"A mathematical theory of evolution": phylogenetic models dating back 100 years

Philosophical Transactions of the Royal Society B Biological Sciences, Год журнала: 2025, Номер 380(1919)

Опубликована: Фев. 13, 2025

Open AccessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Rosenberg Noah A., Stadler Tanja and Steel Mike 2025"A mathematical theory of evolution": phylogenetic models dating back 100 yearsPhil. Trans. R. Soc. B38020230297http://doi.org/10.1098/rstb.2023.0297SectionOpen AccessIntroduction"A years A. https://orcid.org/0000-0002-1829-8664 Department Biology, Stanford University, Stanford, CA, USA [email protected] Contribution: Conceptualization, Writing – original draft, review editing Google Scholar Find author on PubMed Search for more papers by , Stadler2 https://orcid.org/0000-0001-6431-535X Biosystems Science Engineering, ETH Zürich, Basel, Switzerland SIB Swiss Institute Bioinformatics, Lausanne, https://orcid.org/0000-0001-7015-4644 Biomathematics Research Centre, University Canterbury, Christchurch, New Zealand Published:20 February 2025https://doi.org/10.1098/rstb.2023.02971. IntroductionCharles Darwin's 1859 Origin Species [1] famously contained only a single figure: schematic depiction tree. In several pages accompanying text that amounted an extended caption his tree figure, Darwin explained how the could both represent descent biological lineages provide scheme taxonomic grouping:The limbs divided into great branches, these lesser were themselves once, when was small, budding twigs; connexion former present buds ramifying branches may well classification all extinct living species in groups subordinate groups. [1, p. 129]Darwin's description life appeared almost simultaneously with another event would later become milestone phylogenetics: Arthur Cayley's 1857 publication 'On analytical forms called trees', perhaps first effort define trees as objects graph [2]. seeking describe sequences which strings operators can be applied, Cayley made connection between structures symbols. A version idea persists phylogenetics basis Newick notation evolutionary relationships.The temporal proximity figure is tantalizing historical juxtaposition. not far from orbit; paper immediately followed it The London, Edinburgh, Dublin Philosophical Magazine Journal letter 'the Rev. Prof. Sedgwick, M.A., F.R.S. &c'—Darwin's geology teacher correspondent, Adam Sedgwick [3]. Yet no major link many decades. himself researcher, having written autobiography:I attempted mathematics, even went during summer 1828 private tutor (a very dull man) Barmouth, but I got slowly. work repugnant me … after have deeply regretted did proceed enough at least understand something leading principles mathematics [4, 58]The interpretation tree-like process emerge 1925 George Udny Yule much-celebrated [5], evolution, based conclusions Dr J. C. Willis, F. S. Yule, who lived 1871 1951, intellectually broad scholar known valuing freedom across areas [6]—a 'loafer world' Yule's own phrase [7]. Trained engineering experimental physics, he became statistician just field statistics emerging, remembered one its pioneers [8,9]. noted important contributor beginnings quantitative social science; had interest economic population early project formulating testing science hypotheses statistically [10]. He worked number applications, including 1902 contribution reconcile Mendel's newly rediscovered laws particulate inheritance often-continuous nature phenotypic variation [9,11].A friendship botanist John Christopher Willis [7, 8] led seminal article. As described Pennell MacPherson themed collection [12], proposed hypothesis linked age area species. Recognizing statistical Willis's hypothesis, formulated model sequential bifurcation lineages, predictions about relationship size genus age. We now regard implied pioneering phylogenetics—but among contributions contingency tables, correlation, regression, time series analysis, epidemiology, literary attribution science, widely used textbook, occupies small place overall oeuvre Although soon probability stochastic processes [13], line approach pursuing problems applied areas, develop programme further research building article; monumental new detailed tedious calculation dozens figures tables stand work.Curiously, Lambert comments [14], although what we know birth branching second modern reader, view bifurcating genera terms trees, instead focusing use counting within relating group It decades before study evolving merge 1960s 1970s—in multiple contexts, palaeobiology, inference, genetics urn probability—solidifying 1990s mature field, [5] recognized prescient founding document anticipated challenges persist [12,14].A reader will find much enjoy paper. To modeller, resonates perspective mathematically simplest choice often suitable absence empirical support alternatives; scale natural rather than years, familiar molecular evolution coalescent theory; deliberate communicating results less oriented readers ('I endeavour summarize reached general hope comprehensible non-mathematical biologist' [5, 25]). approaches last task opening analysis significance findings, afterwards introducing undergirds claims. Juxtaposed modernity, has delightful archaisms, such mutation does simply occur 'thrown' ancestral descendant. One also encounters reminders unknown 1925—for example, timing geologic periods, needed numerical estimates 76].This collection—on occasion 100th anniversary unusually article, largely lost biology decades—explores modelling: modelling focuses divergence recovering features those they produce. Three articles focus legacy rest sections covering (i) developments models, (ii) methods (iii) applications diverse biology, macroevolution epidemics immunology.2. collection(a) Background paperThe begins close reading & [12] relation macroevolution, topic originally sought address. They debates speciation taking connecting broader geographic range older cover recognition approached probabilistic model, recapitulating derivation distribution clade function rate length since bifurcation—before contrasting derivations. note rejection viewed finding stochasticity alone explain pattern sizes, previewing role researchers chance macroevolution.A long section commentary describes excitement palaeobiology upon rediscovery macroevolutionary 1970s emerging acknowledgement contribution. concludes remarks three topics anticipated: potential consider diversification different hierarchical levels, challenge reconciling variable practices concerning level organisms are assigned, within-species underlie decisions parameters. Commenting prescience paper, write:Reading today jarring experience. While presentation certainly consistent time, style way thinks problem seems right home literature late twentieth century.Lambert [14] provides insight central highlighting some lesser-known aspects, detailing various ways been overlooked, sometimes misinterpreted following precise (in language) frequency sizes genera, then extends directions. highlight triples times, ages main theorem (Theorem 3.2), using point theory. Two propositions conditions under long-tail distributions (of type identified) might expected two time-homogeneous settings (linear birth–death constant rates, pure-birth singleton jumps). Viewing scheme, compares contrasts other schemes: Hoppe Simon urns. By extending (tied previous propositions), presents tail arises sizes.The Tavaré [13] concise summary properties linear processes, generate (noting distinction complete reconstructed tree). impact immigration setting, extension dates Kendall 1940s. This leads celebrated Ewens Sampling Formula counts families given conditional total time. application—to ecological considered Fisher—is presented through recent lens. final part shows approximate Bayesian computation cell populations, aim deriving posterior split parameters.(b) Mathematical modellingThe next delves combinatorial aspects trees. Probabilistic associated spaces possible involving discrete sets along continuous branch lengths. Analyses structure understanding interest.The [15] examines shape. Explaining balance topical most phylogenies typically balanced ones biologists reconstruct data (at extreme, uniform overly imbalanced). question biodiversity conservation: predict loss due rapid extinction present? Various measures possible, simple Dan Faith's 'phylogenetic diversity' (PD) measure. PD reviewed, compared considers underlying PD, where feature gain superimposed lead similar (but identical) predictions, explicit formulae.Considering Fuchs [16] explains equivalence induced process—often termed Yule–Harding or Yule–Harding–Kingman shape—and random binary search computer science. particular, constructed permutations {1,2,…,n−1} placed correspondence labelled histories, events give rise n leaves. studied detail investigations running algorithms, theoretical derive corresponding phylogenetics. useful concept additive shape parameter, obtained sum quantities: computed left subtree, subtree quantity root. examples derived concept, indices balance—the Sackin index, cherry index cophenetic index.Dickey [17] perform expanding beyond process, multifurcating Supposing each internal node possesses exactly r child nodes, Dickey conduct variety enumerative studies histories count r-furcating topologies specified leaves specific topology. allow same time—providing recursion enumerating extend classic scenario generalizations: multifurcation simultaneity. directions launched suggest open problems.The Chauve et al. [18] continues investigation (as class networks). authors novel encoding rooted rearrangement operation (the 'HOP' operator), turn measure distances Unlike existing metrics operations (e.g. nearest-neighbour interchange, subtree-prune-and-regraft, tree-bisect-and-reconnect), NP-hard compute, metric remarkable property being computable near-linear so applicable large datasets. compare their ones, show tree–child networks.Moving Bienvenu [19] overview techniques networks. network tractable, ideas enumerate sample networks, complementing traditional asymptotic enumeration. Properties networks approaches, limiting B2 statistics. addition standard (method moments Stein–Chen method), points notion viewing certain classes 'blowups' Galton–Watson promising investigating 'geometry' networks.(c) Statistics inference modelsFour analyses models. Rannala Yang [20] rates itself. generalization 'generalized model,' allows vary over maintaining assumption shared extant lineages. identifiability, whether principle infer measured Reviewing results, compute probabilities outcomes generalized showing identifiable, values parameter vector produce lineage-through-time data. discuss modified versions piecewise arbitrarily varying rates. relaxed parameters constrained, identifiability achieved.Focusing shapes, Kersting [21] Each statistic calculated unlabelled tree; treating null shape, simulations alternative calculate power reject null. tabulates performing conditions. while trends observable, consistently higher array consider. suggests numerous remain relevant problems, offering software facilitate continued use.The emerges Kingman genetics. Zhang Palacios [22] explores extensions Λ-coalescent, mergers (rather pairwise mergers). Λ-coalescent one-parameter beta mergers, (α) estimated topology alone. devise technique carry out joint α effective (which time) genealogy. simulated test performance method, real datasets—two infectious viral diseases third Japanese sardine populations.A Teo [23] calculations Their itself, trait network; information influencing passes nodes via paths. Determining patterns key fixed belief propagation graphical scenarios traits, devoting attention logic computations inference.(d) Applications domainsFinally, five application. Across fields, Yule-like commonly assumed generative enabling 'phylodynamic analysis' [24] (i.e. quantification dynamics—such transmission rates—based trees). widespread started incorporate death incomplete present-day sampling phylodynamic [25]. discussed framework influential More recently, availability sequentially sampled pathogens epidemics, [26]—a adopted fossil [27].In Petrucci [28] employ sampling-through-time ('fossilized process', FBD) combine FBD so-called state-dependent [29], depends trait, finite set (often two, trait). way, traits thus fitness. demonstrate fossils data, accuracy trait-dependent increases considerably, though regarding spurious correlations neutral rates.Veron [30] assume occurs instantaneously, plausible there initiation speciation, completion speciation—so microevolutionary populations influence between-species processes. Building protracted Etienne Rosindell [31] [32], implications Based properties, common time-varying analyse care must taken interpreting towards present, yet reach completion, past primarily influenced These explanation apparent lack association speed acquire reproductive isolation observed data.Koelle Rasmussen [33] explore fitness pathogen strains epidemic, adopting [28]. For pathogens, differences—varying individuals—might attributable few states. Instead, deleterious effects (increased decreased rates). Thus far, considering mutations available [34]. Koelle robustness presence possibly mutations. simulate apply growth investigated, epidemiological reliably despite ignoring mutations.Finally, applications. First, Zwaans [35] single-cell division death. represents divisions Recent CRISPR-Cas9 technology introduces barcodes cell, barcode accumulating changes reconstruction introduce it, combination zebrafish development.In framework, Dumm [36] improve B setting immunology. Again, corresponds apoptosis. advances GCtree, tool relies abundances sequences. structures, benchmarking computational runtime remains feasible.3. ProspectsIt curious academic efforts, regression sciences [37], authorship texts [38] course, volume eventually come anticipating bodies research—long somewhat hidden domains Looking fact 1800s 1900s, developed separately mathematician wide-ranging taste scientific knack intuition indirect if application prepared make insight.Since development distinctive century, tradition produced rich theory, settings. finds issues whose rudiments seen [12]—including estimation [20,28,30], inferences modes [15,21,33] interface [22,23,30]—have finally risen prominence field. illustrate genetics, others [13,16], fields generally [13,14]. exciting phenomena modelling—including [17,22], lineage-dependent [28,33], [18,19,23] types [13,33,35,36]. guiding generation pass efforts century.EthicsThis require ethical approval human subject animal welfare committee.Data accessibilityThis additional data.Declaration AI useWe AI-assisted technologies creating article.Authors' contributionsN.A.R.: conceptualization, writing—original writing—review editing; T.S.: M.S.: editing.All gave agreed held accountable performed therein.Conflict declarationThis theme issue put together Guest Editor team supervision journal's Editorial staff, Royal Society's codes best-practice guidelines. invited handled process. Individual Editors involved assessing personal, professional financial conflict described. Independent reviewers assessed papers. Invitation contribute guarantee inclusion.FundingWe acknowledge National Foundation grant BCS-2116322 Center Computational, Evolutionary, Human Genomics University.T.S. received funding European Council (ERC) Union's Horizon 2020 innovation agreement No 101001077.AcknowledgementsWe thank Joe Felsenstein Arne Mooers draft grateful collection, Helen Eaton her coordinating publication.FootnotesOne 18 '"A years'.© 2025 Author(s).Published Society Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, permits unrestricted use, provided source credited. Next Article VIEW FULL TEXTDOWNLOAD FiguresRelatedReferencesDetails Issue20 2025Volume 380Issue 1919Theme issue'"A years'compiled edited Rosenberg, InformationDOI:https://doi.org/10.1098/rstb.2023.0297PubMed:39976405Published by:Royal SocietyPrint ISSN:0962-8436Online ISSN:1471-2970History: Manuscript received07/12/2024Manuscript accepted09/12/2024Published online20/02/2025 License:© Keywordsmathematical modelsphylogeneticsstochastic Subjectsevolution

Язык: Английский

Negative global-scale association between genetic diversity and speciation rates in mammals

Nature Communications, Год журнала: 2025, Номер 16(1)

Опубликована: Фев. 20, 2025

Genetic diversity is critical for species evolution and their adaptability to global changes, while speciation rate explaining large-scale patterns of richness. Exploring correlates variation in genetic rates across a major interest evolutionary biologists, but these two questions have mostly been investigated independently. Here, we assess the relationship between intra-specific 1897 mammal (~one third total diversity) covering all mammalian orders. We find negative association mitochondrial clades globally. This not accounted by differences ecological attributes species. Our findings suggest systematic link micro- macroevolutionary processes that need be better understood considered when investigating determinants either or rates.

Язык: Английский