Evolution of Group Reproduction in the Transition to Multicellularity: A Bottom-Up Modeling Approach
Using Agent-Based Models to Advance ETI Theory in the Evolution of Multicellularity
My Master’s thesis used an agent-based model in PhysiCell to study early steps in the evolution of multicellularity, inspired by volvocine algae. The simulations showed that while multicellular clusters and group reproduction readily evolved, no shift in the unit of selection occurred. My working hypothesis is that when energy dynamics are modeled explicitly, mechanisms like energy sharing and flexible allocation strategies may be necessary for groups to transition into true evolutionary individuals (i.e. units of selection).
Master’s Thesis, MSc Complex Adaptive Systems, Chalmers University of Technology (2025)
Advisor: Claes Andersson, Ph.D.
Background
The volvocine algae are a classic case study in the evolution of multicellularity, because different species within the lineage can be seen as points along a continuum from unicellular (Chlamydomonas) to simple colonial (Gonium) to fully differentiated multicellular forms (Volvox).
In Chlamydomonas, daughter cells remain connected briefly via cytoplasmic bridges, which normally dissolve, releasing independent individuals. In the simplest multicellular species in the Volvocrine lineage such as Gonium, however, those cytoplasmic bridges do not dissolve, and cells remain attached until right before mitosis.
Maliet et al. formalized these insights in a mathematical model, building on prior work by Michod and colleagues. They proposed that the co-evolution of two traits — growth time (t₍gr₎) and attachment proportion (p) — could drive the emergence of group reproduction and a “ratcheting” effect toward full evolutionary transitions in individuality.
t₍gr₎: the length of the growth phase (how long a cell grows before division).
p: the proportion of the growth phase a cell spends attached.
In their model, if p = 0, cells always separate, producing a fully unicellular cycle; if p = 1, cells never separate, producing a fully multicellular cycle. Because cells were assumed to grow at a constant rate, t₍gr₎ , and death was a probability that also only depended on time, t₍gr₎ ,acted as a proxy for a fecundity trade-off: longer growth increased cell size and offspring number but also increased likelihood of death.
Figure from Maliet, O., Shelton, D. E., & Michod, R. E. (2015). A model for the origin of group reproduction during the evolutionary transition to multicellularity. Biology Letters, 11(6), 20150157. https://doi.org/10.1098/rsbl.2015.0157(CC BY 4.0).
The volvocine lineage illustrates how simple changes in life cycle organization can lead to major evolutionary differences. Maliet et al. (2015) captured this in a mathematical model, where two parameters—growth time (t₍gr₎) and attachment proportion (p)—govern whether cells reproduce as individuals or groups. The figure above summarizes their framework: when p = 0, the cycle is unicellular; when p = 1, it becomes fully multicellular.
Model Design
Agent Design and Behavior
I modeled each cell as a Darwinian agent with its own heritable behavioral strategy. Each cell contains a static neural network (a proxy for a gene regulatory network) that determines its behaviors based on environmental inputs and cell state variables.
Key in the evolvable cell cycle was that the network determined when a cell should divide and whether to remain attached to siblings.
From these micro-decisions, familiar life-history traits such as growth time (t₍gr₎) and attachment proportion (p)emerged dynamically and could be measured post hoc.
Each agent incorporated the following features:
Energy absorption: Cells absorbed “light” energy from the environment, which fueled growth and survival. Larger energy uptake allowed greater division potential.
Division by multiple fission: As in Chlamydomonas reinhardtii, cells divided into 2ⁿ daughter cells depending on size at division. More growth → more offspring.
Mutation of network weights: At each mitosis, the neural network weights mutated, creating heritable variation in behavioral strategies (division timing, adhesion, motility).
Differential reproductive success: Strategies that balanced energy acquisition, division timing, and attachment differently led to variation in reproductive output — enabling natural selection to act on evolving populations.
Through this design, each cell satisfied the classical criteria for Darwinian individuality: reproduction, heritable variation, and differential success. Crucially, group-level traits arose only through the accumulation of cell-level decisions, not through predefined rules.
Figure 1: The evolvable cell cycle in my model. Each cell can either grow and divide as an independent individual or remain attached to siblings after mitosis, forming a colony. These two micro-decisions — division and separation — determine whether the life cycle unfolds at the single-cell level or as a collective, allowing group reproduction to emerge.
Figure 2: Decision-making within each cell was controlled by a static neural network, a proxy for a gene regulatory system. Input neurons (e.g., light detected, energy level, cell volume) fed into hidden nodes, producing outputs that determined whether the cell divided or separated. Mutations to network weights at each division created heritable behavioral variation, enabling evolution to act on strategies.
Evolutionary Setup
The simulation environment was designed to allow selection to emerge from ecological constraints rather than imposed fitness equations:
Initial conditions: Populations were seeded with independent unicells carrying randomly initialized neural networks.
Mutation and selection: Mutations to network weights occurred stochastically during mitosis. Cells and groups with more successful strategies persisted, while others went extinct under ecological pressures.
Spatial environment and energy field: Agents lived in a 2D spatial arena (micronviornment) with a distributed energy field representing light availability. Cells competed locally for resources, creating ecological feedbacks that shaped evolution.
Metrics tracked over generations: Across thousands of generations, I tracked emergent group-level traits, including average growth time (t₍gr₎), attachment proportion (p), group size, and reproductive success, in order to assess whether transitions toward group-level reproduction occurred.
Time-structured selective pressures:
Higher death probability for attached cells in the first 180,000 steps → evolution of unicellular cycle; reversed in the second half → evolution of multicellular cycle
Day/Night cycles
This setup allowed me to observe how Darwinian cells evolved under realistic energetic constraints and whether collective reproduction — and potentially higher-level individuality — could emerge from bottom-up dynamics.
Figure 3: Schematic representation of PhysiCell’s three main interconnected parts in my model. The three parts are: the microenvironment representation in BioFVM (green, bottom left), which models the sunlight gradient and enforces Dirichlet boundary conditions; the physical representation of cells as dynamic spheres in PhysiCell (blue, top); and the internal signaling and behavior module (grey, bottom right), which includes a GRN proxy modeled as a static neural network. This proxy governs only a subset of cellular decisions (e.g., division, separation, motility), while other processes (e.g., growth, attachment dynamics, and death) follow predefined code-level protocols.
Technical Implementation Note: PhysiCell
Simulating evolutionary transitions in individuality is computationally demanding — requiring thousands of interacting agents evolving over thousands of generations, and was previously thought to be a barrier. By leveraging PhysiCell, a peer reviewed high-performance agent-based modeling platform originally designed for tissue and tumor modeling, I was able to overcome many of the performance bottlenecks that previously limited such experiments, making this one of the first attempts to simulate the evolution of group reproduction from the bottom up.
While PhysiCell’s strengths lie in handling complex cellular microenvironments, it was not built with evolutionary timescales in mind. To adapt it for my purposes, I:
Disabled many built-in biophysical modules (e.g. detailed cell mechanics, diffusion solvers for signaling molecules), and pre-built cell cycle settings and cell behaviors that were unnecessary for my ecological setup.
Redirected computational resources toward evolutionary dynamics, enabling simulations of tens of thousands of cells across many thousands of generations.
Customized core functions to allow for static neural networks, mutational inheritance, cell cycle and energy-based ecological interactions.
This adaptation transformed PhysiCell into an evolutionary laboratory where group reproduction and individuality could be explored bottom-up at scale. The ability to harness such computational efficiency was critical to achieving emergent group reproduction — something that would not have been feasible in less optimized platforms.
Example Recording of PhysiCell Simulation in PhysiCell Studio
There are many more important details to this simulation — from ecological cycles (e.g. day/night energy dynamics) to time-varying selective pressures and model customizations than I can possibly do justice to here. For the sake of clarity, I have only outlined the essentials here. If you’re interested in the technical details, please feel free to reach out — I’d be happy to discuss further.
-
Above is a screen recording of the first phase of the simulation, viewed through the PhysiCell Studio interface. In this phase, attached cells carry an extra death probability, which drives the system toward unicellular life cycles.
00:00 — Energy dynamics.
At the start, cell color represents energy level (see horizontal legend, bottom). The vertical legend (right) shows the amount of sunlight in the microenvironment. Initially, the environment is empty, but it quickly develops into a linear gradient of sunlight with a peak at x = 0.The light cycle alternates: 600 time steps (minutes) of light on, then 600 off. This produces the flashing pattern in the video, as well as a day/night ecological rhythm: populations expand during the day and die back at night.
00:29 — Division decisions.
Cell color now reflects the binary attribute divide: yellow = true, purple = false. You can see that cells begin to synchronize their mitotic events fairly quickly.00:53 — Light input (GRN proxy).
Cell color now represents input_0, the first input to each cell’s neural-network proxy for a gene regulatory network (GRN). This value corresponds to the light level experienced by each cell.Notice that in the center of the arena, where the light gradient peaks and cell density is highest, cells report lower light input than expected from their position. This shading effect creates competition: attached cells experience more shading than unattached cells, a biologically realistic constraint that influences their evolutionary trajectories.
Results
What Evolved
When selective pressures favored attached cells, my model successfully evolved group-level reproduction. Cells shifted from a unicellular life cycle — separating immediately after mitosis (p = 0) — to a clonal multicellular cycle, where offspring remained attached for their entire life cycle (p = 1). This trait was heritable, carried from generation to generation. Groups of cells began reproducing as clusters rather than as isolated individuals, fulfilling the criteria for collective reproduction. This dynamic closely mirrors the earliest colonial volvocine algae, where clonal adhesion marks the first step toward multicellularity.
Did the ratcheting occur towards a full ETI or higher unit of selection?
Although group reproduction evolved, the transition stalled before reaching full evolutionary individuality. There was no evidence of variation among groups that could fuel group-level selection. In other words, groups reproduced, but they did not compete as distinct evolutionary entities. The “ratcheting” effect described by Maliet et al. (2015) did not appear. However, my findings suggest this was not because the idea is wrong, but because key evolvable mechanisms were missing from the system.
Takeaway
Group reproduction alone is not enough to drive individuality upward. For collective reproduction to ratchet into a new level of individuality, two additional capacities seem essential:
Energy sharing — tying the survival of individuals to the group’s collective success.
Evolvable control of energy allocation — allowing cells to evolve different investment strategies (e.g., growth vs. reproduction), which opens the door to division of labor.
Because my model lacked these mechanisms, selection never shifted fully from cells to groups. Instead, the system found structural workarounds — like clustering to reduce mortality risk by packing into high-light zones — but these strategies did not amount to true metabolic cooperation.
From this perspective, individuality is best perhaps best understood not only as cooperation or cohesion, but as a reconfiguration of energetic interdependence.
-
[1] Maliet, O., Shelton, D. E., & Michod, R. E. (2015). A model for the origin of group reproduction during the evolutionary transition to multicellularity. Biology Letters, 11(12), 20150157. https://doi.org/10.1098/rsbl.2015.0157
[2] Ghaffarizadeh, A., Heiland, R., Friedman, S. H., Mumenthaler, S. M., & Macklin, P. (2018). PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems. PLoS Computational Biology, 14(2), e1005991. https://doi.org/10.1371/journal.pcbi.1005991