r/K selection theory

In ecology, r/K selection theory relates to the selection of combinations of traits in an organism that trade off between quantity and quality of offspring. The focus on either an increased quantity of offspring at the expense of individual parental investment of r-strategists, or on a reduced quantity of offspring with a corresponding increased parental investment of K-strategists, varies widely, seemingly to promote success in particular environments.

The terminology of r/K-selection was coined by the ecologists Robert MacArthur and E. O. Wilson in 1967[1] based on their work on island biogeography;[2] although the concept of the evolution of life history strategies has a longer history[3] (see e.g. plant strategies).

The theory was popular in the 1970s and 1980s, when it was used as a heuristic device, but lost importance in the early 1990s, when it was criticized by several empirical studies.[4][5] A life-history paradigm has replaced the r/K selection paradigm but continues to incorporate many of its important themes.[6]

Eubalaena glacialis with calf
A North Atlantic right whale with solitary calf. Whale reproduction follows a K-selection strategy, with few offspring, long gestation, long parental care, and a long period until sexual maturity.


Mouse litter
A litter of mice with their mother. The reproduction of mice follows an r-selection strategy, with many offspring, short gestation, less parental care, and a short time until sexual maturity.

In r/K selection theory, selective pressures are hypothesised to drive evolution in one of two generalized directions: r- or K-selection.[1] These terms, r and K, are drawn from standard ecological algebra as illustrated in the simplified Verhulst model of population dynamics:[7]

where N is the population, r is the maximum growth rate, K is the carrying capacity of the local environment, and dN/dt, the derivative of N with respect to time t, is the rate of change in population with time. Thus, the equation relates the growth rate of the population N to the current population size, incorporating the effect of the two constant parameters r and K. (Note that decrease is negative growth.) The choice of the letter K came from the German Kapazitätsgrenze (capacity limit), while r came from rate.


r-selected species are those that emphasize high growth rates, typically exploit less-crowded ecological niches, and produce many offspring, each of which has a relatively low probability of surviving to adulthood (i.e., high r, low K).[8] A typical r species is the dandelion (genus Taraxacum).

In unstable or unpredictable environments, r-selection predominates due to the ability to reproduce rapidly. There is little advantage in adaptations that permit successful competition with other organisms, because the environment is likely to change again. Among the traits that are thought to characterize r-selection are high fecundity, small body size, early maturity onset, short generation time, and the ability to disperse offspring widely.

Organisms whose life history is subject to r-selection are often referred to as r-strategists or r-selected. Organisms that exhibit r-selected traits can range from bacteria and diatoms, to insects and grasses, to various semelparous cephalopods and small mammals, particularly rodents. As with K-selection, below, the r/K paradigm (Differential K theory) has controversially been associated with human behavior and separately evolved populations.


About to Launch (26075320352)
A Bald eagle, an individual of a typical K-strategist species. K-strategists have longer life expectancies, produce relatively fewer offspring and tend to be altricial, requiring extensive care by parents when young.

By contrast, K-selected species display traits associated with living at densities close to carrying capacity and typically are strong competitors in such crowded niches that invest more heavily in fewer offspring, each of which has a relatively high probability of surviving to adulthood (i.e., low r, high K). In scientific literature, r-selected species are occasionally referred to as "opportunistic" whereas K-selected species are described as "equilibrium".[8]

In stable or predictable environments, K-selection predominates as the ability to compete successfully for limited resources is crucial and populations of K-selected organisms typically are very constant in number and close to the maximum that the environment can bear (unlike r-selected populations, where population sizes can change much more rapidly).

Traits that are thought to be characteristic of K-selection include large body size, long life expectancy, and the production of fewer offspring, which often require extensive parental care until they mature. Organisms whose life history is subject to K-selection are often referred to as K-strategists or K-selected.[9] Organisms with K-selected traits include large organisms such as elephants, humans, and whales, but also smaller, long-lived organisms such as Arctic terns,[10] parrots and eagles.

Continuous spectrum

Although some organisms are identified as primarily r- or K-strategists, the majority of organisms do not follow this pattern. For instance, trees have traits such as longevity and strong competitiveness that characterise them as K-strategists. In reproduction, however, trees typically produce thousands of offspring and disperse them widely, traits characteristic of r-strategists.[11]

Similarly, reptiles such as sea turtles display both r- and K-traits: although sea turtles are large organisms with long lifespans (provided they reach adulthood), they produce large numbers of unnurtured offspring.

The r/K dichotomy can be re-expressed as a continuous spectrum using the economic concept of discounted future returns, with r-selection corresponding to large discount rates and K-selection corresponding to small discount rates.[12]

Ecological succession

In areas of major ecological disruption or sterilisation (such as after a major volcanic eruption, as at Krakatoa or Mount Saint Helens), r- and K-strategists play distinct roles in the ecological succession that regenerates the ecosystem. Because of their higher reproductive rates and ecological opportunism, primary colonisers typically are r-strategists and they are followed by a succession of increasingly competitive flora and fauna. The ability of an environment to increase energetic content, through photosynthetic capture of solar energy, increases with the increase in complex biodiversity as r species proliferate to reach a peak possible with K strategies.[13]

Eventually a new equilibrium is approached (sometimes referred to as a climax community), with r-strategists gradually being replaced by K-strategists which are more competitive and better adapted to the emerging micro-environmental characteristics of the landscape. Traditionally, biodiversity was considered maximized at this stage, with introductions of new species resulting in the replacement and local extinction of endemic species.[14] However, the Intermediate Disturbance Hypothesis posits that intermediate levels of disturbance in a landscape create patches at different levels of succession, promoting coexistence of colonizers and competitors at the regional scale.


While usually applied at the level of species, r/K selection theory is also useful in studying the evolution of ecological and life history differences between subspecies, for instance the African honey bee, A. m. scutellata, and the Italian bee, A. m. ligustica.[15] At the other end of the scale, it has also been used to study the evolutionary ecology of whole groups of organisms, such as bacteriophages.[16]

Some researchers, such as Lee Ellis, J. Philippe Rushton, and Aurelio José Figueredo, have applied r/K selection theory to various human behaviors, including crime,[17] sexual promiscuity, fertility, IQ, and other traits related to life history theory.[18][19] Rushton's work resulted in him developing "differential K theory" to attempt to explain many variations in human behavior across geographic areas, a theory which has been criticized by many other researchers.[19][20] Other researchers have proposed that the evolution of human inflammatory responses is related to r/K selection.[21]


Although r/K selection theory became widely used during the 1970s,[22][23][24][25] it also began to attract more critical attention.[26][27][28][29] In particular, a review by the ecologist Stephen C. Stearns drew attention to gaps in the theory, and to ambiguities in the interpretation of empirical data for testing it.[30]

In 1981, a review of the r/K selection literature by Parry demonstrated that there was no agreement among researchers using the theory about the definition of r- and K-selection, which led him to question whether the assumption of a relation between reproductive expenditure and packaging of offspring was justified.[31] A 1982 study by Templeton and Johnson showed that in a population of Drosophila mercatorum under K-selection the population actually produced a higher frequency of traits typically associated with r-selection.[32] Several other studies contradicting the predictions of r/K selection theory were also published between 1977 and 1994.[33][34][35][36]

When Stearns reviewed the status of the theory in 1992,[37] he noted that from 1977 to 1982 there was an average of 42 references to the theory per year in the BIOSIS literature search service, but from 1984 to 1989 the average dropped to 16 per year and continued to decline. He concluded that r/K theory was a once useful heuristic that no longer serves a purpose in life history theory.[38]

More recently, the panarchy theories of adaptive capacity and resilience promoted by C. S. Holling and Lance Gunderson have revived interest in the theory, and use it as a way of integrating social systems, economics and ecology.[39]

Writing in 2002, Reznick and colleagues reviewed the controversy regarding r/K selection theory and concluded that:

The distinguishing feature of the r- and K-selection paradigm was the focus on density-dependent selection as the important agent of selection on organisms' life histories. This paradigm was challenged as it became clear that other factors, such as age-specific mortality, could provide a more mechanistic causative link between an environment and an optimal life history (Wilbur et al. 1974;[26] Stearns 1976,[40] 1977[30]). The r- and K-selection paradigm was replaced by new paradigm that focused on age-specific mortality (Stearns, 1976;[40] Charlesworth, 1980[41]). This new life-history paradigm has matured into one that uses age-structured models as a framework to incorporate many of the themes important to the rK paradigm.

— Reznick, Bryant and Bashey, 2002[6]

See also


  1. ^ a b Pianka, E.R. (1970). "On r and K selection". American Naturalist. 104 (940): 592–597. doi:10.1086/282697.
  2. ^ MacArthur, R.; Wilson, E.O. (1967). The Theory of Island Biogeography (2001 reprint ed.). Princeton University Press. ISBN 978-0-691-08836-5.
  3. ^ For example: Margalef, R. (1959). "Mode of evolution of species in relation to their places in ecological succession". XVth International Congress of Zoology.
  4. ^ Roff, Derek A. (1993). Evolution Of Life Histories: Theory and Analysis. Springer. ISBN 978-0-412-02391-0.
  5. ^ Stearns, Stephen C. (1992). The Evolution of Life Histories. Oxford University Press. ISBN 978-0-19-857741-6.
  6. ^ a b Reznick, D; Bryant, MJ; Bashey, F (2002). "r-and K-selection revisited: the role of population regulation in life-history evolution" (PDF). Ecology. 83 (6): 1509–1520. doi:10.1890/0012-9658(2002)083[1509:RAKSRT]2.0.CO;2.
  7. ^ Verhulst, P.F. (1838). "Notice sur la loi que la population pursuit dans son accroissement". Corresp. Math. Phys. 10: 113–121.
  8. ^ a b For example: Weinbauer, M.G.; Höfle, M.G. (1 October 1998). "Distribution and Life Strategies of Two Bacterial Populations in a Eutrophic Lake". Appl. Environ. Microbiol. 64 (10): 3776–3783. PMC 106546. PMID 9758799.
  9. ^ "r and K selection". University of Miami Department of Biology. Retrieved February 4, 2011.
  10. ^ John H. Duffus; Douglas M. Templeton; Monica Nordberg (2009). Concepts in Toxicology. Royal Society of Chemistry. p. 171. ISBN 978-0-85404-157-2.
  11. ^ Hrdy, Sarah Blaffer (2000), "Mother Nature: Maternal Instincts and How They Shape the Human Species" (Ballantine Books)
  12. ^ Reluga, T.; Medlock, J.; Galvani, A. (2009). "The discounted reproductive number for epidemiology". Mathematical Biosciences and Engineering. 6 (2): 377–393. doi:10.3934/mbe.2009.6.377. PMC 3685506. PMID 19364158.
  13. ^ Gunderson, Lance H.; Holling, C.S. (2001). Panarchy: Understanding Transformations In Human And Natural Systems. Island Press. ISBN 978-1-55963-857-9.
  14. ^ McNeely, J. A. (1994). "Lessons of the past: Forests and Biodiversity". Biodiversity and Conservation. 3: 3–20. CiteSeerX doi:10.1007/BF00115329.
  15. ^ Fewell, Jennifer H.; Susan M. Bertram (2002). "Evidence for genetic variation in worker task performance by African and European honeybees". Behavioral Ecology and Sociobiology. 52 (4): 318–25. doi:10.1007/s00265-002-0501-3.
  16. ^ Keen, E. C. (2014). "Tradeoffs in bacteriophage life histories". Bacteriophage. 4 (1): e28365. doi:10.4161/bact.28365. PMC 3942329. PMID 24616839.
  17. ^ Ellis, Lee (1987-01-01). "Criminal behavior and r/K selection: An extension of gene‐based evolutionary theory". Deviant Behavior. 8 (2): 149–176. doi:10.1080/01639625.1987.9967739. ISSN 0163-9625.
  18. ^ Figueredo, Aurelio José; Vásquez, Geneva; Brumbach, Barbara Hagenah; Schneider, Stephanie M. R. (2007-03-01). "The K-factor, Covitality, and personality". Human Nature. 18 (1): 47–73. doi:10.1007/bf02820846. ISSN 1045-6767. PMID 26181744.
  19. ^ a b Weizmann, Fredric; Wiener, Neil I.; Wiesenthal, David L.; Ziegler, Michael (1990). "Differential K theory and racial hierarchies". Canadian Psychology. 31 (1): 1–13. doi:10.1037/h0078934.
  20. ^ Peregrine, P (2003). "Cross-cultural evaluation of predicted associations between race and behavior". Evolution and Human Behavior. 24 (5): 357–364. doi:10.1016/s1090-5138(03)00040-0.
  21. ^ VAN BODEGOM, D.; MAY, L.; MEIJ, H. J.; WESTENDORP, R. G. J. (2007). "Regulation of Human Life Histories: The Role of the Inflammatory Host Response". Annals of the New York Academy of Sciences. 1100 (1): 84–97. doi:10.1196/annals.1395.007.
  22. ^ Gadgil, M.; Solbrig, O.T. (1972). "Concept of r-selection and K-selection — evidence from wild flowers and some theoretical consideration". Am. Nat. 106 (947): 14–31. doi:10.1086/282748. JSTOR 2459833.
  23. ^ Long, T.; Long, G. (1974). "Effects of r-selection and K-selection on components of variance for 2 quantitative traits". Genetics. 76 (3): 567–573. PMC 1213086. PMID 4208860.
  24. ^ Grahame, J. (1977). "Reproductive effort and r-selection and K-selection in 2 species of Lacuna (Gastropoda-Prosobranchia)". Mar. Biol. 40 (3): 217–224. doi:10.1007/BF00390877.
  25. ^ Luckinbill, L.S. (1978). "r and K selection in experimental populations of Escherichia coli". Science. 202 (4373): 1201–1203. doi:10.1126/science.202.4373.1201. PMID 17735406.
  26. ^ a b Wilbur, H.M.; Tinkle, D.W.; Collins, J.P. (1974). "Environmental certainty, trophic level, and resource availability in life history evolution". American Naturalist. 108 (964): 805–816. doi:10.1086/282956. JSTOR 2459610.
  27. ^ Barbault, R. (1987). "Are still r-selection and K-selection operative concepts?". Acta Oecologica-Oecologia Generalis. 8: 63–70.
  28. ^ Kuno, E. (1991). "Some strange properties of the logistic equation defined with r and K – inherent defects or artifacts". Researches on Population Ecology. 33: 33–39. doi:10.1007/BF02514572.
  29. ^ Getz, W.M. (1993). "Metaphysiological and evolutionary dynamics of populations exploiting constant and interactive resources – r-K selection revisited". Evolutionary Ecology. 7 (3): 287–305. doi:10.1007/BF01237746.
  30. ^ a b Stearns, S.C. (1977). "Evolution of life-history traits – critique of theory and a review of data" (PDF). Annu. Rev. Ecol. Syst. 8: 145–171. doi:10.1146/annurev.es.08.110177.001045. Archived from the original (PDF) on 2008-12-16.
  31. ^ Parry, G.D. (March 1981). "The Meanings of r- and K-selection". Oecologia. 48 (2): 260–4. doi:10.1007/BF00347974.
  32. ^ Templeton A.R.; Johnson, J.S. (1982). "Life History Evolution Under Pleiotropy and K-selection in a Natural Population of Drosophila mercatorum". In Barker, J.S.F.; Starmer, W.T. (eds.). Ecological genetics and evolution: the cactus-yeast-drosophila model system. Academic Press. pp. 225–239. ISBN 978-0-12-078820-0.
  33. ^ Snell, Terry W.; King, Charles E. (December 1977). "Lifespan and Fecundity Patterns in Rotifers: The Cost of Reproduction". Evolution. 31 (4): 882–890. doi:10.2307/2407451. JSTOR 2407451. PMID 28563718.
  34. ^ Taylor, Charles E.; Condra, Cindra (November 1980). "r- and K-Selection in Drosophila pseudoobscura". Evolution. 34 (6): 1183–93. doi:10.2307/2408299. JSTOR 2408299.
  35. ^ Hollocher, H.; Templeton, A.R. (April 1994). "The molecular through ecological genetics of abnormal abdomen in Drosophila mercatorum. VI. The non-neutrality of the Y chromosome rDNA polymorphism". Genetics. 136 (4): 1373–84. PMC 1205918. PMID 8013914.
  36. ^ Templeton, A.R.; Hollocher, H.; Johnston, J.S. (June 1993). "The molecular through ecological genetics of abnormal abdomen in Drosophila mercatorum. V. Female phenotypic expression on natural genetic backgrounds and in natural environments". Genetics. 134 (2): 475–85. PMC 1205491. PMID 8325484.
  37. ^ Stearns, S.C. (1992). The Evolution of Life Histories. Oxford University Press. ISBN 978-0-19-857741-6.
  38. ^ Graves, J. L. (2002). "What a tangled web he weaves Race, reproductive strategies and Rushton's life history theory". Anthropological Theory. 2 (2): 2 131–154. doi:10.1177/1469962002002002627. Archived from the original on 2015-06-06.
  39. ^ Gunderson, L. H. and Holling C. S. (2001) Panarchy: Understanding Transformations in Human and Natural Systems Island Press. ISBN 9781597269391.
  40. ^ a b Stearns, S.C. (1976). "Life history tactics: a review of the ideas". Quarterly Review of Biology. 51: 3–47. doi:10.1086/409052.
  41. ^ Charlesworth, B. (1980). Evolution in age structured populations. Cambridge, UK: Cambridge University Press.

Bacterivores are free-living, generally heterotrophic organisms, exclusively microscopic, which obtain energy and nutrients primarily or entirely from the consumption of bacteria. Many species of amoeba are bacterivores, as well as other types of protozoans. Commonly, all species of bacteria will be prey, but spores of some species, such as Clostridium perfringens, will never be prey, because of their cellular attributes.

Clutch (eggs)

A clutch of eggs is the group of eggs produced by birds, amphibians, or reptiles, often at a single time, particularly those laid in a nest.

In birds, destruction of a clutch by predators (or removal by humans, for example the California condor breeding program) results in double-clutching. The technique is used to double the production of a species' eggs, in the California condor case, specifically to increase population size. The act of putting one's hand in a nest to remove eggs is known as "dipping the clutch".

Competition (biology)

Competition is an interaction between organisms or species in which both the organisms or species are harmed. Limited supply of at least one resource (such as food, water, and territory) used by both can be a factor. Competition both within and between species is an important topic in ecology, especially community ecology. Competition is one of many interacting biotic and abiotic factors that affect community structure. Competition among members of the same species is known as intraspecific competition, while competition between individuals of different species is known as interspecific competition. Competition is not always straightforward, and can occur in both a direct and indirect fashion.According to the competitive exclusion principle, species less suited to compete for resources should either adapt or die out, although competitive exclusion is rarely found in natural ecosystems. According to evolutionary theory, this competition within and between species for resources is important in natural selection. However, competition may play less of a role than expansion among larger clades; this is termed the 'Room to Roam' hypothesis.


A copiotroph is an organism found in environments rich in nutrients, particularly carbon. They are the opposite to oligotrophs, which survive in much lower carbon concentrations.

Copiotrophic organisms tend to grow in high organic substrate conditions. For example, copiotrophic organisms grow in Sewage lagoons. They grow in organic substrate conditions up to 100x higher than oligotrophs.


Decomposers are organisms that break down dead or decaying organisms, and in doing so, they carry out the natural process of decomposition. Like herbivores and predators, decomposers are heterotrophic, meaning that they use organic substrates to get their energy, carbon and nutrients for growth and development. While the terms decomposer and detritivore are often interchangeably used, detritivores must ingest and digest dead matter via internal processes while decomposers can directly absorb nutrients through chemical and biological processes hence breaking down matter without ingesting it. Thus, invertebrates such as earthworms, woodlice, and sea cucumbers are technically detritivores, not decomposers, since they must ingest nutrients and are unable to absorb them externally.

Dominance (ecology)

Ecological dominance is the degree to which a taxon is more numerous than its competitors in an ecological community, or makes up more of the biomass.

Most ecological communities are defined by their dominant species.

In many examples of wet woodland in western Europe, the dominant tree is alder (Alnus glutinosa).

In temperate bogs, the dominant vegetation is usually species of Sphagnum moss.

Tidal swamps in the tropics are usually dominated by species of mangrove (Rhizophoraceae)

Some sea floor communities are dominated by brittle stars.

Exposed rocky shorelines are dominated by sessile organisms such as barnacles and limpets.

Feeding frenzy

In ecology, a feeding frenzy occurs when predators are overwhelmed by the amount of prey available. For example, a large school of fish can cause nearby sharks, such as the lemon shark, to enter into a feeding frenzy. This can cause the sharks to go wild, biting anything that moves, including each other or anything else within biting range. Another functional explanation for feeding frenzy is competition amongst predators. This term is most often used when referring to sharks or piranhas. It has also been used as a term within journalism.

Index of evolutionary biology articles

This is a list of topics in evolutionary biology.

J. Philippe Rushton

John Philippe Rushton (December 3, 1943 – October 2, 2012) was a Canadian psychologist and author. He taught at the University of Western Ontario and became known to the general public during the 1980s and 1990s for research on race and intelligence, race and crime, and other apparent racial variations. His book Race, Evolution, and Behavior (1995) is about the application of r/K selection theory to humans.

Rushton's controversial work was heavily criticized by the scientific community for the questionable quality of its research, with many alleging that it was conducted under a racist agenda. From 2002 until his death, he served as the head of the Pioneer Fund, a research foundation that has been accused of being racist, with its founders being American sympathizers for the Nazi eugenicist program.Rushton was a Fellow of the Canadian Psychological Association and a onetime Fellow of the John Simon Guggenheim Memorial Foundation.

Life history theory

Life history theory is an analytical framework designed to study the diversity of life history strategies used by different organisms throughout the world, as well as the causes and results of the variation in their life cycles. It is a theory of biological evolution that seeks to explain aspects of organisms' anatomy and behavior by reference to the way that their life histories—including their reproductive development and behaviors, life span and post-reproductive behavior—have been shaped by natural selection. A life history strategy is the "age- and stage-specific patterns" and timing of events that make up an organism's life, such as birth, weaning, maturation, death, etc. These events, notably juvenile development, age of sexual maturity, first reproduction, number of offspring and level of parental investment, senescence and death, depend on the physical and ecological environment of the organism.

The theory was developed in the 1950s and is used to answer questions about topics such as organism size, age of maturation, number of offspring, life span, and many others. In order to study these topics, life history strategies must be identified, and then models are constructed to study their effects. Finally, predictions about the importance and role of the strategies are made, and scientists use these predictions to understand how evolution affects the ordering and length of life history events in an organism's life, particularly the lifespan and period of reproduction. Life history theory draws on an evolutionary foundation, and studies the effects of natural selection on organisms, both throughout their lifetime and across generations. It also uses measures of evolutionary fitness to determine if organisms are able to maximize or optimize this fitness, by allocating resources to a range of different demands throughout the organism's life. It serves as a method to investigate further the "many layers of complexity of organisms and their worlds".Organisms have evolved a great variety of life histories, from Pacific salmon, which produce thousands of eggs at one time and then die, to human beings, who produce a few offspring over the course of decades. The theory depends on principles of evolutionary biology and ecology and is widely used in other areas of science.

Mesotrophic soil

Mesotrophic soils are soils with a moderate inherent fertility. An indicator of soil fertility is its base status, which is expressed as a ratio relating the major nutrient cations (calcium, magnesium, potassium and sodium) found there to the soil's clay percentage. This is commonly expressed in hundredths of a mole of cations per kilogram of clay, i.e. cmol (+) kg−1 clay.


A mycotroph is a plant that gets all or part of its carbon, water, or nutrient supply through symbiotic association with fungi. The term can refer to plants that engage in either of two distinct symbioses with fungi:

Many mycotrophs have a mutualistic association with fungi in any of several forms of mycorrhiza. The majority of plant species are mycotrophic in this sense. Examples include Burmanniaceae.

Some mycotrophs are parasitic upon fungi in an association known as myco-heterotrophy.


An organotroph is an organism that obtains hydrogen or electrons from organic substrates. This term is used in microbiology to classify and describe organisms based on how they obtain electrons for their respiration processes. Some organotrophs such as animals and many bacteria, are also heterotrophs. Organotrophs can be either anaerobic or aerobic.

Antonym: Lithotroph, Adjective: Organotrophic.


A planktivore is an aquatic organism that feeds on planktonic food, including zooplankton and phytoplankton.

Recruitment (biology)

In biology, especially marine biology, recruitment occurs when a juvenile organism joins a population, whether by birth or immigration, usually at a stage whereby the organisms are settled and able to be detected by an observer.There are two types of recruitment: closed and open.In the study of fisheries, recruitment is "the number of fish surviving to enter the fishery or to some life history stage such as settlement or maturity".

Relative abundance distribution

In the field of ecology, the relative abundance distribution (RAD) or species abundance distribution describes the relationship between the number of species observed in a field study as a function of their observed abundance. The graphs obtained in this manner are typically fitted to a Zipf–Mandelbrot law, the exponent of which serves as an index of biodiversity in the ecosystem under study.

Survivorship curve

A survivorship curve is a graph showing the number or proportion of individuals surviving to each age for a given species or group (e.g. males or females). Survivorship curves can be constructed for a given cohort (a group of individuals of roughly the same age) based on a life table.

There are three generalized types of survivorship curves:

Type I or convex curves are characterized by high age-specific survival probability in early and middle life, followed by a rapid decline in survival in later life. They are typical of species that produce few offspring but care for them well, including humans and many other large mammals.

Type II or diagonal curves are an intermediate between Types I and III, where roughly constant mortality rate/survival probability is experienced regardless of age. Some birds and some lizards follow this pattern.

Type III or concave curves have the greatest mortality (lowest age-specific survival) early in life, with relatively low rates of death (high probability of survival) for those surviving this bottleneck. This type of curve is characteristic of species that produce a large number of offspring (see r/K selection theory). This includes most marine invertebrates. For example, oysters produce millions of eggs, but most larvae die from predation or other causes; those that survive long enough to produce a hard shell live relatively long.The number or proportion of organisms surviving to any age is plotted on the y-axis (generally with a logarithmic scale starting with 1000 individuals), while their age (often as a proportion of maximum life span) is plotted on the x-axis.

In mathematical statistics, the survival function is one specific form of survivorship curve and plays a basic part in survival analysis.

There are various reasons that a species exhibits their particular survivorship curve, but one contributor can be environmental factors that decrease survival. For example, an outside element that is nondiscriminatory in the ages that it affects (of a particular species) is likely to yield a Type II survivorship curve, in which the young and old are equally likely to be affected. On the other hand, an outside element that preferentially reduces the survival of young individuals is likely to yield a Type III curve. Finally, if an outside element only reduces the survival of organisms later in life, this is likely to yield a Type I curve.

The Theory of Island Biogeography

The Theory of Island Biogeography is a 1967 book by Robert MacArthur and Edward O. Wilson. It is widely regarded as a seminal piece in island biogeography and ecology. The Princeton University Press reprinted the book in 2001 as a part of the "Princeton Landmarks in Biology" series. The book popularized the theory that insular biota maintain a dynamic equilibrium between immigration and extinction rates. The book also popularized the concepts and terminology of r/K selection theory.

Theoretical ecology

Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis. Effective models improve understanding of the natural world by revealing how the dynamics of species populations are often based on fundamental biological conditions and processes. Further, the field aims to unify a diverse range of empirical observations by assuming that common, mechanistic processes generate observable phenomena across species and ecological environments. Based on biologically realistic assumptions, theoretical ecologists are able to uncover novel, non-intuitive insights about natural processes. Theoretical results are often verified by empirical and observational studies, revealing the power of theoretical methods in both predicting and understanding the noisy, diverse biological world.

The field is broad and includes foundations in applied mathematics, computer science, biology, statistical physics, genetics, chemistry, evolution, and conservation biology. Theoretical ecology aims to explain a diverse range of phenomena in the life sciences, such as population growth and dynamics, fisheries, competition, evolutionary theory, epidemiology, animal behavior and group dynamics, food webs, ecosystems, spatial ecology, and the effects of climate change.

Theoretical ecology has further benefited from the advent of fast computing power, allowing the analysis and visualization of large-scale computational simulations of ecological phenomena. Importantly, these modern tools provide quantitative predictions about the effects of human induced environmental change on a diverse variety of ecological phenomena, such as: species invasions, climate change, the effect of fishing and hunting on food network stability, and the global carbon cycle.

Food webs
Example webs
Ecology: Modelling ecosystems: Other components

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