ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps wi ...

, the species discovery curve (also known as a species accumulation curve or collector's curve) is a graph recording the cumulative number of

species In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...

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 In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...

ic function and the negative

exponential function The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, a ...

. The advantage of the negative exponential function is that it tends to an

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 one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, ...

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. An example in which one would not expect the function to asymptote is in the study of genetic sequences where new mutations and sequencing errors may lead to infinite variants. 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 Butterflies are insects in the macrolepidopteran clade Rhopalocera from the Order (biology), order Lepidoptera, which also includes moths. Adult butterflies have large, often brightly coloured wings, and conspicuous, fluttering flight. The ...

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 Ethology is the scientific study of animal behaviour, usually with a focus on behaviour under natural conditions, and viewing behaviour as an evolutionarily adaptive trait. Behaviourism as a term also describes the scientific and objectiv ...

, it can be applied to the number of distinct

fixed action pattern A fixed action pattern is an ethological term describing an instinctive behavioral sequence that is highly stereotyped and species-characteristic. Fixed action patterns are said to be produced by the innate releasing mechanism, a "hard-wired" neura ...

s that will be discovered as a function of cumulative effort studying the behaviour of a species of animal; in

molecular genetics Molecular genetics is a sub-field of biology that addresses how differences in the structures or expression of DNA molecules manifests as variation among organisms. Molecular genetics often applies an "investigative approach" to determine the ...

it is now being applied to the number of distinct

gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a ba ...

s that are discovered; and in literary studies, it can be used to estimate the total

vocabulary A vocabulary is a set of familiar words within a person's language. A vocabulary, usually developed with age, serves as a useful and fundamental tool for communication and acquiring knowledge. Acquiring an extensive vocabulary is one of the la ...

of a writer from the given sample of his or her recorded works (see Efron & Thisted, 1976).

References

{{Reflist * Chao, A., & Shen, T. J. (2004). Nonparametric prediction in species sampling. ''Journal of Agricultural Biological and Environmental Statistics, 9'', 253–269. *Efron, B., & Thisted, R. (1976). Estimating the number of unseen species: How many words did Shakespeare know? ''Biometrika, 63'', 435–447. *Fisher, R. A., Corbet, A. S., & Williams, C. B. (1943). The relation between the number of species and the number of individuals in a random sample of an animal population. ''Journal of Animal Ecology, 12'', 42–58. Population ecology Community ecology