ecology Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere lev ...

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

species A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), ...

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 Regression or regressions may refer to: Arts and entertainment * ''Regression'' (film), a 2015 horror film by Alejandro Amenábar, starring Ethan Hawke and Emma Watson * ''Regression'' (magazine), an Australian punk rock fanzine (1982–1984) * ...

techniques. Commonly used functional forms include the

logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...

ic function and the negative exponential function. 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 winged insects from the lepidopteran superfamily Papilionoidea, characterized by large, often brightly coloured wings that often fold together when at rest, and a conspicuous, fluttering flight. The oldest butterfly fossi ...

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 Zipf's law (; ) is an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the -th entry is often approximately inversely proportional to . The best known instance of Zipf's law applies to the ...

. The same approach is used in many other fields. For example, in

ethology Ethology is a branch of zoology that studies the behavior, behaviour of non-human animals. It has its scientific roots in the work of Charles Darwin and of American and German ornithology, ornithologists of the late 19th and early 20th cen ...

, it can be applied to the number of distinct

fixed action pattern "Fixed action pattern" is an Ethology, 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-wi ...

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 branch 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 st ...

it is now being applied to the number of distinct

gene In biology, the word gene has two meanings. The Mendelian gene is a basic unit of heredity. The molecular gene is a sequence of nucleotides in DNA that is transcribed to produce a functional RNA. There are two types of molecular genes: protei ...

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

vocabulary A vocabulary (also known as a lexicon) is a set of words, typically the set in a language or the set known to an individual. The word ''vocabulary'' originated from the Latin , meaning "a word, name". It forms an essential component of languag ...

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