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \\ \begin{matrix} \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=3}{0} & \scriptsize 1 & \scriptsize 2 \end{matrix} \\ \end{matrix} $$ $$ A = \begin{matrix} \scriptsize 3 \\ \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=4}{2} \\ \scriptsize 1 \\ \scriptsize 0 \\ \\ \end{matrix} \begin{matrix} \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \\ \begin{matrix} \scriptsize 0 & \scriptsize 1 & \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=4}{2} \end{matrix} \\ \end{matrix} $$ $$ A = \begin{matrix} \scriptsize 3 \\ \scriptsize 2 \\ \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=5}{1} \\ \scriptsize 0 \\ \\ \end{matrix} \begin{matrix} \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 2 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \\ \begin{matrix} \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=5}{0} & \scriptsize 1 & \scriptsize 2 \end{matrix} \\ \end{matrix} $$ $$ A = \begin{matrix} \scriptsize 3 \\ \scriptsize 2 \\ \scriptsize 1 \\ \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=7}{0} \\ \\ \end{matrix} \begin{matrix} \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 2 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix} \\ \begin{matrix} \scriptsize 0 & \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=7}{1} & \scriptsize 2 \end{matrix} \\ \end{matrix} $$ $$ A = \begin{matrix} \scriptsize 3 \\ \scriptsize 2 \\ \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=8}{1} \\ \scriptsize 0 \\ \\ \end{matrix} \begin{matrix} \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 3 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix} \\ \begin{matrix} \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=8}{0} & \scriptsize 1 & \scriptsize 2 \end{matrix} \\ \end{matrix} $$ $$ A = \begin{matrix} \scriptsize 3 \\ \scriptsize 2 \\ \scriptsize 1 \\ \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=9}{0} \\ \\ \end{matrix} \begin{matrix} \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 3 & 0 & 0 \\ 0 & 2 & 0 \end{pmatrix} \\ \begin{matrix} \scriptsize 0 & \scriptsize \htmlData{class=fragment highlight-current-blue, fragment-index=9}{1} & \scriptsize 2 \end{matrix} \\ \end{matrix} $$

Site Frequency Spectrum

EasySFS Tutoral

Go to the directory: 3_easySFS_tutorial

Notebook: 3_easySFS_tutorial.ipynb

Online link

Demographic Inference

Demographic Inference Tools

Demographic Inference

Tools

Demographic Inference

Tools

Examples:

$\partial a \partial i$ [Gutenkunst et al. 2009]
moments [Jouganous et al. 2017]
momentsLD [Ragsdale and Gravel 2019, 2020]
momi2 [Kamm et al. 2020]
fastsimcoal2 [Excoffier et al. 2013, 2021]
Dical2 [Steinrücken et al. 2019]

Issues of Existing Tools

Issue 1: Model Specification

Specification
for $\partial a \partial i$

Issue 2: Model Selection

Issue 3: Optimization

Most tools use local search optimization algorithms:

BFGS
Nelder–Mead method
Powell's method
EM, ECM

They require initial estimation and perform search for local optimum.

Local vs Global Optimization

GADMA — Global search Algorithm for Demographic Model Analysis

Several likelihood engines ($\partial a \partial i$, moments, momi2, momentsLD)
Common interface
New model specification
Effective global optimization