Workshop

Demographic Inference using GADMA

Ekaterina (Katya) Noskova

16-17 October 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

Download the repository with all the materials:
- $ git clone https://github.com/noscode/GADMA_workshops.git
Go to:
- $ cd GADMA_workshops/2025-10-GADMA_Worshop/tutorials
Run your conda environment:
- $ conda activate gadma_workshop_env
Optionally you can install and run jupyter notebook:
- Install: $ pip install notebook
- Run it: $ jupyter notebook
You can always view those notebooks online here

Demes Tutoral

Go to the directory: $ cd 1_demes_tutorial

Notebook: 1_demes_tutorial.ipynb

Online link

Data Preparation Tutoral

Go to the directory: $ cd 2_data_preparation_tutorial

Notebook: 2_data_preparation_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

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

EasySFS Tutoral

Go to the directory: $ cd ../3_easySFS_tutorial

Notebook: 3_easySFS_tutorial.ipynb

Online link

Site Frequency Spectrum

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

Demographic Inference

for Four and Five Populations

Demographic Inference

for Four and Five Populations

Challenges:

Time-expensive likelihood evaluations
Many phylogenetic tree topologies
Great number of model parameters

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