Statistical Analysis of the Michaelis-Menten Equation

Raaijmakers, Jeroen G. W.

doi:10.2307/2531533

Cited by 158 publications

(92 citation statements)

References 18 publications

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“…The rarefaction curve was based on 100 randomizations of the number of replicates sampled. We focused our investigation on five non-parametric estimators as well as on the asymptotic Michaelis-Menten (MM) richness estimator (Raaijmakers 1987) (Table 1). These six estimators were previously used in several evaluations and were reported to perform well (Walther and Moore 2005, see their table 3).…”

Section: Materials and Proceduresmentioning

confidence: 99%

Estimation of regional richness in marine benthic communities: quantifying the error

Canning-Clode

Valdivia

Molis

et al. 2008

Limnology & Ocean Methods

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Species richness is the most widely used measure of biodiversity. It is considered crucial for testing numerous ecological theories. While local species richness is easily determined by sampling, the quantification of regional richness relies on more or less complete species inventories, expert estimation, or mathematical extrapolation from a number of replicated local samplings. However the accuracy of such extrapolations is rarely known. In this study, we compare the common estimators MM (Michaelis-Menten), Chao1, Chao2, ACE (Abundance-based Coverage Estimator), and the first and second order Jackknifes against the asymptote of the species accumulation curve, which we use as an estimate of true regional richness. Subsequently, we quantified the role of sample size, i.e., number of replicates, for precision, accuracy, and bias of the estimation. These replicates were sub-sets of three large data sets of benthic assemblages from the NE Atlantic: (i) soft-bottom sediment communities in the Western Baltic (n = 70); (ii) hard-bottom communities from emergent rock on the Island of Helgoland, North Sea (n = 52), and (iii) hardbottom assemblages grown on artificial substrata in Madeira Island, Portugal (n = 56). For all community types, Jack2 showed a better performance in terms of bias and accuracy while MM exhibited the highest precision. However, in virtually all cases and across all sampling efforts, the estimators underestimated the regional species richness, regardless of habitat type, or selected estimator. Generally, the amount of underestimation decreased with sampling effort. A logarithmic function was applied to quantify the bias caused by low replication using the best estimator, Jack2. The bias was more obvious in the soft-bottom environment, followed by the natural hard-bottom and the artificial hard-bottom habitats, respectively. If a weaker estimator in terms of performance is chosen for this quantification, more replicates are required to obtain a reliable estimation of regional richness.

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Section: Materials and Proceduresmentioning

confidence: 99%

Estimation of regional richness in marine benthic communities: quantifying the error

Canning-Clode

Valdivia

Molis

et al. 2008

Limnology & Ocean Methods

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“…This is known as the Eadie-Hofstee equation and is recommended by Colwell and Coddington (1994) as being least likely to produce biased estimates. If Xi = S ( n )/ n and Yi = S ( n ), then Raaijmakers (1987) showed that the maximum likelihood estimate for ␤ is…”

Section: Species Richness In Same-day Versus Different-day Surveysmentioning

confidence: 99%

“…For each approach, we calculate the trajectory of the species accumulation curve and its predicted final asymptote (i.e. the total species richness), using maximum likelihood methods (Raaijmakers 1987). We also examine the dependence of species richness estimates in the different-day surveys on the temporal spacing of repeat visits.…”

Section: Introductionmentioning

confidence: 99%

Estimating bird species richness: How should repeat surveys be organized in time?

FIELD¹,

Tyre²,

Possingham³

2008

Austral Ecology

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Estimates of species richness for a given area require that repeat surveys be taken, so that the statistical robustness of the estimate can be assessed. But how should these repeat surveys be organized in time? Here we present a case study of Australian woodland birds, surveyed using the 'active timed area search' method, which has become the standard unit for the Australian Bird Atlas, a continental-scale bird survey. To date, there has been no assessment of how estimates of species richness derived from this method are affected by the temporal organization of the repeat surveys. For instance, can conducting the repeat surveys in sequence on the same day effectively capture richness, or will additional species be obtained by repeating the surveys on different days within a season? If so, does the spacing of the repeat visits throughout the season have an effect? To answer these questions, we surveyed woodland birds in the Mount Lofty Ranges, South Australia, during late spring-summer 1999-2000, and compared the performance of two different temporal configurations of repeat visits to sites: (i) six repeat surveys performed on the same day; and (ii) three repeat surveys on different days. For both, we calculated the average number of species actually sighted and also estimated total species richness. The data supported our hypothesis that the sameday surveys would yield fewer species and underestimate total species richness. The different-day repeats captured significantly more species per unit of survey effort, and yielded a higher richness estimate. However, the timespan over which different-day surveys were conducted within a season did not have a significant influence on species richness estimates, evincing a qualitative advantage to surveying on different days, regardless of the spacing of repeat visits. These results may be of assistance to conservation managers when planning cost-efficient monitoring regimes.

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“…This estimator is calculated by repetitive random sampling and fitting an asymptotic model, following the method of Raaijmakers (1987). For each sample size (from 2 to the number of observations -1), the average number of species in the sample is calculated over the random samples (the default is 100 samples for each sample size, but a higher number may be better for some data).…”

Section: Michaelis-mentenmentioning

confidence: 99%

“…This is the Michaelis-Menten equation used in enzyme kinetics and thus there is an extensive literature discussing the estimation of its parameters, which unfortunately presents considerable statistical difficulties (Colwell and Coddington, 1994). The method implemented in DIVA-GIS, favored by Raaijmakers (1987), is to calculate S max and B using their maximum likelihood estimators as follows:…”

Section: (Equation 3)mentioning

confidence: 99%

Jamaican Nightshade (Solanum jamaicense): A Threat to Florida's Hammocks

Díaz

Overholt

Langeland

2008

Invasive plant sci. manag.

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Jamaican nightshade is a prickly, perennial, invasive shrub in central and southern peninsular Florida. It was first seen in Florida in 1930 near St. Cloud, and has since been reported at several other locations in the state. Jamaican nightshade is primarily found in wooded habitats, where it can quickly become dominant in the understory, but it also occasionally grows in isolated patches in the open. Although the distribution of Jamaican nightshade does not appear to be rapidly expanding in Florida, land mangers should be made aware of the potential of this weed to establish at new sites, and initiate control efforts during the early stages of colonization at newly invaded sites.

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Statistical Analysis of the Michaelis-Menten Equation

Cited by 158 publications

References 18 publications

Estimation of regional richness in marine benthic communities: quantifying the error

Estimation of regional richness in marine benthic communities: quantifying the error

Estimating bird species richness: How should repeat surveys be organized in time?

Jamaican Nightshade (Solanum jamaicense): A Threat to Florida's Hammocks

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