Species discovery curve
Encyclopedia
In ecology
, the species discovery curve is a graph recording the cumulative number of species
of living things recorded in a particular environment as a function of the cumulative effort expended searching for them (usually measured in person-hours). It is related to, but not identical with, the species-area curve
.
The species discovery curve will necessarily be increasing, and will normally be negatively accelerated (that is, its rate of increase will slow down). Plotting the curve gives a way of estimating the number of additional species that will be discovered with further effort. This is usually done by fitting some kind of functional form to the curve, either by eye or by using non-linear regression
techniques. Commonly used functional forms include the logarithm
ic function and the negative exponential function
. The advantage of the negative exponential function is that it tends to an asymptote
which equals the number of species that would be discovered if infinite effort is expended. However, some theoretical approaches imply that the logarithmic curve may be more appropriate, implying that though species discovery will slow down with increasing effort, it will never entirely cease, so there is no asymptote, and if infinite effort was expended, an infinite number of species would be discovered.
The first theoretical investigation of the species-discovery process was in a classic paper by Fisher, Corbet and Williams (1943), which was based on a large collection of butterflies
made in Malaya
. Theoretical statistical work on the problem continues, see for example the recent paper by Chao and Shen (2004). The theory is linked to that of Zipf's law.
The same approach is used in many other fields. For example, in ethology
, it can be applied to the number of distinct fixed action pattern
s that will be discovered as a function of cumulative effort studying the behaviour of a species of animal; in molecular genetics
it is now being applied to the number of distinct gene
s that are discovered; and in literary studies, it can be used to estimate the total vocabulary
of a writer from the given sample of his or her recorded works (see Efron & Thisted, 1976).
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
, the species discovery curve is a graph recording the cumulative number of species
Species
In biology, a species is one of the basic units of biological classification and a taxonomic rank. A species is often defined as a group of organisms capable of interbreeding and producing fertile offspring. While in many cases this definition is adequate, more precise or differing measures are...
of living things recorded in a particular environment as a function of the cumulative effort expended searching for them (usually measured in person-hours). It is related to, but not identical with, the species-area curve
Species-area curve
In ecology, a species-area curve is a relationship between the area of a habitat, or of part of a habitat, and the number of species found within that area. Larger areas tend to contain larger numbers of species, and empirically, the relative numbers seem to follow systematic mathematical...
.
The species discovery curve will necessarily be increasing, and will normally be negatively accelerated (that is, its rate of increase will slow down). Plotting the curve gives a way of estimating the number of additional species that will be discovered with further effort. This is usually done by fitting some kind of functional form to the curve, either by eye or by using non-linear regression
Regression analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...
techniques. Commonly used functional forms include the logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
ic function and the negative exponential function
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
. The advantage of the negative exponential function is that it tends to an asymptote
Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors...
which equals the number of species that would be discovered if infinite effort is expended. However, some theoretical approaches imply that the logarithmic curve may be more appropriate, implying that though species discovery will slow down with increasing effort, it will never entirely cease, so there is no asymptote, and if infinite effort was expended, an infinite number of species would be discovered.
The first theoretical investigation of the species-discovery process was in a classic paper by Fisher, Corbet and Williams (1943), which was based on a large collection of butterflies
Butterfly
A butterfly is a mainly day-flying insect of the order Lepidoptera, which includes the butterflies and moths. Like other holometabolous insects, the butterfly's life cycle consists of four parts: egg, larva, pupa and adult. Most species are diurnal. Butterflies have large, often brightly coloured...
made in Malaya
British Malaya
British Malaya loosely described a set of states on the Malay Peninsula and the Island of Singapore that were brought under British control between the 18th and the 20th centuries...
. Theoretical statistical work on the problem continues, see for example the recent paper by Chao and Shen (2004). The theory is linked to that of Zipf's law.
The same approach is used in many other fields. For example, in ethology
Ethology
Ethology is the scientific study of animal behavior, and a sub-topic of zoology....
, it can be applied to the number of distinct fixed action pattern
Fixed action pattern
In ethology, a fixed action pattern , or modal action pattern, is an instinctive behavioral sequence that is indivisible and runs to completion...
s that will be discovered as a function of cumulative effort studying the behaviour of a species of animal; in molecular genetics
Molecular genetics
Molecular genetics is the field of biology and genetics that studies the structure and function of genes at a molecular level. The field studies how the genes are transferred from generation to generation. Molecular genetics employs the methods of genetics and molecular biology...
it is now being applied to the number of distinct gene
Gene
A gene is a molecular unit of heredity of a living organism. It is a name given to some stretches of DNA and RNA that code for a type of protein or for an RNA chain that has a function in the organism. Living beings depend on genes, as they specify all proteins and functional RNA chains...
s that are discovered; and in literary studies, it can be used to estimate the total vocabulary
Vocabulary
A person's vocabulary is the set of words within a language that are familiar to that person. A vocabulary usually develops with age, and serves as a useful and fundamental tool for communication and acquiring knowledge...
of a writer from the given sample of his or her recorded works (see Efron & Thisted, 1976).