The improbability of animal phyla with few species

Paleobiology ◽  
1983 ◽  
Vol 9 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Richard R. Strathmann ◽  
Montgomery Slatkin
Keyword(s):  
Short Duration ◽  
Alternative Model ◽  
Death Process ◽  
Birth And Death Process ◽  
Monophyletic Clade ◽  
Number Of Species ◽  
Extinction Rates ◽  
Animal Phyla ◽  
Speciation Rates ◽  
Initial Radiation

At present there are many animal phyla that contain only a few species. The existence of these small phyla can be used to test assumptions about speciation and extinction in multicellular animals.We first model the number of species in a monophyletic clade with a birth and death process that assumes rates of speciation and extinction are constant. If no new phyla have evolved since the Cambrian and speciation and extinction rates for minor phyla are similar to or greater than those estimated from fossils, then our model shows that the probabilities of minor phyla surviving to the present are small. Random variation in extinction and speciation rates does not improve the chances for persistence. If speciation rates exceed extinction rates at the initial radiation of the clade, but before the clade becomes large, speciation rates come to equal extinction rates and both are low, persistence from before the Ordovician up to the present becomes likely. These models show that if speciation and extinction rates are independent of the number of species in a clade, then conditions before the Ordovician strongly influence today's distribution of species among taxa.We also discuss a model in which speciation and extinction rates depend on the number of species in a clade. This alternative model can account for the persistence of phyla with few species to the present and predicts a short duration for phyla that did not exceed a threshold number of species.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

scholarly journals Geographic contingency, not species sorting, dominates macroevolutionary dynamics in an extinct clade of neogastropods (Volutospina; Volutidae)

Paleobiology ◽  
2021 ◽  
pp. 1-15
Author(s):  
Dana S. Friend ◽  
Brendan M. Anderson ◽  
Warren D. Allmon
Keyword(s):  
Middle Eocene ◽  
Ecological Factors ◽  
Geographic Range ◽  
Late Eocene ◽  
Range Size ◽  
Species Sorting ◽  
Extinction Rates ◽  
Geographic Range Size ◽  
Speciation Rates ◽  
Planktotrophic Larvae

Abstract Rates of speciation and extinction are often linked to many ecological factors, traits (emergent and nonemergent) such as environmental tolerance, body size, feeding type, and geographic range. Marine gastropods in particular have been used to examine the role of larval dispersal in speciation. However, relatively few studies have been conducted placing larval modes in species-level phylogenetic context. Those that have, have not incorporated fossil data, while landmark macroevolutionary studies on fossil clades have not considered both phylogenetic context and net speciation (speciation–extinction) rates. This study utilizes Eocene volutid Volutospina species from the U.S. Gulf Coastal Plain and the Hampshire Basin, U.K., to explore the relationships among larval mode, geographic range, and duration. Based on the phylogeny of these Volutospina, we calculated speciation and extinction rates in order to compare the macroevolutionary effects of larval mode. Species with planktotrophic larvae had a median duration of 9.7 Myr, which compared significantly to 4.7 Myr for those with non-planktotrophic larvae. Larval mode did not significantly factor into geographic-range size, but U.S. and U.K. species do differ, indicating a locality-specific component to maximum geographic-range size. Non-planktotrophs (NPTs)were absent among the Volutospina species during the Paleocene–early Eocene. The relative proportions of NPTs increased in the early middle Eocene, and the late Eocene was characterized by disappearance of planktotrophs (PTs). The pattern of observed lineage diversity shows an increasing preponderance of NPTs; however, this is clearly driven by a dramatic extinction of PTs, rather than higher NPT speciation rates during the late Eocene. This study adds nuance to paleontology's understanding of the macroevolutionary consequences of larval mode.

A stochastic process related to language change

1970 ◽  
Vol 7 (01) ◽  
pp. 69-78 ◽  
Author(s):  
Barron Brainerd
Keyword(s):  
Stochastic Process ◽  
Language Change ◽  
Death Process ◽  
Birth And Death Process ◽  
Standard Methods

The purpose of this note is two-fold. First, to introduce the mathematical reader to a group of problems in the study of language change which has received little attention from mathematicians and probabilists. Secondly, to introduce a birth and death process, arising naturally out of this group of problems, which has received little attention in the literature. This process can be solved using the standard methods and the solution is exhibited here.

Multi-Location Inventory Model Considering Bidirectional and Unidirectional Transshipments Simultaneously

2013 ◽  
Vol 694-697 ◽  
pp. 2742-2745
Author(s):  
Jin Hong Zhong ◽  
Yun Zhou
Keyword(s):  
Process Model ◽  
Approximate Calculation ◽  
Inventory Model ◽  
Inventory System ◽  
Death Process ◽  
Birth And Death Process ◽  
Inventory Models ◽  
Continuous Review ◽  
Poisson Demand ◽  
Queue Theory

Abstract. A cross-regional multi-site inventory system with independent Poisson demand and continuous review (S-1,S) policy, in which there is bidirectional transshipment between the locations at the same area, and unidirectional transshipment between the locations at the different area. According to the M/G/S/S queue theory, birth and death process model and approximate calculation policy, we established inventory models respectively for the loss sales case and backorder case, and designed corresponding procedures to solve them. Finally, we verify the effectiveness of proposed models and methods by means of a lot of contrast experiments.

AN AGE-DEPENDENT BIRTH AND DEATH PROCESS

Biometrika ◽  
1955 ◽  
Vol 42 (3-4) ◽  
pp. 291-306 ◽  
Author(s):  
W. A. O'N WAUGH
Keyword(s):  
Death Process ◽  
Birth And Death Process ◽  
Age Dependent

scholarly journals Reconciliation ecology and the future of species diversity

Oryx ◽  
2003 ◽  
Vol 37 (2) ◽  
pp. 194-205 ◽  
Author(s):  
Michael L. Rosenzweig
Keyword(s):  
Steady State ◽  
Species Diversity ◽  
Natural Area ◽  
Reconciliation Ecology ◽  
Anthropogenic Habitats ◽  
Extinction Rates ◽  
Broad Array ◽  
Speciation Rates ◽  
Species Area ◽  
Biogeographical Province

Species-area relationships (SPARs) dictate a sea change in the strategies of biodiversity conservation. SPARs exist at three ecological scales: Sample-area SPARs (a larger area within a biogeographical province will tend to include more habitat types, and thus more species, than a smaller one), Archipelagic SPARs (the islands of an archipelago show SPARs that combine the habitat-sampling process with the problem of dispersal to an island), and Interprovincial SPARs (other things being equal, the speciation rates of larger biogeographical provinces are higher and their extinction rates are lower, leading to diversities in proportion to provincial area). SPARs are the products of steady-state dynamics in diversity, and such dynamics appears to have characterized the earth for most of the last 500 million years. As people reduce the area available to wild species, they impose a linear reduction of the earth's species diversity that will follow the largest of these scales, i.e. each 1% reduction of natural area will cost about 1% of steady-state diversity. Reserving small tracts of wild habitat can only delay these reductions. But we can stop most of them by redesigning anthropogenic habitats so that their use is compatible with use by a broad array of other species. That is reconciliation ecology. Many pilot projects, whether intentionally or inadvertently espousing reconciliation ecology, are demonstrating that it can be done.

On a property of finite-state birth and death processes

1986 ◽  
Vol 23 (04) ◽  
pp. 859-866
Author(s):  
A. J. Branford
Keyword(s):  
Simple Proof ◽  
Death Process ◽  
Birth And Death Process ◽  
Birth And Death Processes ◽  
Converse Result ◽  
Finite State ◽  
Event Times

A simple proof is given of the result that the ‘overflow' from a finite-state birth and death process is a renewal stream characterized by hyperexponential inter-event times. Our structure is utilized to give a converse result that any hyperexponential renewal stream can be so produced as the overflow from a finite-state birth and death process.

A stochastic model for two interacting populations

1970 ◽  
Vol 7 (3) ◽  
pp. 544-564 ◽  
Author(s):  
Niels G. Becker
Keyword(s):  
Stochastic Model ◽  
Linear Models ◽  
Death Process ◽  
Linear Component ◽  
Birth And Death Process ◽  
Linear Interaction ◽  
Interacting Populations ◽  
Non Linear ◽  
The Subject ◽  
Interaction Component

To explain the growth of interacting populations, non-linear models need to be proposed and it is this non-linearity which proves to be most awkward in attempts at solving the resulting differential equations. A model with a particular non-linear component, initially proposed by Weiss (1965) for the spread of a carrier-borne epidemic, was solved completely by different methods by Dietz (1966) and Downton (1967). Immigration parameters were added to the model of Weiss and the resulting model was made the subject of a paper by Dietz and Downton (1968). It is the aim here to further generalize the model by introducing birth and death parameters so that the result is a linear birth and death process with immigration for each population plus the non-linear interaction component.

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