{
  "id": 5130896,
  "title": "When biology inspires mathematics: Hidden symmetries explain why widely used evolutionary methods can give false answers",
  "url": "https://urgent.news/2026/09/02/when-biology-inspires-mathematics-hidden-symmetries-explain-why",
  "topic": "science",
  "section": "Science",
  "published": "2026-09-02T17:00:05.000Z",
  "source": {
    "name": "Phys.org",
    "slug": "phys-org",
    "url": "https://phys.org/news/2026-09-biology-mathematics-hidden-symmetries-widely.html"
  },
  "original_language": "en",
  "account": "Evolutionary biologists utilize mathematical models to examine how biological traits and environmental factors impact species formation and extinction. These models have become essential tools in modern biology, with over 1,000 studies employing them. However, they carry a known flaw: they can occasionally lead to incorrect conclusions. The reason behind this ambiguity has remained unclear for years.\n\nResearch conducted by Sergei Tarasov of the Finnish Museum of Natural History and Josef Uyeda from Virginia Tech has shed light on this issue. They began by considering a simple classification question: should two green apples be grouped together or treated as different colors? This led them to explore lumpability, a mathematical concept introduced in the 1960s, which addresses when different states of a Markov model can be safely grouped without altering the system's behavior.\n\nBuilding upon lumpability, the researchers discovered a novel way to represent Markov models, a concept known as Hidden Expansion. This new representation reveals previously hidden mathematical symmetries, transforming a complex problem into a solvable one. The study, published in Nature Communications, demonstrates that these hidden symmetries also affect sophisticated models used to study biodiversity. The misleading conclusions sometimes produced by these models are not mere statistical errors but stem from a deeper mathematical ambiguity inherent in the models themselves.\n\nThe researchers reanalyzed a dataset on stick insects (Phasmatodea) and found that standard statistical methods favored scenarios suggesting that male weapons affected diversification, even though the original study found no evidence supporting this claim. This example illustrates how the same dataset can appear to support a compelling but ultimately incorrect biological explanation. While the new framework does not completely eliminate the ambiguity, it clarifies where misleading results can arise and highlights the limits of current methods in addressing this longstanding problem in evolutionary biology.",
  "summary": "Why do some groups of organisms contain thousands of species while others have only a handful? Evolutionary biologists have spent decades trying to answer this question using mathematical models that estimate how biological traits and environmental factors influence the formation and extinction of species.",
  "key_points": [
    "Evolutionary models can produce false answers due to hidden symmetries",
    "Researchers discovered mathematical representation called Hidden Expansion",
    "Study clarifies limitations of current methods in evolutionary biology"
  ],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}