A single statistical picture
An arXiv preprint reports that a stripped-down model of plankton populations matched several patterns seen in observations when it combined changing growth rates with effective spatial dispersal. The patterns included how abundance fluctuates, how nearby samples resemble one another, how abundance is distributed, and how patchiness changes with the size of the area measured.
The observed agreement is a statistical match, not a unique identification of what drives plankton patterns in nature. The framework asks whether one set of dynamics can reproduce several patterns, but matching those patterns does not by itself identify one natural mechanism.
How the model was tested
The framework represents local environmental growth-rate fluctuations and effective dispersal in a one-dimensional geometry. In this setup, diffusion is a coarse-grained stand-in for turbulent mixing and advection that the model does not resolve directly.
The numerical tests used a periodic one-dimensional lattice. The sweep comprised 140 simulations with 170 sites, 20 values of lambda from 1 to 2, and seven values of Gamma from 3 to 14. Gamma is the model's spatial correlation length, the characteristic distance over which abundance patterns remain linked.
Empirical checks drew on an LTER-MC microscopy time series, GRUMP global rRNA metabarcoding samples, and Tara Pacific and Tara Microbiome transects with chlorophyll measurements.
The abundance patterns
In the LTER-MC analysis, which used an average seven-day sampling time, the size of abundance fluctuations rose roughly with the square of abundance. The same pattern appeared for both individual focal species and total abundance across diatoms, dinoflagellates and coccolithophores.
The model also predicted a change in the shape of abundance distributions. When the fitted slope lambda was about 1.5 or lower, cases were lognormal-like; at about 1.5 or higher, higher-variation cases were GIG-like. These are names for the two statistical fits used by the study, not separate plankton groups. Lambda is the power-law slope used to characterize the abundance distribution.
Observed data broadly followed this split. In GRUMP examples, the eukaryote case had a fitted slope of 1.9 and the prokaryote case 1.1, corresponding to GIG and lognormal fits respectively. LTER-MC species-abundance distributions all had slopes below 1.5 and did not favor GIG over lognormal, while most analyzed Tara chlorophyll transects were lognormal-like.
One complication was seasonality. Pooled total-abundance data from LTER-MC showed departures from the model, but separating observations by month recovered the predicted distribution transition at lambda 1.5 for each group.
A scale for spatial structure
The model's spatial logic is simple: abundance correlations decay exponentially with distance. Local variance is the zero-distance value of that correlation, so one emergent correlation length links local variation with patterns measured across longer transects.
Within the model and under its stated parameter limits, larger effective diffusion corresponds to larger characteristic patches, while stronger growth-rate variability corresponds to greater spatial heterogeneity. The approximate relation says the correlation length is four times effective diffusion divided by the square of growth-rate noise.
This produces two scale regimes for Taylor's law, which tracks how variance changes as the sampled length grows. At windows shorter than the correlation length, integrated-abundance variance grows with the square of length; at longer windows, it grows linearly.
In GRUMP's spatial data, most prokaryote transects showed exponential decay, with reported correlation lengths on the order of 100 to 10,000 kilometers. Observed and theoretical Taylor exponents agreed with an R-squared of 0.52.
Where the model lost ground
Patchiness, measured here as conditional spatial variance, followed another two-scale pattern. It increased linearly with observation length at short scales, then saturated at long scales.
Tara chlorophyll transects reported a correlation length of about 6.9 kilometers. But theoretical patchiness was higher than observed, particularly in transects classified as oligotrophic, where the model fit was weaker.
A framework, not a final explanation
The gaps matter because the model compresses several physical processes into effective diffusion and uses a one-dimensional setting. Its agreement with observed correlations is therefore a statistical match, not proof that fluctuating growth or diffusion is the unique cause of plankton diversity patterns.
The evidence also has uneven reach. The fluctuation result comes from one coastal time series, so it does not establish open-ocean universality. The Tara patchiness comparison was weaker in oligotrophic regions, and the supplied analysis does not identify which additional processes account for that gap.
Seasonal structure was a material part of the comparison: aggregated LTER-MC distributions deviated from the model, while monthly stratification recovered the transition at lambda 1.5.
The manuscript is an arXiv preprint dated 30 September 2026. Its evidence supports a compact statistical framework for connecting several plankton patterns, but leaves open how far it travels beyond the sampled systems.
Paper data and sources
Original title: Fluctuating growth rate and spatial diffusion shape plankton diversity
Authors: Giorgio Vittorio Visco, Kobe Simoens, Emanuele Pigani et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-09-30
DOI: Not available
Original paper · Full text