scholarly journals A critical branching process model for biodiversity

2005 ◽  
Vol 37 (04) ◽  
pp. 1094-1115 ◽  
Author(s):  
David Aldous ◽  
Lea Popovic

We study the following model for a phylogenetic tree on n extant species: the origin of the clade is a random time in the past whose (improper) distribution is uniform on (0,∞); thereafter, the process of extinctions and speciations is a continuous-time critical branching process of constant rate, conditioned on there being the prescribed number n of species at the present time. We study various mathematical properties of this model as n→∞: namely the time of origin and of the most recent common ancestor, the pattern of divergence times within lineage trees, the time series of the number of species, the total number of extinct species, the total number of species ancestral to the extant ones, and the ‘local’ structure of the tree itself. We emphasize several mathematical techniques: the association of walks with trees; a point process representation of lineage trees; and Brownian limits.

2005 ◽  
Vol 37 (4) ◽  
pp. 1094-1115 ◽  
Author(s):  
David Aldous ◽  
Lea Popovic

We study the following model for a phylogenetic tree on n extant species: the origin of the clade is a random time in the past whose (improper) distribution is uniform on (0,∞); thereafter, the process of extinctions and speciations is a continuous-time critical branching process of constant rate, conditioned on there being the prescribed number n of species at the present time. We study various mathematical properties of this model as n→∞: namely the time of origin and of the most recent common ancestor, the pattern of divergence times within lineage trees, the time series of the number of species, the total number of extinct species, the total number of species ancestral to the extant ones, and the ‘local’ structure of the tree itself. We emphasize several mathematical techniques: the association of walks with trees; a point process representation of lineage trees; and Brownian limits.


2010 ◽  
Vol 7 (11) ◽  
pp. 3387-3402 ◽  
Author(s):  
S. Trajanovski ◽  
C. Albrecht ◽  
K. Schreiber ◽  
R. Schultheiß ◽  
T. Stadler ◽  
...  

Abstract. Ancient Lake Ohrid on the Balkan Peninsula is considered to be the oldest ancient lake in Europe with a suggested Plio-/Pleistocene age. Its exact geological age, however, remains unknown. Therefore, molecular clock data of Lake Ohrid biota may serve as an independent constraint of available geological data, and may thus help to refine age estimates. Such evolutionary data may also help unravel potential biotic and abiotic factors that promote speciation events. Here, mitochondrial sequencing data of one of the largest groups of endemic taxa in the Ohrid watershed, the leech genus Dina, is used to test whether it represents an ancient lake species flock, to study the role of potential horizontal and vertical barriers in the watershed for evolutionary events, to estimate the onset of diversification in this group based on molecular clock analyses, and to compare this data with data from other endemic species for providing an approximate time frame for the origin of Lake Ohrid. Based on the criteria speciosity, monophyly and endemicity, it can be concluded that Dina spp. from the Ohrid watershed, indeed, represents an ancient lake species flock. Lineage sorting of its species, however, does not seem to be complete and/or hybridization may occur. Analyses of population structures of Dina spp. in the Ohrid watershed indicate a horizontal zonation of haplotypes from spring and lake populations, corroborating the role of lake-side springs, particularly the southern feeder springs, for evolutionary processes in endemic Ohrid taxa. Vertical differentiation of lake taxa, however, appears to be limited, though differences between populations from the littoral and the profundal are apparent. Molecular clock analyses indicate that the most recent common ancestor of extant species of this flock is approximately 1.99 ± 0.83 million years (Ma) old, whereas the split of the Ohrid Dina flock from a potential sister taxon outside the lake is estimated at 8.30 ± 3.60 Ma. Comparisons with other groups of endemic Ohrid species indicated that in all cases, diversification within the watershed started ≤2 Ma ago. Thus, this estimate may provide information on a minimum age for the origin of Lake Ohrid. Maximum ages are less consistent and generally less reliable. But cautiously, a maximum age of 3 Ma is suggested. Interestingly, this time frame of approximately 2–3 Ma ago for the origin of Lake Ohrid, generated based on genetic data, well fits the time frame most often used in the literature by geologists.


2010 ◽  
Vol 7 (4) ◽  
pp. 5011-5045 ◽  
Author(s):  
S. Trajanovski ◽  
C. Albrecht ◽  
K. Schreiber ◽  
R. Schultheiß ◽  
T. Stadler ◽  
...  

Abstract. Ancient Lake Ohrid on the Balkan Peninsula is considered to be the oldest ancient lake in Europe with a suggested Plio-Pleistocene age. Its exact geological age, however, remains unknown. Therefore, molecular clock data of Lake Ohrid biota may serve as an independent constraint of available geological data, and may thus also help to refine age estimates. Such evolutionary data may also help unravel potential biotic and abiotic factors that promote speciation events. Here, mitochondrial sequencing data of one of the largest groups of endemic taxa in Lake Ohrid, the leech genus Dina, is used to test whether it represents an ancient lake species flock, to study the role of horizontal and vertical barriers in Lake Ohrid for evolutionary events, to estimate the onset of intralacustrine diversification in this group based on molecular clock analyses, and to compare this data with data from other endemic species for providing an approximate time frame for the origin of Lake Ohrid. Based on the criteria speciosity, monophyly and endemicity, it can be concluded that Lake Ohrid Dina, indeed, represents an ancient lake species flock. Lineage sorting of its species, however, does not seem to be complete. Analyses of population structures of Dina spp. in the Ohrid watershed indicate a horizontal zonation of haplotypes from spring and lake populations, corroborating the role of lake-side springs, particularly the southern feeder springs, for evolutionary processes in endemic Ohrid taxa. Vertical differentiation of lake taxa, however, appears to be limited, though differences between populations from the littoral and the profundal are apparent. Molecular clock analyses indicate that the most recent common ancestor of extant species of this flock is approximately 1.99±0.83 Ma old, whereas the split of the Lake Ohrid Dina flock from a potential sister taxon outside the lake is estimated at 8.30±3.60 Ma. Comparisons with other groups of endemic Ohrid species indicated that in all cases, intralacustrine diversification started ≤2 Ma ago. Thus, this estimate may provide information on a minimum age for the origin of Lake Ohrid. Maximum ages are less consistent and generally less reliable. But cautiously, a maximum age of 3 Ma is suggested. Interestingly, this time frame of approximately 2–3 Ma for the origin of Lake Ohrid, generated based solely on evolutionary data, well fits the time frame most often used in the literature by geologists. Future studies must show whether this concurrence holds true.


2016 ◽  
Vol 53 (3) ◽  
pp. 802-817
Author(s):  
Jyy-I Hong

AbstractConsider a d-type (d<∞) Galton–Watson branching process, conditioned on the event that there are at least k≥2 individuals in the nth generation, pick k individuals at random from the nth generation and trace their lines of descent backward in time till they meet. In this paper, the limit behaviors of the distributions of the generation number of the most recent common ancestor of any k chosen individuals and of the whole population are studied for both critical and subcritical cases. Also, we investigate the limit distribution of the joint distribution of the generation number and their types.


2021 ◽  
Vol 17 (3) ◽  
Author(s):  
Jessica A. Oswald ◽  
Ryan S. Terrill ◽  
Brian J. Stucky ◽  
Michelle J. LeFebvre ◽  
David W. Steadman ◽  
...  

Worldwide decline in biodiversity during the Holocene has impeded a comprehensive understanding of pre-human biodiversity and biogeography. This is especially true on islands, because many recently extinct island taxa were morphologically unique, complicating assessment of their evolutionary relationships using morphology alone. The Caribbean remains an avian hotspot but was more diverse before human arrival in the Holocene. Among the recently extinct lineages is the enigmatic genus Nesotrochis, comprising three flightless species. Based on morphology, Nesotrochis has been considered an aberrant rail (Rallidae) or related to flufftails (Sarothruridae). We recovered a nearly complete mitochondrial genome of Nesotrochis steganinos from fossils, discovering that it is not a rallid but instead is sister to Sarothruridae, volant birds now restricted to Africa and New Guinea, and the recently extinct, flightless Aptornithidae of New Zealand. This result suggests a widespread or highly dispersive most recent common ancestor of the group. Prior to human settlement, the Caribbean avifauna had a far more cosmopolitan origin than is evident from extant species.


2003 ◽  
Vol 35 (04) ◽  
pp. 1071-1089 ◽  
Author(s):  
Amaury Lambert

We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a branching process founded t units of time ago, in both the discrete and continuous (time and state-space) settings. We obtain limiting distributions as t→∞ in the subcritical case. In the continuous setting, these distributions are specified for quadratic branching mechanisms (corresponding to Brownian motion and Brownian motion with positive drift), and we also extend our results for two individuals to the joint distribution of coalescence times for any finite number of individuals sampled in the current generation.


2003 ◽  
Vol 35 (4) ◽  
pp. 1071-1089 ◽  
Author(s):  
Amaury Lambert

We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a branching process founded t units of time ago, in both the discrete and continuous (time and state-space) settings. We obtain limiting distributions as t→∞ in the subcritical case. In the continuous setting, these distributions are specified for quadratic branching mechanisms (corresponding to Brownian motion and Brownian motion with positive drift), and we also extend our results for two individuals to the joint distribution of coalescence times for any finite number of individuals sampled in the current generation.


1995 ◽  
Vol 27 (02) ◽  
pp. 418-442 ◽  
Author(s):  
Neil O'Connell

We obtain a weak approximation for the reduced family tree in a near-critical Markov branching process when the time interval considered is long; we also extend Yaglom's theorem and the exponential law to this case. These results are then applied to the problem of estimating the age of our most recent common female ancestor, using mitochondrial DNA sequences taken from a sample of contemporary humans.


2013 ◽  
Vol 9 (6) ◽  
pp. 20130748 ◽  
Author(s):  
Sankar Subramanian ◽  
Gabrielle Beans-Picón ◽  
Siva K. Swaminathan ◽  
Craig D. Millar ◽  
David M. Lambert

Penguins are a remarkable group of birds, with the 18 extant species living in diverse climatic zones from the tropics to Antarctica. The timing of the origin of these extant penguins remains controversial. Previous studies based on DNA sequences and fossil records have suggested widely differing times for the origin of the group. This has given rise to widely differing biogeographic narratives about their evolution. To resolve this problem, we sequenced five introns from 11 species representing all genera of living penguins. Using these data and other available DNA sequences, together with the ages of multiple penguin fossils to calibrate the molecular clock, we estimated the age of the most recent common ancestor of extant penguins to be 20.4 Myr (17.0–23.8 Myr). This time is half of the previous estimates based on molecular sequence data. Our results suggest that most of the major groups of extant penguins diverged 11–16 Ma. This overlaps with the sharp decline in Antarctic temperatures that began approximately 12 Ma, suggesting a possible relationship between climate change and penguin evolution.


1995 ◽  
Vol 27 (2) ◽  
pp. 418-442 ◽  
Author(s):  
Neil O'Connell

We obtain a weak approximation for the reduced family tree in a near-critical Markov branching process when the time interval considered is long; we also extend Yaglom's theorem and the exponential law to this case. These results are then applied to the problem of estimating the age of our most recent common female ancestor, using mitochondrial DNA sequences taken from a sample of contemporary humans.


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