Confidence intervals on stratigraphic ranges with nonrandom distributions of fossil horizons

Paleobiology ◽  
1997 ◽  
Vol 23 (2) ◽  
pp. 165-173 ◽  
Author(s):  
Charles R. Marshall
Keyword(s):  
Confidence Intervals ◽  
Potential Function ◽  
Water Depth ◽  
Plane Surface ◽  
Quantitative Measure ◽  
A Priori Estimate ◽  
Bedding Plane ◽  
Recovery Potential ◽  
Stratigraphic Position ◽  
Stratigraphic Ranges

A generalized method for calculating confidence intervals on the position of the true end point of a stratigraphic range when the distributions of fossil horizons is nonrandom is presented. The method requires a quantitative measure of collecting and/or preservation biases with stratigraphic position. This fossil recovery potential function may be based on (among other variables) bedding-plane surface areas, or, given a water depth curve, an a priori estimate of the preservation potential with water depth. The approach assumes that the observed distribution of fossil horizons is consistent with the distribution predicted by the fossil recovery potential function, an assumption that must be tested before the method is applied. Unlike previous methods for calculating confidence intervals on the end points of stratigraphic ranges, this method may be applied when the number of fossil horizons is correlated with stratigraphic position. The approach should only be applied to sections that have been sampled continuously, or approximately continuously. Its efficacy will depend on how accurately fossil recovery potentials can be determined. A method is also presented for estimating the probability that a species became extinct during a major hiatus in the rock record.

Confidence intervals on stratigraphic ranges: partial relaxation of the assumption of randomly distributed fossil horizons

Paleobiology ◽  
1994 ◽  
Vol 20 (4) ◽  
pp. 459-469 ◽  
Author(s):  
Charles R. Marshall
Keyword(s):  
Confidence Intervals ◽  
Fossil Record ◽  
Continuous Distribution ◽  
Random Processes ◽  
Upper Bounds ◽  
Restrictive Assumption ◽  
End Points ◽  
New Approach ◽  
Stratigraphic Position ◽  
Stratigraphic Ranges

The equations for calculating classical confidence intervals on the end points of stratigraphic ranges are based on the restrictive assumption of randomly distributed fossil finds. Herein, a method is presented for calculating confidence intervals on the end-points of stratigraphic ranges that partially relaxes this assumption: the method will work for any continuous distribution of gap sizes, not just those generated by random processes. The price paid for the generality of the new approach is twofold: (1) there are uncertainties associated with the sizes of the confidence intervals, and (2) for large confidence values (e.g., 95%) a rich fossil record is required to place upper bounds on the corresponding confidence intervals. This new method is not universal; like the method for calculating classical confidence intervals it is based on the assumption that there is no correlation between gap size and stratigraphic position. The fossil record of the Neogene Caribbean bryozoan Metrarabdotos is analyzed with the new approach. The equations developed here, like those for classical confidence intervals, should not be applied to stratigraphic ranges based on discrete sampling regimes, such as those typically established from deep-sea drilling cores, though there are exceptions to this rule.

Using Confidence Intervals to Quantify the Uncertainty in the End-Points of Stratigraphic Ranges

2010 ◽  
Vol 16 ◽  
pp. 291-316 ◽  
Author(s):  
Charles R. Marshall
Keyword(s):  
Environmental Change ◽  
Confidence Intervals ◽  
Mass Extinction ◽  
Relative Importance ◽  
End Points ◽  
Western Tethys ◽  
Space And Time ◽  
Biotic Events ◽  
Stratigraphic Ranges ◽  
The Many

One of the many contributions paleontology makes to our understanding of the biosphere and its evolution is a direct temporal record of biotic events. However, assuming fossils have been correctly identified and accurately dated, stratigraphic ranges underestimate true temporal ranges: observed first occurrences are too young, and observed last occurrences are too old. Here I introduce the techniques developed for placing confidence intervals on the end-points of stratigraphic ranges. I begin with the analysis of single taxa in local sections – with the simplest of assumptions – random fossilization. This is followed by a discussion of the methods developed to handle the fact that the recovery of fossils is often non-random in space and time. After discussion of how confidence intervals can be used to test for simultaneous origination and extinctions, I conclude with an example application of confidence intervals to unravel the relative importance of background extinction, environmental change and mass extinction of ammonite species at the end of the Cretaceous in western Tethys.

Stratigraphic tests of cladistic hypotheses

Paleobiology ◽  
1995 ◽  
Vol 21 (2) ◽  
pp. 153-178 ◽  
Author(s):  
Peter J. Wagner
Keyword(s):  
Confidence Intervals ◽  
Fossil Record ◽  
Evolutionary Dynamics ◽  
Test Group ◽  
Individual Species ◽  
Stratigraphic Record ◽  
Long Time ◽  
Morphologic Evolution ◽  
Phylogenetic Hypotheses ◽  
Stratigraphic Ranges

Cladograms predict the order in which fossil taxa appeared and, thus, make predictions about general patterns in the stratigraphic record. Inconsistencies between cladistic predictions and the observed stratigraphic record reflect either inadequate sampling of a clade's species, incomplete estimates of stratigraphic ranges, or homoplasy producing an incorrect phylogenetic hypothesis. A method presented in this paper attempts to separate the effects of homoplasy from the effects of inadequate sampling. Sampling densities of individual species are used to calculate confidence intervals on their stratigraphic ranges. The method uses these confidence intervals to test the order of branching predicted by a cladogram. The Lophospiridae (“Archaeogastropoda”) of the Ordovician provide a useful test group because the clade has a good fossil record and it produced species over a long time. Confidence intervals reject several cladistic hypotheses that postulate improbable “ghost lineages.” Other hypotheses are acceptable only with explicit ancestor-descendant relationships. The accepted cladogram is the shortest one that stratigraphic data cannot reject. The results caution against evaluating phylogenetic hypotheses of fossil taxa without considering both stratigraphic data and the possible presence of ancestral species, as both factors can affect interpretations of a clade's evolutionary dynamics and its patterns of morphologic evolution.

Confidence intervals on stratigraphic ranges

Paleobiology ◽  
1990 ◽  
Vol 16 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Charles R. Marshall
Keyword(s):  
Confidence Intervals ◽  
Fossil Record ◽  
Morphological Evolution ◽  
Radiometric Dating ◽  
Phylogenetic Hypotheses ◽  
Stratigraphic Ranges ◽  
Taxonomic Assignments ◽  
Fossil Records ◽  
Source Of Error ◽  
Stratigraphic Range

Observed stratigraphic ranges almost always underestimate true longevities. Strauss and Sadler (1987, 1989) provide a method for calculating confidence intervals on the endpoints of local stratigraphic ranges. Their method can also be applied to composite sections; confidence intervals may be placed on times of origin and extinction for entire species or lineages. Confidence interval sizes depend only on the length of the stratigraphic range and the number of fossil horizons. The technique's most important assumptions are that fossil horizons are distributed randomly and that collecting intensity has been uniform over the stratigraphic range. These assumptions are more difficult to test and less likely to be fulfilled for composite sections than for local sections.Confidence intervals give useful baseline estimates of the incompleteness of the fossil record, even if the underlying assumptions cannot be tested. Confidence intervals, which can be very large, should be calculated when the fossil record is used to assess absolute rates of molecular or morphological evolution, especially for poorly preserved groups. Confidence intervals have other functions: to determine how rich the fossil record has to be before radiometric dating errors become the dominant source of error in estimated times of origin or extinction; to predict future fossil finds; to predict which species with fossil records should be extant; and to assess phylogenetic hypotheses and taxonomic assignments.

Adaptive credible intervals on stratigraphic ranges when recovery potential is unknown

Paleobiology ◽  
2016 ◽  
Vol 42 (2) ◽  
pp. 240-256 ◽  
Author(s):  
Steve C. Wang ◽  
Philip J. Everson ◽  
Heather Jianan Zhou ◽  
Dasol Park ◽  
David J. Chudzicki
Keyword(s):  
A Priori ◽  
Sampling Effort ◽  
Recovery Potential ◽  
Point Estimates ◽  
Stratigraphic Architecture ◽  
Coverage Probabilities ◽  
Credible Intervals ◽  
Nominal Coverage ◽  
Stratigraphic Ranges ◽  
Stratigraphic Range

AbstractNumerous methods exist for estimating the true stratigraphic range of a fossil taxon based on the stratigraphic positions of its fossil occurrences. Many of these methods require the assumption of uniform fossil recovery potential—that fossils are equally likely to be found at any point within the taxon's true range. This assumption is unrealistic, because factors such as stratigraphic architecture, sampling effort, and the taxon's abundance and geographic range affect recovery potential. Other methods do not make this assumption, but they instead require a priori quantitative knowledge of recovery potential that may be difficult to obtain. We present a new Bayesian method, the Adaptive Beta method, for estimating the true stratigraphic range of a taxon that works for both uniform and non-uniform recovery potential. In contrast to existing methods, we explicitly estimate recovery potential from the positions of the occurrences themselves, so that a priori knowledge of recovery potential is not required. Using simulated datasets, we compare the performance of our method with existing methods. We show that the Adaptive Beta method performs well in that it achieves or nearly achieves nominal coverage probabilities and provides reasonable point estimates of the true extinction in a variety of situations. We demonstrate the method using a dataset of the Cambrian molluscAnabarella.

scholarly journals Stratigraphic signatures of mass extinctions: ecological and sedimentary determinants

2018 ◽  
Vol 285 (1886) ◽  
pp. 20181191 ◽  
Author(s):  
Rafał Nawrot ◽  
Daniele Scarponi ◽  
Michele Azzarone ◽  
Troy A. Dexter ◽  
Kristopher M. Kusnerik ◽  
...  
Keyword(s):  
Mass Extinction ◽  
Local Community ◽  
Empirical Studies ◽  
Mass Extinctions ◽  
Sea Level Changes ◽  
Sequence Stratigraphic ◽  
Recovery Potential ◽  
Mollusc Species ◽  
Stratigraphic Ranges ◽  
Extinction Events

Stratigraphic patterns of last occurrences (LOs) of fossil taxa potentially fingerprint mass extinctions and delineate rates and geometries of those events. Although empirical studies of mass extinctions recognize that random sampling causes LOs to occur earlier than the time of extinction (Signor–Lipps effect), sequence stratigraphic controls on the position of LOs are rarely considered. By tracing stratigraphic ranges of extant mollusc species preserved in the Holocene succession of the Po coastal plain (Italy), we demonstrated that, if mass extinction took place today, complex but entirely false extinction patterns would be recorded regionally due to shifts in local community composition and non-random variation in the abundance of skeletal remains, both controlled by relative sea-level changes. Consequently, rather than following an apparent gradual pattern expected from the Signor–Lipps effect, LOs concentrated within intervals of stratigraphic condensation and strong facies shifts mimicking sudden extinction pulses. Methods assuming uniform recovery potential of fossils falsely supported stepwise extinction patterns among studied species and systematically underestimated their stratigraphic ranges. Such effects of stratigraphic architecture, co-produced by ecological, sedimentary and taphonomic processes, can easily confound interpretations of the timing, duration and selectivity of mass extinction events. Our results highlight the necessity of accounting for palaeoenvironmental and sequence stratigraphic context when inferring extinction dynamics from the fossil record.

scholarly journals Support Vector Machine Based Mobile Robot Motion Control and Obstacle Avoidance

Robotics ◽  
2013 ◽  
pp. 85-111 ◽  
Author(s):  
Lihua Jiang ◽  
Mingcong Deng
Keyword(s):  
Mobile Robot ◽  
Potential Function ◽  
Motion Control ◽  
Plane Surface ◽  
Support Vector ◽  
Function Estimation ◽  
Local Minima ◽  
Noise Effect ◽  
Virtual Force ◽  
Measured Information

Considering the noise effect during the navigation of a two wheeled mobile robot, SVM and LS-SVM based control schemes are discussed under the measured information with uncertainty, and in the different environments. The noise effect is defined as uncertainty in the measured data. One of them focuses on using a potential function and constructing a plane surface for avoiding the local minima in the static environments, where the controller is based on Lyapunov function candidate. Another one addresses to use a potential function and to define a new detouring virtual force for escaping from the local minima in the dynamic environments. Stability of the control system can be guaranteed. However, the motion control of the mobile robot would be affected by the noise effect. The SVM and LS-SVM for function estimation are used for estimating the parameter in the proposed controllers. With the estimated parameter, the noise effect during the navigation of the mobile robot can be reduced.

Tests and confidence intervals for a common upper endpoint in fossil taxa

Paleobiology ◽  
1996 ◽  
Vol 22 (3) ◽  
pp. 406-410 ◽  
Author(s):  
Andrew R. Solow
Keyword(s):  
Confidence Interval ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Upper Bound ◽  
Significance Level ◽  
Stratigraphic Ranges

Statistical inference about the upper and lower endpoints of the stratigraphic ranges of fossil taxa can be based on the pattern of finds. Strauss and Sadler (1989) described a test and confidence interval for a common upper or lower endpoint in two or more taxa. This approach is conservative, in the sense that it provides only an upper bound on the significance level. This paper describes and illustrates a test and confidence interval for which the significance level is known.

scholarly journals Support Vector Machine Based Mobile Robot Motion Control and Obstacle Avoidance

2013 ◽  
pp. 223-251
Author(s):  
Lihua Jiang ◽  
Mingcong Deng
Keyword(s):  
Mobile Robot ◽  
Potential Function ◽  
Motion Control ◽  
Plane Surface ◽  
Support Vector ◽  
Function Estimation ◽  
Local Minima ◽  
Noise Effect ◽  
Virtual Force ◽  
Measured Information

Considering the noise effect during the navigation of a two wheeled mobile robot, SVM and LS-SVM based control schemes are discussed under the measured information with uncertainty, and in the different environments. The noise effect is defined as uncertainty in the measured data. One of them focuses on using a potential function and constructing a plane surface for avoiding the local minima in the static environments, where the controller is based on Lyapunov function candidate. Another one addresses to use a potential function and to define a new detouring virtual force for escaping from the local minima in the dynamic environments. Stability of the control system can be guaranteed. However, the motion control of the mobile robot would be affected by the noise effect. The SVM and LS-SVM for function estimation are used for estimating the parameter in the proposed controllers. With the estimated parameter, the noise effect during the navigation of the mobile robot can be reduced.

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