Is the blunderbuss a misleading visual metaphor for stasis and punctuated evolution?

Mapping Intimacies ◽

10.1101/242297 ◽

2018 ◽

Author(s):

John T. Waller

Keyword(s):

Brownian Motion ◽

Phenotypic Evolution ◽

Visual Metaphor ◽

Phenotypic Divergence ◽

Original Analysis ◽

Influential Paper ◽

Punctuated Evolution

AbstractI discuss the usefulness of the so-called “blunderbuss pattern” of phenotypic evolution as a visual metaphor for stasis and punctuated evolution that was originally put forward in Uyeda et al. (2011) in their highly influential paper “The million-year wait for macroevolutionary bursts”. I argue the blunderbuss pattern is not surprising, and in some cases it is misleading. I review several publications that cite Uyeda et al. (2011) that seem to be confused about the meaning of the pattern and what it implies. I do not critique the original analysis within Uyeda et al (2011), but show the blunderbuss pattern itself would be produced even when assuming a Brownian motion (completely gradual) model of phenotypic divergence. Finally, I discuss how the interesting results of the paper have been overlooked in favor of the surprisingly powerful, but also misleading visual metaphor of the blunderbuss.

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Introductory remarks

Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences ◽

10.1098/rsta.1990.0123 ◽

1990 ◽

Vol 332 (1627) ◽

pp. 417-418

Keyword(s):

Probability Theory ◽

Brownian Motion ◽

Random Walk ◽

Stochastic Processes ◽

Statistical Physics ◽

Late 19Th Century ◽

Fields Of Study ◽

Wide Range ◽

Influential Paper ◽

Telephone Traffic

Stochastic processes are systems that evolve in time probabilistically; their study is the ‘dynamics’ of probability theory as contrasted with rather more traditional ‘static’ problems. The analysis of stochastic processes has as one of its main origins late 19th century statistical physics leading in particular to studies of random walk and brownian motion (Rayleigh 1880; Einstein 1906) and via them to the very influential paper of Chandrasekhar (1943). Other strands emerge from the work of Erlang (1909) on congestion in telephone traffic and from the investigations of the early mathematical epidemiologists and actuarial scientists. There is by now a massive general theory and a wide range of special processes arising from applications in many fields of study, including those mentioned above. A relatively small part of the above work concerns techniques for the analysis of empirical data arising from such systems.

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Sex, Competition and Mimicry : an eco-evolutionary model reveals how ecological interactions shape the evolution of phenotypes in sympatry

10.1101/2020.11.30.403410 ◽

2020 ◽

Author(s):

Boussens-Dumon Grégoire ◽

Llaurens Violaine

Keyword(s):

Species Interactions ◽

Deterministic Model ◽

Evolutionary Model ◽

Sympatric Species ◽

Reproductive Interference ◽

Ecological Interactions ◽

Phenotypic Evolution ◽

Phenotypic Divergence ◽

Colour Patterns ◽

The Impact

1AbstractPhenotypic evolution in sympatric species can be strongly impacted by species interactions, either mutualistic or antagonistic, which may favour local phenotypic divergence or convergence. Interspecific sexual interactions between sympatric species has been shown to favour phenotypic divergence of traits used as sexual cues for example. Those traits may also be involved in local adaptation or in other types of species interactions resulting in complex evolution of traits shared by sympatric species. Here we focus on mimicry and study how reproductive interference may impair phenotypic convergence between species with various levels of defences. We use a deterministic model assuming two sympatric species and where individuals can display two different warning colour patterns. This eco-evolutionary model explores how ecological interactions shape phenotypic evolution within sympatric species. We investigate the effect of (1) the opposing density-dependent selections exerted on colour patterns by predation and reproductive behaviour, and (2) the impact of relative species and phenotype abundances on the fitness costs faced by each individual depending on their species and phenotype. Our model shows that reproductive interference may limit the convergent effect of mimetic interactions and may promote phenotypic divergence between Müllerian mimics. The divergent and convergent evolution of traits also strongly depends on the relative species and phenotype abundances and levels of trophic competition, highlighting how the eco-evolutionary feedbacks between phenotypic evolution and species abundances may result in strikingly different evolutionary routes.

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Are our phylomorphospace plots so terribly tangled? An investigation of disorder in data simulated under adaptive and nonadaptive models

Current Zoology ◽

10.1093/cz/zoaa045 ◽

2020 ◽

Vol 66 (5) ◽

pp. 565-574

Author(s):

C Tristan Stayton

Keyword(s):

Brownian Motion ◽

Character Displacement ◽

Tree Of Life ◽

Tree Size ◽

Phenotypic Traits ◽

Phenotypic Evolution ◽

Developmental Constraint ◽

Simulated Evolution ◽

Varying Parameters ◽

Deterministic Processes

Abstract Contemporary methods for visualizing phenotypic evolution, such as phylomorphospaces, often reveal patterns which depart strongly from a naïve expectation of consistently divergent branching and expansion. Instead, branches regularly crisscross as convergence, reversals, or other forms of homoplasy occur, forming patterns described as “birds’ nests”, “flies in vials”, or less elegantly, “a mess”. In other words, the phenotypic tree of life often appears highly tangled. Various explanations are given for this, such as differential degrees of developmental constraint, adaptation, or lack of adaptation. However, null expectations for the magnitude of disorder or “tangling” have never been established, so it is unclear which or even whether various evolutionary factors are required to explain messy patterns of evolution. I simulated evolution along phylogenies under a number of varying parameters (number of taxa and number of traits) and models (Brownian motion, Ornstein–Uhlenbeck (OU)-based, early burst, and character displacement (CD)] and quantified disorder using 2 measures. All models produce substantial amounts of disorder. Disorder increases with tree size and the number of phenotypic traits. OU models produced the largest amounts of disorder—adaptive peaks influence lineages to evolve within restricted areas, with concomitant increases in crossing of branches and density of evolution. Large early changes in trait values can be important in minimizing disorder. CD consistently produced trees with low (but not absent) disorder. Overall, neither constraints nor a lack of adaptation is required to explain messy phylomorphospaces—both stochastic and deterministic processes can act to produce the tantalizingly tangled phenotypic tree of life.

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Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

Journal of Applied Probability ◽

10.1017/s0021900200003041 ◽

2007 ◽

Vol 44 (02) ◽

pp. 393-408 ◽

Cited By ~ 1

Author(s):

Allan Sly

Keyword(s):

Stochastic Process ◽

Brownian Motion ◽

White Noise ◽

Gaussian Process ◽

Discrete Data ◽

Hölder Exponent ◽

Scaling Properties ◽

Multifractional Brownian Motion ◽

Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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Brownian motion with quadratic killing and some implications

Journal of Applied Probability ◽

10.1017/s0021900200116079 ◽

1986 ◽

Vol 23 (04) ◽

pp. 893-903 ◽

Cited By ~ 2

Author(s):

Michael L. Wenocur

Keyword(s):

Brownian Motion ◽

Weibull Distribution ◽

Special Function ◽

Function Theory ◽

Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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