Fluctuations of Animal Populations and a Measure of Community Stability. MacArthur, R. 36(3):533–536. ![Fluctuations of Animal Populations and a Measure of Community Stability [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex [Excerpt] Three assumptions will be made and a conclusion will be deduced from these. Since the conclusion is not always correct, it mill be justifiable to conclude that one or more of the assumptions is responsible. First, temporarily assume that the amount of energy entering the community (at the lowest trophic level, of course) does not vary with time. Second, assume that the length of time that energy is retained by a species before being passed on to the next doesn't change from time to time. For example, if the animals die young in some year, this would violate the assumption. Third, assume that the population oi each species varies directly with the food energy available. If a species first overeats and then starves (essentially a predator-prey reaction) or follows changes in availahle energy only after a time lag, then this assumption is violated. These three assumptions imply that the population of each species tends to a specific constant, independent of the initial populations of the species. [...] Since populations of species often fluctuate in nature, it can he concluded that one or more of the three assumptions is failing to hold. Furtilermore, it is clear from the theorem that the structure of the food web cannot be responsible for fluctuations. Thereiore, an explanation of the fluctuations must lie in predator-prey relations, time lag phenotnena, or other violations of assumption three; in environtnental variations in available energy, violating assumption one; or in variations in age at death, violating assumption two. [Community stability] In some communities the abundance of species tends to stay quite constant, while in others the abundances vary greatly. We are inclined to call the first stable and the second unstable. This concept can he made more precise, however. Suppose, for some reason, that one species has an abnormal abundance. Then we shall say the community is unstable if the other species change markedly in abundance as a result of the first. The less effect this abnormal abundance has on the other species, the more stable the community. [...] Some interesting conclusions may be drawn from these properties. First, (1) implies that restricted diet lowers stability. But restricted diet is what is essential for efficiency. Furthermore, efficiency and stability are the two features required for survival under natural selection. Efficiency enables individual animals to outcompete others, but stability allows individual communities to outsurvive less stable ones. From this it seems reasonable that natural selection operates for maximum efficiency subject to a certain necessary stability. Combining this with the properties listed above the following seem plausible. [::A] Where there is a small number of species (e.g. in arctic regions) the stability condition is hard or impossible to achieve; species have to eat a wide diet and a large number of trophic levels (compared to number of species) is expected. If the number of species is too small, even this will not assure stability, and, as in the Arctic, populations will vary considerably. [::B] Where there is a large number of species (e.g. in tropical regions) the required stability can be achieved along with a fairly restricted diet; species can specialize along particular lines and a relatively small number of trophic levels (compared to number of species) is possible. [...]
@article{macarthurFluctuationsAnimalPopulations1955,
title = {Fluctuations of Animal Populations and a Measure of Community Stability},
author = {MacArthur, Robert},
date = {1955-07},
journaltitle = {Ecology},
volume = {36},
pages = {533--536},
issn = {1939-9170},
doi = {10.2307/1929601},
url = {http://mfkp.org/INRMM/article/14483057},
abstract = {[Excerpt] Three assumptions will be made and a conclusion will be deduced from these. Since the conclusion is not always correct, it mill be justifiable to conclude that one or more of the assumptions is responsible. First, temporarily assume that the amount of energy entering the community (at the lowest trophic level, of course) does not vary with time. Second, assume that the length of time that energy is retained by a species before being passed on to the next doesn't change from time to time. For example, if the animals die young in some year, this would violate the assumption. Third, assume that the population oi each species varies directly with the food energy available. If a species first overeats and then starves (essentially a predator-prey reaction) or follows changes in availahle energy only after a time lag, then this assumption is violated. These three assumptions imply that the population of each species tends to a specific constant, independent of the initial populations of the species. [...]
Since populations of species often fluctuate in nature, it can he concluded that one or more of the three assumptions is failing to hold. Furtilermore, it is clear from the theorem that the structure of the food web cannot be responsible for fluctuations. Thereiore, an explanation of the fluctuations must lie in predator-prey relations, time lag phenotnena, or other violations of assumption three; in environtnental variations in available energy, violating assumption one; or in variations in age at death, violating assumption two.
[Community stability] In some communities the abundance of species tends to stay quite constant, while in others the abundances vary greatly. We are inclined to call the first stable and the second unstable. This concept can he made more precise, however. Suppose, for some reason, that one species has an abnormal abundance. Then we shall say the community is unstable if the other species change markedly in abundance as a result of the first. The less effect this abnormal abundance has on the other species, the more stable the community. [...] Some interesting conclusions may be drawn from these properties. First, (1) implies that restricted diet lowers stability. But restricted diet is what is essential for efficiency. Furthermore, efficiency and stability are the two features required for survival under natural selection. Efficiency enables individual animals to outcompete others, but stability allows individual communities to outsurvive less stable ones. From this it seems reasonable that natural selection operates for maximum efficiency subject to a certain necessary stability. Combining this with the properties listed above the following seem plausible. [::A] Where there is a small number of species (e.g. in arctic regions) the stability condition is hard or impossible to achieve; species have to eat a wide diet and a large number of trophic levels (compared to number of species) is expected. If the number of species is too small, even this will not assure stability, and, as in the Arctic, populations will vary considerably. [::B] Where there is a large number of species (e.g. in tropical regions) the required stability can be achieved along with a fairly restricted diet; species can specialize along particular lines and a relatively small number of trophic levels (compared to number of species) is possible. [...]},
keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-14483057,~to-add-doi-URL,100-ecology-articles,constraints,diversity,ecology,energy,high-impact-publication,mathematical-reasoning,sustainability,theoretical-approach},
number = {3}
}
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Second, assume that the length of time that energy is retained by a species before being passed on to the next doesn't change from time to time. For example, if the animals die young in some year, this would violate the assumption. Third, assume that the population oi each species varies directly with the food energy available. If a species first overeats and then starves (essentially a predator-prey reaction) or follows changes in availahle energy only after a time lag, then this assumption is violated. These three assumptions imply that the population of each species tends to a specific constant, independent of the initial populations of the species. [...] Since populations of species often fluctuate in nature, it can he concluded that one or more of the three assumptions is failing to hold. Furtilermore, it is clear from the theorem that the structure of the food web cannot be responsible for fluctuations. Thereiore, an explanation of the fluctuations must lie in predator-prey relations, time lag phenotnena, or other violations of assumption three; in environtnental variations in available energy, violating assumption one; or in variations in age at death, violating assumption two. [Community stability] In some communities the abundance of species tends to stay quite constant, while in others the abundances vary greatly. We are inclined to call the first stable and the second unstable. This concept can he made more precise, however. Suppose, for some reason, that one species has an abnormal abundance. Then we shall say the community is unstable if the other species change markedly in abundance as a result of the first. The less effect this abnormal abundance has on the other species, the more stable the community. [...] Some interesting conclusions may be drawn from these properties. First, (1) implies that restricted diet lowers stability. But restricted diet is what is essential for efficiency. Furthermore, efficiency and stability are the two features required for survival under natural selection. Efficiency enables individual animals to outcompete others, but stability allows individual communities to outsurvive less stable ones. From this it seems reasonable that natural selection operates for maximum efficiency subject to a certain necessary stability. Combining this with the properties listed above the following seem plausible. [::A] Where there is a small number of species (e.g. in arctic regions) the stability condition is hard or impossible to achieve; species have to eat a wide diet and a large number of trophic levels (compared to number of species) is expected. If the number of species is too small, even this will not assure stability, and, as in the Arctic, populations will vary considerably. 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Since the conclusion is not always correct, it mill be justifiable to conclude that one or more of the assumptions is responsible. First, temporarily assume that the amount of energy entering the community (at the lowest trophic level, of course) does not vary with time. Second, assume that the length of time that energy is retained by a species before being passed on to the next doesn't change from time to time. For example, if the animals die young in some year, this would violate the assumption. Third, assume that the population oi each species varies directly with the food energy available. If a species first overeats and then starves (essentially a predator-prey reaction) or follows changes in availahle energy only after a time lag, then this assumption is violated. These three assumptions imply that the population of each species tends to a specific constant, independent of the initial populations of the species. [...]\n\nSince populations of species often fluctuate in nature, it can he concluded that one or more of the three assumptions is failing to hold. Furtilermore, it is clear from the theorem that the structure of the food web cannot be responsible for fluctuations. Thereiore, an explanation of the fluctuations must lie in predator-prey relations, time lag phenotnena, or other violations of assumption three; in environtnental variations in available energy, violating assumption one; or in variations in age at death, violating assumption two.\n\n[Community stability] In some communities the abundance of species tends to stay quite constant, while in others the abundances vary greatly. We are inclined to call the first stable and the second unstable. This concept can he made more precise, however. Suppose, for some reason, that one species has an abnormal abundance. Then we shall say the community is unstable if the other species change markedly in abundance as a result of the first. The less effect this abnormal abundance has on the other species, the more stable the community. [...] Some interesting conclusions may be drawn from these properties. First, (1) implies that restricted diet lowers stability. But restricted diet is what is essential for efficiency. Furthermore, efficiency and stability are the two features required for survival under natural selection. Efficiency enables individual animals to outcompete others, but stability allows individual communities to outsurvive less stable ones. From this it seems reasonable that natural selection operates for maximum efficiency subject to a certain necessary stability. Combining this with the properties listed above the following seem plausible. [::A] Where there is a small number of species (e.g. in arctic regions) the stability condition is hard or impossible to achieve; species have to eat a wide diet and a large number of trophic levels (compared to number of species) is expected. If the number of species is too small, even this will not assure stability, and, as in the Arctic, populations will vary considerably. [::B] Where there is a large number of species (e.g. in tropical regions) the required stability can be achieved along with a fairly restricted diet; species can specialize along particular lines and a relatively small number of trophic levels (compared to number of species) is possible. 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