Simulating Natural Selection in Python: Modeling Evolution with Code

Agent-based modeling (ABM) is a computational technique that simulates individual actors (agents) within a system to study emergent behaviors and complex interactions, where the whole system's behavior cannot be predicted from examining individual components alone; Mesa is an open-source Python library that provides tools for building, running, and visualizing ABMs, featuring agent classes, scheduling mechanisms (sequential, random, simultaneous), data collectors, batch runners for parameter sweeps, and web-based visualization capabilities.

This tutorial demonstrates how to build agent-based simulations using the Python Mesa library, which requires defining Agent and Model classes where agents interact with each other and the environment through step methods, using a MultiGrid for spatial positioning and a RandomActivation scheduler to control agent activation order, with visualization provided through a local web server using JavaScript libraries.

Agent-based modeling (ABM) is a computational approach that simulates individual agents interacting with each other to study complex system behaviors, where simple local rules can produce emergent global patterns; Mesa is an open-source Python library for ABM that provides modularity, browser-based visualization, and built-in analysis tools for running and analyzing agent-based models.

Agent-based modeling (ABM) is a computational approach to studying complex adaptive systems where diverse, heterogeneous agents interact locally to produce emergent behaviors that cannot be predicted by analyzing individual components alone; Mesa is an open-source Python platform that provides tools for building ABMs, including agent classes, schedulers for managing activation sequences, spatial grids for modeling geographic interactions, and data collectors for tracking model statistics, enabling researchers to simulate complex systems like economic markets, ecological environments, and social dynamics to better understand and predict real-world phenomena.

This comprehensive section establishes the complete technical foundation for building agent-based models in Mesa. It covers essential object-oriented programming concepts including classes as templates, instances as filled copies, and inheritance enabling code reuse through superclasses and subclasses. Students learn to create agent classes inheriting from Mesa.Agent with proper constructor implementation using super() calls, and model classes inheriting from Mesa.Model containing agent creation logic. The section explains how agents are instantiated within models, the role of the model parameter in agent initialization, and the distinction between agent-level and model-level components. This foundational knowledge enables systematic structuring of complex simulations.

Seaborn offers advanced visualizations beyond basic Matplotlib: (1) histplot() creates histograms with optional kernel density estimate (KDE) for smoother distribution visualization; (2) regplot() creates scatter plots with fitted regression lines showing linear relationships; (3) countplot() creates bar charts showing count of observations for each category; (4) countplot() can display correlation coefficients between variables. Seaborn provides more color palette options and integrates seamlessly with Pandas data frames.

This lecture teaches how to create various types of graphs (line charts, scatter plots, bar charts, histograms, and box plots) using Matplotlib and Seaborn libraries in Python, including how to customize graphs with styles, colors, and multiple subplots, and how to use Pandas for data manipulation and visualization.

This section covers advanced visualization techniques using matplotlib and seaborn. The presenter explains the matplotlib hierarchy with Figure and Axes objects, showing how to create histograms using 'plt.hist()' with bins parameter to control interval size. The section demonstrates scatter plots using 'plt.scatter()' to visualize relationships between two numerical variables. The presenter introduces seaborn's 'relplot()' for creating multiple variable plots showing relationships between three or more variables simultaneously, with color coding by target variable. The section covers creating count plots with 'sns.catplot()' for categorical data. The presenter emphasizes that English is important for data science since most libraries and documentation are in English, and recommends learning English for career advancement in the field.

This final major section advances beyond basic plotting to sophisticated data integration and comparative analysis techniques. After loading processed data into Colab, convert it to Pandas DataFrames for flexible manipulation. Merge genotype data with population metadata using shared keys like sample IDs, enabling richer visualizations. Altair implements the grammar of graphics paradigm, offering more sophisticated styling and interactivity than matplotlib for datasets under 5,000 points. The section demonstrates encoding multiple visual properties (color, size, shape) simultaneously and using category-based color schemes (like category20) to distinguish many populations. Finally, the section compares two fundamental dimensionality reduction techniques: PCA provides a principled mathematical approach where results are reproducible, while t-SNE preserves local structure but has tunable parameters that significantly affect results. This comparative analysis illustrates how different mathematical approaches yield complementary insights into population genetic relationships.

For visualizing time series data, create figures using plt.figure(figsize=(width, height)). Set themes with sns.set_theme(style='whitegrid'). Use bar plots (sns.barplot) to display categorical data over time, where x-axis represents time periods and y-axis represents values like followers gained or total followers.

This section demonstrates computational approaches to studying multivariate evolutionary processes. The simulation models: (1) Diploid individuals with multiple loci contributing to two characters; (2) No dominance, with alleles having numerical values; (3) Mutation adds normally distributed changes to allele contributions; (4) Random weights determine locus contributions to each character, creating genetic covariation; (5) Results show genetic variance accumulating over generations; (6) Drift causes movement primarily along axes of genetic variation; (7) Different weight configurations produce different covariance patterns; (8) Illustrates how mutational input creates genetic covariation that then influences evolutionary trajectories.

The diploid model incorporates sexual reproduction including meiosis and random mating. Three genotypes exist (AA, Aa, aa) with corresponding fitness values. Gametes combine randomly according to Hardy-Weinberg proportions: AA occurs with probability p², Aa with 2pq, and aa with q². After selection acts on adult survival/fertility, the new genotype frequencies are weighted by their fitnesses and normalized by the total mean fitness. This creates a balance between selection building up fitter types and segregation breaking them apart.

This tutorial demonstrates a free online software tool for simulating genetic drift in diploid populations, where users can configure population size (4-100 individuals), number of alleles (2-5), mutation probability, and sex maintenance, then observe how random sampling during reproduction causes allele frequencies to fluctuate across generations through visual graphs and tables.

This segment discusses the complexity of multi-locus population genetics and its relevance to the human genome. The speaker explains that when models move from single-locus to multi-locus systems, the mathematics becomes extremely complex. With each additional gene, the number of possible genotypes increases exponentially. The speaker notes that the human genome contains approximately 20,000 genes, and with each gene potentially having multiple alleles, the mathematical complexity becomes so great that computer simulations are often required. The speaker explains that this complexity is why much of population genetics literature starts with very simplistic single-locus models.

In sexual reproduction, organisms produce gametes (sperm and egg cells) that contain half the normal chromosome number (haploid, N), which for humans is 23 chromosomes, while somatic cells and zygotes contain the full chromosome complement (diploid, 2N, which is 46 chromosomes in humans); this reduction occurs through meiosis in germ cells, ensuring that when gametes fuse during fertilization, the resulting zygote restores the diploid chromosome number necessary for normal development.