Expedition & Expansion (E&E) Dynamics

• E&E is a recurring process where exploratory or founding moves create new footholds that are amplified by local diffusion or proliferation.
• It manifests across disciplines—from serial founder events in human populations and cultural transitions in Neolithization to expansion load in genetics and growth of cosmic civilizations.
• E&E analysis employs interdisciplinary methods to reconstruct pathways, quantify selection dynamics, and optimize hybrid exploration algorithms in artificial life.

Searching arXiv for the specified papers and closely related work to ground the article. Expedition and Expansion (E&E) denotes a recurrent structure of directed spread in which exploratory or founding moves generate new footholds that are then amplified by local proliferation, diffusion, or occupation. In the literature considered here, that structure appears in several technically distinct forms: serial founder settlement across Polynesia, staged demic and cultural diffusion during the Neolithic transition in western Eurasia, mutation accumulation at an expansion front, stochastic domain growth by cosmological civilizations, and a hybrid exploration algorithm for continuous cellular automata that alternates novelty-driven local search with goal-directed semantic jumps (Ioannidis et al., 2022, Lemmen et al., 2011, Peischl et al., 2013, Olson, 2018, Khajehabdollahi et al., 4 Sep 2025).

1. Conceptual scope and recurrent structure

In human population history, E&E corresponds to a range expansion: repeated founding events from previously colonized areas, small effective population sizes at the wave front, and limited back-migration. This produces serial founder effects, decreasing diversity with distance from the source, and directional allele-frequency asymmetries that can be used to reconstruct settlement order (Ioannidis et al., 2022). In western Eurasian Neolithization, the same broad theme appears as a spatial process whose observable front can be generated by demic diffusion, cultural diffusion, or mixed regimes, with local adoption thresholds and environmental heterogeneity determining where expansion accelerates, pauses, or becomes endogenous (Lemmen et al., 2011).

In evolutionary genetics, the emphasis shifts from route reconstruction to fitness consequences. A range expansion creates an expansion front where densities are low, growth is fast, and local effective population size is small. Under these conditions, both beneficial and deleterious mutations can surf, but weakly deleterious mutations surf and fix much more often than in a stationary population, generating an expansion load that persists behind the front for long periods (Peischl et al., 2013).

In relativistic cosmology, E&E is formalized as stochastic nucleation of ambitious civilizations in comoving spacetime followed by spherical domain growth at a common expansion speed $v$. The resulting model yields closed-form expressions for the life-saturated fraction of the universe, the expected number of visible domains, and the sky fraction eclipsed by expansionistic activity (Olson, 2018). In artificial life, E&E names a specific hybrid algorithm for Flow Lenia: local “expansion” is performed by Novelty Search in CLIP space, whereas “expedition” is performed by a Vision-LLM that proposes linguistic goals and a sep-CMA-ES optimizer that searches toward those goals in the same semantic space (Khajehabdollahi et al., 4 Sep 2025).

2. Settlement sequences, diffusion regimes, and staged advance

A canonical empirical case is Polynesia. Ancestry-specific analyses of genome-wide SNP data from 430 modern individuals were used to distinguish a serial range expansion from recurrent post-settlement admixture. The analytic core combines local ancestry inference, ancestry-specific allele frequencies, $F_4$-statistics, the directionality statistic $\psi$, bottleneck signatures such as runs of homozygosity and rare-variant surfing, and ancestry-specific IBD dating. The central conclusion is that the settlement of Remote Polynesia is best modeled as a serial founder range expansion originating in western Polynesia, especially the Tonga/Samoa region, with limited post-settlement gene flow. In this framework, $F_4$-statistics were used explicitly to test for post-settlement gene flow between islands and, except for a few exceptions, yielded no detectable allele-frequency signal of significant post-settlement gene flow between islands. The settlement path itself was reconstructed from allele-frequency asymmetries and a directed arborescence using the Chu–Liu–Edmonds algorithm, while IBD-based estimates were used only to place terminus ante quem bounds on settlement times rather than to infer the settlement order (Ioannidis et al., 2022).

The Neolithic transition in western Eurasia provides a second, methodologically different E&E model. The Global Land Use and technological Evolution Simulator (GLUES) partitions western Eurasia into 71 approximately country-size simulation regions with mean area about $130{,}000\ \text{km}^2$, each carrying state variables for population density, technology $T$, share of agropastoralism $f$, and economic diversity $E$. The simulation starts at 9500 simulated BC with all regions at $f \approx 0.04$, low but nonzero Mesolithic technology, and broad-spectrum subsistence. Migration and information exchange are uncoupled: demic diffusion acts through a population flux, whereas cultural diffusion acts through trait exchange, and information travels about $100\times$ faster than people (Lemmen et al., 2011).

GLUES reproduces a staged advance rather than a simple linear wave. In the mixed reference scenario, the initial origin within the modeled domain is the Levant/coastal Syria–Lebanon/adjacent coastal Anatolia around 7000 simulated BC, followed by secondary buildup in northern Greece and a southern route through the Aegean and Mediterranean as well as a northern route through the Balkans and Danubian corridor into central and northern Europe. The average model front speed is reported as $F_4$0, comparable to the empirical range $F_4$1–$F_4$2. Crucially, both demic-only and cultural-only variants reproduce the lag–distance relationship and onset chronology “well enough” that phenology alone does not discriminate between them. In the mixed scenario, local adoption dominates: in region F (Hungary), agropastoralists are 22% migrants and 78% local adopters, and in region H (southern Poland), 41% migrants and 59% adopters (Lemmen et al., 2011).

Taken together, these two cases establish that E&E is not reducible to a single mechanism. In Polynesia, the dominant signature is a clean serial founder expansion with limited later gene flow; in Neolithization, similar large-scale spatiotemporal fronts can emerge under either demic or cultural diffusion, provided local environmental and sociocultural thresholds are crossed (Ioannidis et al., 2022, Lemmen et al., 2011).

3. Population-genetic dynamics at the expansion front

The genetic theory of E&E is centered on the expansion front. In the individual-based models of range expansion on a lattice of demes, colonization proceeds by serial founder events, each followed by logistic growth to carrying capacity. This repeated bottlenecking weakens selection relative to drift. The fixation probability of a mutation of effect $F_4$3 entering the front at frequency $F_4$4 is approximated by

$F_4$5

where $F_4$6 is deme carrying capacity, $F_4$7 is migration probability, and $F_4$8 is the growth rate. The effective selection coefficient $F_4$9 is smaller in magnitude than the true $\psi$0, so selection is always less effective at the expanding front than in a stationary deme of size $\psi$1 (Peischl et al., 2013).

This reduction in efficacy generates expansion load. Deleterious mutations are assumed to be much more frequent than beneficial ones, and although both can surf, the net effect at the front is a steady decline in mean fitness. The critical fraction of deleterious mutations above which mean fitness declines is

$\psi$2

For the baseline parameters used in the paper, if at least 57% of selected mutations are deleterious, fitness at the front declines; with $\psi$3, it declines rapidly. More than half of the total mutation load in newly colonized regions comes from mutations that arose on the front, and the resulting fitness reduction is not confined to the leading edge but persists across a large fraction of newly colonized habitat for thousands of generations (Peischl et al., 2013).

The empirical human test is the out-of-Africa expansion. Reanalysis of exome data showed that non-Africans have a significantly higher proportion of deleterious exonic mutations than Africans, especially among private alleles, where the predicted deleterious proportion is about 27% in non-Africans versus about 21% in Africans. In HGDP-CEPH data, neutral heterozygosity and heterozygosity at selected sites both decrease linearly with geographic distance from Ethiopia, with slopes of about $\psi$4 and $\psi$5 per km, respectively. The relative reduction in heterozygosity at selected sites, $\psi$6, is about $\psi$7 in Africa and $\psi$8 outside Africa, indicating that purifying selection is globally more efficient in Africa and that many sites behaved effectively neutrally during the expansion itself (Peischl et al., 2013).

4. Cosmological E&E and the visibility of expanding domains

In the cosmological version of E&E, ambitious civilizations appear as a homogeneous Poisson process in comoving volume and cosmic time with rate $\psi$9, where $F_4$0 specifies the time dependence and $F_4$1 the peak appearance rate. A civilization appearing at time $F_4$2 expands at constant speed $F_4$3 in comoving coordinates, reaching comoving radius

$F_4$4

in a spatially flat FLRW universe with $F_4$5CDM parameters and present cosmic time $F_4$6 (Olson, 2018).

The core integral is

$F_4$7

which is the weighted comoving spacetime volume inside the past light cone from which an expander could have affected the present observer. For the present epoch, the numerical value is about $F_4$8 in the full numerical model and about $F_4$9–$130{,}000\ \text{km}^2$0 in analytic approximations (Olson, 2018).

From this setup follow the central observables. The unsaturated fraction of space is

$130{,}000\ \text{km}^2$1

and the saturated fraction is $130{,}000\ \text{km}^2$2. The expected number of visible expanding domains is

$130{,}000\ \text{km}^2$3

while the fraction of the sky with no line-of-sight intersection with a visible domain is

$130{,}000\ \text{km}^2$4

Eliminating $130{,}000\ \text{km}^2$5 yields

$130{,}000\ \text{km}^2$6

which makes explicit that high expansion speed suppresses visibility even when the saturated fraction is large. This is the formal basis of the “extragalactic Fermi paradox”: zero visible civilizations beyond the Milky Way can coexist with a universe in which a substantial fraction of space is already saturated (Olson, 2018).

The paper also proposes an anthropic “maximum-$130{,}000\ \text{km}^2$7-slope” condition,

$130{,}000\ \text{km}^2$8

under which $130{,}000\ \text{km}^2$9 and $T$0. In that regime, all present-day observables become functions of $T$1 alone; for example,

$T$2

Thus, if $T$3, the expected visible number is only about $T$4, even though about 63% of space is already saturated (Olson, 2018).

5. E&E as a hybrid exploration algorithm in Flow Lenia

In artificial life, Expedition & Expansion is a concrete algorithm for discovering diverse patterns in Flow Lenia, a continuous cellular automaton with 235 real-valued parameters. A parameter vector $T$5 is simulated for $T$6 steps to produce a final-state image $T$7, which is then embedded by CLIP into a shared semantic space. Novelty is defined as the average cosine distance to the $T$8 nearest neighbors in the archive:

$T$9

where $f$0 is the CLIP embedding of the behavior (Khajehabdollahi et al., 4 Sep 2025).

The algorithm alternates two phases. In expansion, it performs Novelty Search in CLIP space: a parent is sampled from the archive with probability proportional to $f$1, Gaussian mutation is applied in parameter space, the mutant is simulated, embedded, and added to the archive. The best-performing setting for Novelty Search alone is $f$2, whereas higher values increase CLIP diversity but reduce DINO diversity, indicating overfitting to CLIP semantics (Khajehabdollahi et al., 4 Sep 2025).

In expedition, performed periodically every $f$3 iterations, a Vision-LLM generates a linguistic goal from 25 novelty-weighted archive images and the history of prior goals. The goal text is embedded into the same CLIP space, the nearest archived behavior initializes a sep-CMA-ES run, and the optimizer minimizes $f$4 relative to the goal embedding. The implementation uses 6 predefined seed goals, OpenAI o4-mini for goal generation, sep-CMA-ES with population size 16, 350 optimization steps, and initial step-size $f$5. Total runs use $f$6 iterations with a seeding phase of $f$7; $f$8 was evaluated, and $f$9 was selected as the most robust setting (Khajehabdollahi et al., 4 Sep 2025).

The results are explicitly comparative. Random parameter search yields the lowest diversity; random GA is only slightly higher; Novelty Search initially increases diversity but plateaus around iteration 3000; E&E continues to increase diversity beyond that plateau and achieves the highest diversity in both CLIP and DINO spaces. Genealogical analysis shows that expedition-origin solutions are disproportionately consequential. With $E$0, there are 179 expedition steps. Under a random-GA null, the expected fraction of final archive solutions descended from those 179 solutions is about $E$1, whereas the empirical value is $E$2; by contrast, solutions generated in the $E$3 iterations around each expedition contribute only $E$4. This indicates that expeditions seed new behavioral niches that later expansions exploit (Khajehabdollahi et al., 4 Sep 2025).

6. Comparative significance, controversies, and open problems

Several recurrent issues cut across these literatures. First, macroscopic expansion patterns are not by themselves diagnostic of mechanism. In GLUES, demic-only and cultural-only scenarios both match the lag–distance relationship and onset chronology of the radiocarbon data, so phenology alone cannot establish whether people or ideas dominated the spread (Lemmen et al., 2011). In Polynesia, later inter-island contacts are acknowledged, but the argument is that they are too weak at the allele-frequency level to erase the signature of a directional serial expansion, and that IBD-based dates should be treated as upper bounds rather than direct estimators of settlement order (Ioannidis et al., 2022).

Second, expansion has consequences beyond spatial occupation. In population genetics, serial founder propagation changes the efficacy of selection and can create persistent deleterious burden through expansion load (Peischl et al., 2013). In cosmology, expansion speed that is optimal for claiming volume can simultaneously make other domains hard to observe, so a heavily saturated universe can still present an apparently empty sky (Olson, 2018). In artificial life, expeditions that succeed in making large semantic jumps can unlock fertile local neighborhoods, but the same semantic representation can be exploited: CLIP-based novelty is susceptible to novelty hacking, and expedition steps are computationally expensive, taking about three minutes on an A100 versus about one second for an expansion step (Khajehabdollahi et al., 4 Sep 2025).

A plausible implication is that E&E is best understood not as a single theory but as a recurring analytical form. The shared pattern is a punctuated exploratory move into a region that is difficult to reach by strictly local dynamics, followed by a phase in which local diffusion, reproduction, mutation, or optimization amplifies that foothold. In Polynesia the footholds are island founder populations; in GLUES they are sociocultural thresholds crossed under environmental constraints; in expansion load they are newly colonized demes at the wave front; in cosmology they are nucleated domains; and in Flow Lenia they are semantically distant behaviors discovered by VLM-guided expeditions (Ioannidis et al., 2022, Lemmen et al., 2011, Peischl et al., 2013, Olson, 2018, Khajehabdollahi et al., 4 Sep 2025).