scholarly journals ACDC: Analysis of Congruent Diversification Classes

2022 ◽  
Author(s):  
Sebastian Hoehna ◽  
Bjoern Tore Kopperud ◽  
Andrew F Magee
Keyword(s):  
Congruence Class ◽  
R Package ◽  
Rate Function ◽  
Diversification Rate ◽  
Extinction Rate ◽  
Diversification Rates ◽  
Common Features ◽  
Alternative Hypotheses ◽  
Rate Functions ◽  
Congruence Classes

Diversification rates inferred from phylogenies are not identifiable. There are infinitely many combinations of speciation and extinction rate functions that have the exact same likelihood score for a given phylogeny, building a congruence class. The specific shape and characteristics of such congruence classes have not yet been studied. Whether speciation and extinction rate functions within a congruence class share common features is also not known. Instead of striving to make the diversification rates identifiable, we can embrace their inherent non-identifiable nature. We use two different approaches to explore a congruence class: (i) testing of specific alternative hypotheses, and (ii) randomly sampling alternative rate function within the congruence class. Our methods are implemented in the open-source R package ACDC (https://github.com/afmagee/ACDC). ACDC provides a flexible approach to explore the congruence class and provides summaries of rate functions within a congruence class. The summaries can highlight common trends, i.e. increasing, flat or decreasing rates. Although there are infinitely many equally likely diversification rate functions, these can share common features. ACDC can be used to assess if diversification rate patterns are robust despite non-identifiability. In our example, we clearly identify three phases of diversification rate changes that are common among all models in the congruence class. Thus, congruence classes are not necessarily a problem for studying historical patterns of biodiversity from phylogenies.

scholarly journals Tip rates, phylogenies, and diversification: what are we estimating, and how good are the estimates?

2018 ◽  
Author(s):  
Pascal O. Title ◽  
Daniel L. Rabosky
Keyword(s):  
Diversification Rate ◽  
Rate Variation ◽  
Terminal Branch ◽  
List Type ◽  
Large Set ◽  
Extinction Rate ◽  
Diversification Rates ◽  
Speciation Rate ◽  
Model Based ◽  
Model Free

AbstractSpecies-specific diversification rates, or “tip rates”, can be computed quickly from phylogenies and are widely used to study diversification rate variation in relation to geography, ecology, and phenotypes. These tip rates provide a number of theoretical and practical advantages, such as the relaxation of assumptions of rate homogeneity in trait-dependent diversification studies. However, there is substantial confusion in the literature regarding whether these metrics estimate speciation or net diversification rates. Additionally, no study has yet compared the relative performance and accuracy of tip rate metrics across simulated diversification scenarios.We compared the statistical performance of three model-free rate metrics (inverse terminal branch lengths; node density metric; DR statistic) and a model-based approach (BAMM). We applied each method to a large set of simulated phylogenies that had been generated under different diversification processes; scenarios included multi-regime time-constant and diversity-dependent trees, as well as trees where the rate of speciation evolves under a diffusion process. We summarized performance in relation to the type of rate variation, the magnitude of rate heterogeneity and rate regime size. We also compared the ability of the metrics to estimate both speciation and net diversification rates.We show decisively that model-free tip rate metrics provide a better estimate of the rate of speciation than of net diversification. Error in net diversification rate estimates increases as a function of the relative extinction rate. In contrast, error in speciation rate estimates is low and relatively insensitive to extinction. Overall, and in particular when relative extinction was high, BAMM inferred the most accurate tip rates and exhibited lower error than non-model-based approaches. DR was highly correlated with true speciation rates but exhibited high error variance, and was the best metric for very small rate regimes.We found that, of the metrics tested, DR and BAMM are the most useful metrics for studying speciation rate dynamics and trait-dependent diversification. Although BAMM was more accurate than DR overall, the two approaches have complementary strengths. Because tip rate metrics are more reliable estimators of speciation rate, we recommend that empirical studies using these metrics exercise caution when drawing biological interpretations in any situation where the distinction between speciation and net diversification is important.

scholarly journals The Evolution of Nest Site Specialization and its Macroevolutionary Consequences in Passerine Birds

2021 ◽  
Author(s):  
Rosana Zenil-Ferguson ◽  
Jay P McEntee ◽  
John Gordon Burleigh ◽  
Renee A Duckworth
Keyword(s):  
Nest Site ◽  
Comparative Methods ◽  
Diversification Rate ◽  
Extinction Rate ◽  
Passerine Birds ◽  
Evolutionary Transitions ◽  
Background Rate ◽  
Diversification Rates ◽  
Resource Specialization ◽  
Dead End

A long-standing hypothesis in evolutionary biology is that the evolution of resource specialization can lead to an evolutionary dead end, where specialists have low diversification rates and limited ability to evolve into generalists. However, in recent years, advances in comparative methods investigating trait-based differences associated with diversification have enabled more robust tests of this idea and have found mixed support. Here we test the evolutionary dead end hypothesis by estimating net diversification rate differences associated with nest site specialization among 3,224 species of passerine birds. In particular, we test whether the adoption of hole-nesting, a nest site specialization that decreases predation, results in reduced diversification rates relative to nesting outside of holes. Further, we examine whether evolutionary transitions to the specialist hole-nesting state have been more frequent than transitions out of hole-nesting. Using diversification models that accounted for background rate heterogeneity and different extinction rate scenarios, we found that hole-nesting specialization was not associated with diversification rate differences. Furthermore, contrary to the assumption that specialists rarely evolve into generalists, we found that transitions out of hole-nesting occur more frequently than transitions into hole-nesting. These results suggest that interspecific competition may limit adoption of hole-nesting, but that such competition does not result in limited diversification of hole-nesters. In conjunction with other recent studies using robust comparative methods, our results add to growing evidence that evolutionary dead ends are not a typical outcome of resource specialization.

scholarly journals SUMS OF PRODUCTS OF CONGRUENCE CLASSES AND OF ARITHMETIC PROGRESSIONS

2009 ◽  
Vol 05 (04) ◽  
pp. 625-634
Author(s):  
SERGEI V. KONYAGIN ◽  
MELVYN B. NATHANSON
Keyword(s):  
Arithmetic Progression ◽  
Congruence Class ◽  
Arithmetic Progressions ◽  
Sum Of Products ◽  
Sums Of Products ◽  
Positive Integers ◽  
Congruence Classes

Consider the congruence class Rm(a) = {a + im : i ∈ Z} and the infinite arithmetic progression Pm(a) = {a + im : i ∈ N0}. For positive integers a,b,c,d,m the sum of products set Rm(a)Rm(b) + Rm(c)Rm(d) consists of all integers of the form (a+im) · (b+jm)+(c+km)(d+ℓm) for some i,j,k,ℓ ∈ Z. It is proved that if gcd (a,b,c,d,m) = 1, then Rm(a)Rm(b) + Rm(c)Rm(d) is equal to the congruence class Rm(ab+cd), and that the sum of products set Pm(a)Pm(b)+Pm(c)Pm eventually coincides with the infinite arithmetic progression Pm(ab+cd).

scholarly journals Congruence Class Sizes in Finite Sectionally Complemented Lattices

2004 ◽  
Vol 47 (2) ◽  
pp. 191-205 ◽  
Author(s):  
G. Grätzer ◽  
E. T. Schmidt
Keyword(s):  
Congruence Class ◽  
Typical Result ◽  
Complemented Lattices ◽  
The Family ◽  
Complemented Lattice ◽  
Congruence Classes

AbstractThe congruences of a finite sectionally complemented lattice L are not necessarily uniform (any two congruence classes of a congruence are of the same size). To measure how far a congruence Θ of L is from being uniform, we introduce Spec Θ, the spectrum of Θ, the family of cardinalities of the congruence classes of Θ. A typical result of this paper characterizes the spectrum S = (mj | j < n) of a nontrivial congruence Θ with the following two properties:

Initial and final behaviour of failure rate functions for mixtures and systems

2003 ◽  
Vol 40 (03) ◽  
pp. 721-740 ◽  
Author(s):  
Henry W. Block ◽  
Yulin Li ◽  
Thomas H. Savits
Keyword(s):  
Asymptotic Behaviour ◽  
Failure Rate ◽  
Rate Function ◽  
Coherent Systems ◽  
Failure Rate Function ◽  
Rate Functions ◽  
Limiting Behaviour

In this paper we consider the initial and asymptotic behaviour of the failure rate function resulting from mixtures of subpopulations and formation of coherent systems. In particular, it is shown that the failure rate of a mixture has the same limiting behaviour as the failure rate of the strongest subpopulation. A similar result holds for systems except the role of strongest subpopulation is replaced by strongest min path set.

scholarly journals Diversification rates and species richness across the Tree of Life

2016 ◽  
Vol 283 (1838) ◽  
pp. 20161334 ◽  
Author(s):  
Joshua P. Scholl ◽  
John J. Wiens
Keyword(s):  
Species Richness ◽  
Positive Relationship ◽  
Tree Of Life ◽  
Diversification Rate ◽  
Substantial Variation ◽  
Diversification Rates ◽  
Higher Taxa ◽  
Over Time

Species richness varies dramatically among clades across the Tree of Life, by over a million-fold in some cases (e.g. placozoans versus arthropods). Two major explanations for differences in richness among clades are the clade-age hypothesis (i.e. species-rich clades are older) and the diversification-rate hypothesis (i.e. species-rich clades diversify more rapidly, where diversification rate is the net balance of speciation and extinction over time). Here, we examine patterns of variation in diversification rates across the Tree of Life. We address how rates vary across higher taxa, whether rates within higher taxa are related to the subclades within them, and how diversification rates of clades are related to their species richness. We find substantial variation in diversification rates, with rates in plants nearly twice as high as in animals, and rates in some eukaryotes approximately 10-fold faster than prokaryotes. Rates for each kingdom-level clade are then significantly related to the subclades within them. Although caution is needed when interpreting relationships between diversification rates and richness, a positive relationship between the two is not inevitable. We find that variation in diversification rates seems to explain most variation in richness among clades across the Tree of Life, in contrast to the conclusions of previous studies.

scholarly journals The Large Deviation Principle for the On-Off Weibull Sojourn Process

2008 ◽  
Vol 45 (01) ◽  
pp. 107-117 ◽  
Author(s):  
Ken R. Duffy ◽  
Artem Sapozhnikov
Keyword(s):  
Renewal Process ◽  
Time Scale ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Rate Function ◽  
Compact Set ◽  
Natural Processes ◽  
Deviation Principle ◽  
Rate Functions ◽  
Nonlinear Scale

This article proves that the on-off renewal process with Weibull sojourn times satisfies the large deviation principle on a nonlinear scale. Unusually, its rate function is not convex. Apart from on a compact set, the rate function is infinite, which enables us to construct natural processes that satisfy the large deviation principle with nontrivial rate functions on more than one time scale.

scholarly journals A Bayesian Approach for Detecting Mass-Extinction Events When Rates of Lineage Diversification Vary

2015 ◽  
Author(s):  
Michael R. May ◽  
Sebastian Höhna ◽  
Brian R. Moore
Keyword(s):  
Mass Extinction ◽  
Process Model ◽  
Sequence Data ◽  
Diversification Rate ◽  
Rate Variation ◽  
Specific Rate ◽  
Extinction Rate ◽  
Molecular Sequence Data ◽  
Extinction Events ◽  
Mass Extinction Events

The paleontological record chronicles numerous episodes of mass extinction that severely culled the Tree of Life. Biologists have long sought to assess the extent to which these events may have impacted particular groups. We present a novel method for detecting mass-extinction events from phylogenies estimated from molecular sequence data. We develop our approach in a Bayesian statistical framework, which enables us to harness prior information on the frequency and magnitude of mass-extinction events. The approach is based on an episodic stochastic-branching process model in which rates of speciation and extinction are constant between rate-shift events. We model three types of events: (1) instantaneous tree-wide shifts in speciation rate; (2) instantaneous tree-wide shifts in extinction rate, and; (3) instantaneous tree-wide mass-extinction events. Each of the events is described by a separate compound Poisson process (CPP) model, where the waiting times between each event are exponentially distributed with event-specific rate parameters. The magnitude of each event is drawn from an event-type specific prior distribution. Parameters of the model are then estimated using a reversible-jump Markov chain Monte Carlo (rjMCMC) algorithm. We demonstrate via simulation that this method has substantial power to detect the number of mass-extinction events, provides unbiased estimates of the timing of mass-extinction events, while exhibiting an appropriate (i.e., below 5%) false discovery rate even in the case of background diversification rate variation. Finally, we provide an empirical application of this approach to conifers, which reveals that this group has experienced two major episodes of mass extinction. This new approach?the CPP on Mass Extinction Times (CoMET) model?provides an effective tool for identifying mass-extinction events from molecular phylogenies, even when the history of those groups includes more prosaic temporal variation in diversification rate.

scholarly journals gen3sis: A general engine for eco-evolutionary simulations of the processes that shape Earth’s biodiversity

PLoS Biology ◽  
2021 ◽  
Vol 19 (7) ◽  
pp. e3001340
Author(s):  
Oskar Hagen ◽  
Benjamin Flück ◽  
Fabian Fopp ◽  
Juliano S. Cabral ◽  
Florian Hartig ◽  
...  
Keyword(s):  
Biotic Interactions ◽  
R Package ◽  
Biological Processes ◽  
Ecological Traits ◽  
Biodiversity Patterns ◽  
Diversity Gradient ◽  
Dynamic Landscapes ◽  
Alternative Hypotheses ◽  
Model Engine ◽  
Evolutionary Simulations

Understanding the origins of biodiversity has been an aspiration since the days of early naturalists. The immense complexity of ecological, evolutionary, and spatial processes, however, has made this goal elusive to this day. Computer models serve progress in many scientific fields, but in the fields of macroecology and macroevolution, eco-evolutionary models are comparatively less developed. We present a general, spatially explicit, eco-evolutionary engine with a modular implementation that enables the modeling of multiple macroecological and macroevolutionary processes and feedbacks across representative spatiotemporally dynamic landscapes. Modeled processes can include species’ abiotic tolerances, biotic interactions, dispersal, speciation, and evolution of ecological traits. Commonly observed biodiversity patterns, such as α, β, and γ diversity, species ranges, ecological traits, and phylogenies, emerge as simulations proceed. As an illustration, we examine alternative hypotheses expected to have shaped the latitudinal diversity gradient (LDG) during the Earth’s Cenozoic era. Our exploratory simulations simultaneously produce multiple realistic biodiversity patterns, such as the LDG, current species richness, and range size frequencies, as well as phylogenetic metrics. The model engine is open source and available as an R package, enabling future exploration of various landscapes and biological processes, while outputs can be linked with a variety of empirical biodiversity patterns. This work represents a key toward a numeric, interdisciplinary, and mechanistic understanding of the physical and biological processes that shape Earth’s biodiversity.

scholarly journals Shifts in diversification rates and host jump frequencies shaped the diversity of host range amongSclerotiniaceaefungal plant pathogens

2017 ◽  
Author(s):  
Olivier Navaud ◽  
Adelin Barbacci ◽  
Andrew Taylor ◽  
John P. Clarkson ◽  
Sylvain Raffaele
Keyword(s):  
Host Range ◽  
Plant Pathogens ◽  
Phylogenetic Analyses ◽  
Dominant Mode ◽  
Diversification Rate ◽  
Broad Host Range ◽  
Diversification Rates ◽  
Host Jump ◽  
Duplication Events ◽  
Range Variation

AbstractThe range of hosts that a parasite can infect in nature is a trait determined by its own evolutionary history and that of its potential hosts. However, knowledge on host range diversity and evolution at the family level is often lacking. Here, we investigate host range variation and diversification trends within theSclerotiniaceae, a family of Ascomycete fungi. Using a phylogenetic framework, we associate diversification rates, the frequency of host jump events, and host range variation during the evolution of this family. Variations in diversification rate during the evolution of the Sclerotiniaceae define three major macro-evolutionary regimes with contrasted proportions of species infecting a broad range of hosts. Host-parasite co-phylogenetic analyses pointed towards parasite radiation on distant hosts long after host speciation (host jump or duplication events) as the dominant mode of association with plants in theSclerotiniaceae. The intermediate macro-evolutionary regime showed a low diversification rate, high frequency of duplication events, and the highest proportion of broad host range species. Consistent with previous reports on oomycete parasites, our findings suggest that host jump and radiation, possibly combined with low speciation rates, could associate with the emergence of generalist pathogens. These results have important implications for our understanding of fungal parasites evolution and are of particular relevance for the durable management of disease epidemics.

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