{"history":[],"article":{"id":"1310d76f-74b3-488d-a18b-2d4ea5425fa7","title":"Allee effect","slug":"allee-effect","content":":::summary\n:::\n\n# \nThe **Allee effect** is a phenomenon in [biology](https://bliptext.com/articles/biology) characterized by a correlation between [population size](https://bliptext.com/articles/population-size) or density and the mean individual [fitness](https://bliptext.com/articles/fitness-biology) (often measured as [per capita](https://bliptext.com/articles/per-capita) [population growth rate](https://bliptext.com/articles/population-growth-rate)) of a population or species.\n\n# History and background\nAlthough the concept of Allee effect had no title at the time, it was first described in the 1930s by its namesake, [Warder Clyde Allee](https://bliptext.com/articles/warder-clyde-allee).\nThrough experimental studies, Allee was able to demonstrate that [goldfish](https://bliptext.com/articles/goldfish) have a greater survival rate when there are more individuals within the tank.\nThis led him to conclude that aggregation can improve the survival rate of individuals, and that cooperation may be crucial in the overall evolution of social structure.\nThe term \"Allee principle\" was introduced in the 1950s, a time when the field of ecology was heavily focused on the role of competition among and within species.\nThe classical view of population dynamics stated that due to competition for resources, a population will experience a reduced overall growth rate at higher density and increased growth rate at lower density.\nIn other words, individuals in a population would be better off when there are fewer individuals around due to a limited amount of resources (see [logistic growth](https://bliptext.com/articles/logistic-function)).\nHowever, the concept of the Allee effect introduced the idea that the reverse holds true when the [population density](https://bliptext.com/articles/population-density) is low.\nIndividuals within a species often require the assistance of another individual for more than simple reproductive reasons in order to persist.\nThe most obvious example of this is observed in animals that hunt for prey or defend against predators as a group.\n\n# Definition\nThe generally accepted definition of Allee effect is positive density dependence, or the positive correlation between population density and individual fitness.\nIt is sometimes referred to as \"undercrowding\" and it is analogous (or even considered synonymous by some) to \"[depensation](https://bliptext.com/articles/depensation)\" in the field of [fishery sciences](https://bliptext.com/articles/fishery-science).\nListed below are a few significant subcategories of the Allee effect used in the ecology literature.\n\n## Component vs. demographic Allee effects\nThe component Allee effect is the positive relationship between any measurable component of individual fitness and population density.\nThe demographic Allee effect is the positive relationship between the overall individual fitness and population density.\nThe distinction between the two terms lies on the scale of the Allee effect: the presence of a demographic Allee effect suggests the presence of at least one component Allee effect, while the presence of a component Allee effect does not necessarily result in a demographic Allee effect.\nFor example, cooperative hunting and the ability to more easily find mates, both influenced by population density, are component Allee effects, as they influence individual fitness of the population.\nAt low population density, these component Allee effects would add up to produce an overall demographic Allee effect (increased fitness with higher population density).\nWhen population density reaches a high number, negative density dependence often offsets the component Allee effects through resource competition, thus erasing the demographic Allee effect.\nAllee effects might occur even at high population density for some species.\n\n## Strong vs. weak Allee effects\nThe strong Allee effect is a demographic Allee effect with a critical population size or density.\nThe weak Allee effect is a demographic Allee effect without a critical population size or density.\nThe distinction between the two terms is based on whether or not the population in question exhibits a [critical population size or density](https://bliptext.com/articles/extinction-threshold).\nA population exhibiting a weak Allee effect will possess a reduced per capita growth rate (directly related to individual fitness of the population) at lower population density or size.\nHowever, even at this low population size or density, the population will always exhibit a positive per capita growth rate.\nMeanwhile, a population exhibiting a strong Allee effect will have a critical population size or density under which the population growth rate becomes negative.\nTherefore, when the population density or size hits a number below this threshold, the population will be destined for extinction without any further aid.\nA strong Allee effect is often easier to demonstrate empirically using time series data, as one can pinpoint the population size or density at which per capita growth rate becomes negative.\n# [Allee effects are classified by the nature of density dependence at low densities. If the population shrinks for low densities, there is a strong Allee effect. If the proliferation rate is positive and increasing then there is a weak Allee effect. The null hypothesis is that proliferation rates are positive but decreasing at low densities. | upload.wikimedia.org/wikipedia/commons/7/7f/A///graph///showing///the///difference///between///strong///and///weak///Allee///effects.svg]\n\n# Mechanisms\nDue to its definition as the positive correlation between population density and average fitness, the mechanisms for which an Allee effect arises are therefore inherently tied to survival and reproduction.\nIn general, these Allee effect mechanisms arise from cooperation or facilitation among individuals in the species.\nExamples of such cooperative behaviors include better mate finding, environmental conditioning, and group defense against predators.\nAs these mechanisms are more-easily observable in the field, they tend to be more commonly associated with the Allee effect concept.\nNevertheless, mechanisms of Allee effect that are less conspicuous such as [inbreeding depression](https://bliptext.com/articles/inbreeding-depression) and [sex ratio](https://bliptext.com/articles/sex-ratio) bias should be considered as well.\n\n## Ecological mechanism\nAlthough numerous ecological mechanisms for Allee effects exist, the list of most commonly cited facilitative behaviors that contribute to Allee effects in the literature include: mate limitation, cooperative defense, cooperative feeding, and environmental conditioning.\nWhile these behaviors are classified in separate categories, they can overlap and tend to be context dependent (will operate only under certain conditions – for example, cooperative defense will only be useful when there are predators or competitors present).\n\n## Human induced\nClassic economic theory predicts that human exploitation of a population is unlikely to result in species extinction because the escalating costs to find the last few individuals will exceed the fixed price one achieves by selling the individuals on the market.\nHowever, when rare species are more desirable than common species, prices for rare species can exceed high harvest costs.\nThis phenomenon can create an \"anthropogenic\" Allee effect where rare species go extinct but common species are sustainably harvested.\nThe anthropogenic Allee effect has become a standard approach for conceptualizing the threat of economic markets on endangered species.\nHowever, the original theory was posited using a one dimensional analysis of a two dimensional model.\nIt turns out that a two dimensional analysis yields an Allee curve in human exploiter and biological population space and that this curve separating species destined to extinction vs persistence can be complicated.\nEven very high population sizes can potentially pass through the originally proposed Allee thresholds on predestined paths to extinction.\n\n## Genetic mechanisms\nDeclines in population size can result in a loss of genetic diversity, and owing to [genetic variation](https://bliptext.com/articles/genetic-diversity)'s role in the evolutionary potential of a species, this could in turn result in an observable Allee effect.\nAs a species' population becomes smaller, its gene pool will be reduced in size as well.\nOne possible outcome from this [genetic bottleneck](https://bliptext.com/articles/population-bottleneck) is a reduction in fitness of the species through the process of [genetic drift](https://bliptext.com/articles/genetic-drift), as well as [inbreeding depression](https://bliptext.com/articles/inbreeding-depression).\nThis overall fitness decrease of a species is caused by an accumulation of [deleterious mutations](https://bliptext.com/articles/mutation) throughout the population.\nGenetic variation within a species could range from beneficial to detrimental.\nNevertheless, in a smaller sized gene pool, there is a higher chance of a stochastic event in which deleterious alleles become fixed ([genetic drift](https://bliptext.com/articles/genetic-drift)).\nWhile evolutionary theory states that expressed deleterious alleles should be purged through natural selection, purging would be most efficient only at eliminating alleles that are highly detrimental or harmful.\nMildly deleterious alleles such as those that act later in life would be less likely to be removed by natural selection, and conversely, newly acquired beneficial mutations are more likely to be lost by random chance in smaller genetic pools than larger ones.\nAlthough the long-term population persistence of several species with low genetic variation has recently prompted debate on the generality of inbreeding depression, there are various empirical evidences for genetic Allee effects.\nOne such case was observed in the endangered [Florida panther](https://bliptext.com/articles/florida-panther) (Puma concolor coryi).\nThe Florida panther experienced a genetic bottleneck in the early 1990s where the population was reduced to ≈25 adult individuals.\nThis reduction in genetic diversity was correlated with defects that include lower sperm quality, abnormal testosterone levels, cowlicks, and kinked tails.\nIn response, a genetic rescue plan was put in motion and several female pumas from Texas were introduced into the Florida population.\nThis action quickly led to the reduction in the prevalence of the defects previously associated with inbreeding depression.\nAlthough the timescale for this inbreeding depression is larger than of those more immediate Allee effects, it has significant implications on the long-term persistence of a species.\n\n## Demographic stochasticity\nDemographic stochasticity refers to variability in population growth arising from sampling random births and deaths in a population of finite size.\nIn small populations, demographic stochasticity will decrease the population growth rate, causing an effect similar to the Allee effect, which will increase the risk of population extinction.\nWhether or not demographic stochasticity can be considered a part of Allee effect is somewhat contentious however.\nThe most current definition of Allee effect considers the correlation between population density and mean individual fitness.\nTherefore, random variation resulting from birth and death events would not be considered part of Allee effect as the increased risk of extinction is not a consequence of the changing fates of individuals within the population.\nMeanwhile, when demographic stochasticity results in fluctuations of sex ratios, it arguably reduces the mean individual fitness as population declines.\nFor example, a fluctuation in small population that causes a scarcity in one sex would in turn limit the access of mates for the opposite sex, decreasing the fitness of the individuals within the population.\nThis type of Allee effect will likely be more prevalent in [monogamous](https://bliptext.com/articles/monogamy) species than [polygynous](https://bliptext.com/articles/polygyny) species.\n\n# Effects on range-expanding populations\nDemographic and mathematical studies demonstrate that the existence of an Allee effect can reduce the speed of range expansion of a population and can even prevent biological invasions.\nRecent results based on spatio-temporal models show that the Allee effect can also promote genetic diversity in expanding populations.\nThese results counteract commonly held notions that the Allee effect possesses net adverse consequences.\nReducing the growth rate of the individuals ahead of the colonization front simultaneously reduces the speed of colonization and enables a diversity of genes coming from the core of the population to remain on the front.\nThe Allee effect also affects the spatial distribution of diversity.\nWhereas spatio-temporal models which do not include an Allee effect lead to a vertical pattern of genetic diversity (i.e., a strongly structured spatial distribution of genetic fractions), those including an Allee effect lead to a \"horizontal pattern\" of genetic diversity (i.e., an absence of genetic differentiation in space).\n\n# Mathematical models\nA simple mathematical example of an Allee effect is given by the cubic growth model.\nwhere the population has a negative growth rate for 0< N < A, and\na positive growth rate for A < N < K (assuming 0 < A < K).\nThis is a departure from the [logistic growth equation](https://bliptext.com/articles/logistic-function)\nwhere\nAfter dividing both sides of the equation by the population size N, in the logistic growth the left hand side of the equation represents the per capita population growth rate, which is dependent on the population size N, and decreases with increasing N throughout the entire range of population sizes.\nIn contrast, when there is an Allee effect the per-capita growth rate increases with increasing N over some range of population sizes [0, N].\nSpatio-temporal models can take Allee effect into account as well.\nA simple example is given by the reaction-diffusion model\nwhere\nWhen a population is made up of small sub-populations additional factors to the Allee effect arise.\nIf the sub-populations are subject to different environmental variations (i.e. separated enough that a disaster could occur at one sub-population site without affecting the other sub-populations) but still allow individuals to travel between sub-populations, then the individual sub-populations are more likely to go extinct than the total population.\nIn the case of a catastrophic event decreasing numbers at a sub-population, individuals from another sub-population site may be able to repopulate the area.\nIf all sub-populations are subject to the same environmental variations (i.e. if a disaster affected one, it would affect them all) then [fragmentation](https://bliptext.com/articles/population-fragmentation) of the population is detrimental to the population and increases extinction risk for the total population.\nIn this case, the species receives none of the benefits of a small sub-population (loss of the sub-population is not catastrophic to the species as a whole) and all of the disadvantages ([inbreeding](https://bliptext.com/articles/inbreeding) depression, loss of [genetic diversity](https://bliptext.com/articles/genetic-diversity) and increased vulnerability to environmental instability) and the population would survive better unfragmented.\n\n# Allee principles of aggregation\nClumping results due to individuals aggregating in response to: local habitat or landscape differences, daily and seasonal weather changes, reproductive processes, or as the result of social attractions.","current_revision":null,"created_by":"kACnuQmH5k9Nr5VNVEpVeg7XpvUmMctD","created_at":"2025-01-25T21:23:14.463Z","updated_at":"2025-01-25T21:23:14.463Z","search_vector":"'alle':1 'effect':2","search_content":" \n \n\n# \nThe **Allee effect** is a phenomenon in [biology](https://bliptext.com/articles/biology) characterized by a correlation between [population size](https://bliptext.com/articles/population-size) or density and the mean individual [fitness](https://bliptext.com/articles/fitness-biology) (often measured as [per capita](https://bliptext.com/articles/per-capita) [population growth rate](https://bliptext.com/articles/population-growth-rate)) of a population or species.\n\n# History and background\nAlthough the concept of Allee effect had no title at the time, it was first described in the 1930s by its namesake, [Warder Clyde Allee](https://bliptext.com/articles/warder-clyde-allee).\nThrough experimental studies, Allee was able to demonstrate that [goldfish](https://bliptext.com/articles/goldfish) have a greater survival rate when there are more individuals within the tank.\nThis led him to conclude that aggregation can improve the survival rate of individuals, and that cooperation may be crucial in the overall evolution of social structure.\nThe term \"Allee principle\" was introduced in the 1950s, a time when the field of ecology was heavily focused on the role of competition among and within species.\nThe classical view of population dynamics stated that due to competition for resources, a population will experience a reduced overall growth rate at higher density and increased growth rate at lower density.\nIn other words, individuals in a population would be better off when there are fewer individuals around due to a limited amount of resources (see [logistic growth](https://bliptext.com/articles/logistic-function)).\nHowever, the concept of the Allee effect introduced the idea that the reverse holds true when the [population density](https://bliptext.com/articles/population-density) is low.\nIndividuals within a species often require the assistance of another individual for more than simple reproductive reasons in order to persist.\nThe most obvious example of this is observed in animals that hunt for prey or defend against predators as a group.\n\n# Definition\nThe generally accepted definition of Allee effect is positive density dependence, or the positive correlation between population density and individual fitness.\nIt is sometimes referred to as \"undercrowding\" and it is analogous (or even considered synonymous by some) to \"[depensation](https://bliptext.com/articles/depensation)\" in the field of [fishery sciences](https://bliptext.com/articles/fishery-science).\nListed below are a few significant subcategories of the Allee effect used in the ecology literature.\n\n## Component vs. demographic Allee effects\nThe component Allee effect is the positive relationship between any measurable component of individual fitness and population density.\nThe demographic Allee effect is the positive relationship between the overall individual fitness and population density.\nThe distinction between the two terms lies on the scale of the Allee effect: the presence of a demographic Allee effect suggests the presence of at least one component Allee effect, while the presence of a component Allee effect does not necessarily result in a demographic Allee effect.\nFor example, cooperative hunting and the ability to more easily find mates, both influenced by population density, are component Allee effects, as they influence individual fitness of the population.\nAt low population density, these component Allee effects would add up to produce an overall demographic Allee effect (increased fitness with higher population density).\nWhen population density reaches a high number, negative density dependence often offsets the component Allee effects through resource competition, thus erasing the demographic Allee effect.\nAllee effects might occur even at high population density for some species.\n\n## Strong vs. weak Allee effects\nThe strong Allee effect is a demographic Allee effect with a critical population size or density.\nThe weak Allee effect is a demographic Allee effect without a critical population size or density.\nThe distinction between the two terms is based on whether or not the population in question exhibits a [critical population size or density](https://bliptext.com/articles/extinction-threshold).\nA population exhibiting a weak Allee effect will possess a reduced per capita growth rate (directly related to individual fitness of the population) at lower population density or size.\nHowever, even at this low population size or density, the population will always exhibit a positive per capita growth rate.\nMeanwhile, a population exhibiting a strong Allee effect will have a critical population size or density under which the population growth rate becomes negative.\nTherefore, when the population density or size hits a number below this threshold, the population will be destined for extinction without any further aid.\nA strong Allee effect is often easier to demonstrate empirically using time series data, as one can pinpoint the population size or density at which per capita growth rate becomes negative.\n# [Allee effects are classified by the nature of density dependence at low densities. If the population shrinks for low densities, there is a strong Allee effect. If the proliferation rate is positive and increasing then there is a weak Allee effect. The null hypothesis is that proliferation rates are positive but decreasing at low densities. | upload.wikimedia.org/wikipedia/commons/7/7f/A///graph///showing///the///difference///between///strong///and///weak///Allee///effects.svg]\n\n# Mechanisms\nDue to its definition as the positive correlation between population density and average fitness, the mechanisms for which an Allee effect arises are therefore inherently tied to survival and reproduction.\nIn general, these Allee effect mechanisms arise from cooperation or facilitation among individuals in the species.\nExamples of such cooperative behaviors include better mate finding, environmental conditioning, and group defense against predators.\nAs these mechanisms are more-easily observable in the field, they tend to be more commonly associated with the Allee effect concept.\nNevertheless, mechanisms of Allee effect that are less conspicuous such as [inbreeding depression](https://bliptext.com/articles/inbreeding-depression) and [sex ratio](https://bliptext.com/articles/sex-ratio) bias should be considered as well.\n\n## Ecological mechanism\nAlthough numerous ecological mechanisms for Allee effects exist, the list of most commonly cited facilitative behaviors that contribute to Allee effects in the literature include: mate limitation, cooperative defense, cooperative feeding, and environmental conditioning.\nWhile these behaviors are classified in separate categories, they can overlap and tend to be context dependent (will operate only under certain conditions – for example, cooperative defense will only be useful when there are predators or competitors present).\n\n## Human induced\nClassic economic theory predicts that human exploitation of a population is unlikely to result in species extinction because the escalating costs to find the last few individuals will exceed the fixed price one achieves by selling the individuals on the market.\nHowever, when rare species are more desirable than common species, prices for rare species can exceed high harvest costs.\nThis phenomenon can create an \"anthropogenic\" Allee effect where rare species go extinct but common species are sustainably harvested.\nThe anthropogenic Allee effect has become a standard approach for conceptualizing the threat of economic markets on endangered species.\nHowever, the original theory was posited using a one dimensional analysis of a two dimensional model.\nIt turns out that a two dimensional analysis yields an Allee curve in human exploiter and biological population space and that this curve separating species destined to extinction vs persistence can be complicated.\nEven very high population sizes can potentially pass through the originally proposed Allee thresholds on predestined paths to extinction.\n\n## Genetic mechanisms\nDeclines in population size can result in a loss of genetic diversity, and owing to [genetic variation](https://bliptext.com/articles/genetic-diversity)'s role in the evolutionary potential of a species, this could in turn result in an observable Allee effect.\nAs a species' population becomes smaller, its gene pool will be reduced in size as well.\nOne possible outcome from this [genetic bottleneck](https://bliptext.com/articles/population-bottleneck) is a reduction in fitness of the species through the process of [genetic drift](https://bliptext.com/articles/genetic-drift), as well as [inbreeding depression](https://bliptext.com/articles/inbreeding-depression).\nThis overall fitness decrease of a species is caused by an accumulation of [deleterious mutations](https://bliptext.com/articles/mutation) throughout the population.\nGenetic variation within a species could range from beneficial to detrimental.\nNevertheless, in a smaller sized gene pool, there is a higher chance of a stochastic event in which deleterious alleles become fixed ([genetic drift](https://bliptext.com/articles/genetic-drift)).\nWhile evolutionary theory states that expressed deleterious alleles should be purged through natural selection, purging would be most efficient only at eliminating alleles that are highly detrimental or harmful.\nMildly deleterious alleles such as those that act later in life would be less likely to be removed by natural selection, and conversely, newly acquired beneficial mutations are more likely to be lost by random chance in smaller genetic pools than larger ones.\nAlthough the long-term population persistence of several species with low genetic variation has recently prompted debate on the generality of inbreeding depression, there are various empirical evidences for genetic Allee effects.\nOne such case was observed in the endangered [Florida panther](https://bliptext.com/articles/florida-panther) (Puma concolor coryi).\nThe Florida panther experienced a genetic bottleneck in the early 1990s where the population was reduced to ≈25 adult individuals.\nThis reduction in genetic diversity was correlated with defects that include lower sperm quality, abnormal testosterone levels, cowlicks, and kinked tails.\nIn response, a genetic rescue plan was put in motion and several female pumas from Texas were introduced into the Florida population.\nThis action quickly led to the reduction in the prevalence of the defects previously associated with inbreeding depression.\nAlthough the timescale for this inbreeding depression is larger than of those more immediate Allee effects, it has significant implications on the long-term persistence of a species.\n\n## Demographic stochasticity\nDemographic stochasticity refers to variability in population growth arising from sampling random births and deaths in a population of finite size.\nIn small populations, demographic stochasticity will decrease the population growth rate, causing an effect similar to the Allee effect, which will increase the risk of population extinction.\nWhether or not demographic stochasticity can be considered a part of Allee effect is somewhat contentious however.\nThe most current definition of Allee effect considers the correlation between population density and mean individual fitness.\nTherefore, random variation resulting from birth and death events would not be considered part of Allee effect as the increased risk of extinction is not a consequence of the changing fates of individuals within the population.\nMeanwhile, when demographic stochasticity results in fluctuations of sex ratios, it arguably reduces the mean individual fitness as population declines.\nFor example, a fluctuation in small population that causes a scarcity in one sex would in turn limit the access of mates for the opposite sex, decreasing the fitness of the individuals within the population.\nThis type of Allee effect will likely be more prevalent in [monogamous](https://bliptext.com/articles/monogamy) species than [polygynous](https://bliptext.com/articles/polygyny) species.\n\n# Effects on range-expanding populations\nDemographic and mathematical studies demonstrate that the existence of an Allee effect can reduce the speed of range expansion of a population and can even prevent biological invasions.\nRecent results based on spatio-temporal models show that the Allee effect can also promote genetic diversity in expanding populations.\nThese results counteract commonly held notions that the Allee effect possesses net adverse consequences.\nReducing the growth rate of the individuals ahead of the colonization front simultaneously reduces the speed of colonization and enables a diversity of genes coming from the core of the population to remain on the front.\nThe Allee effect also affects the spatial distribution of diversity.\nWhereas spatio-temporal models which do not include an Allee effect lead to a vertical pattern of genetic diversity (i.e., a strongly structured spatial distribution of genetic fractions), those including an Allee effect lead to a \"horizontal pattern\" of genetic diversity (i.e., an absence of genetic differentiation in space).\n\n# Mathematical models\nA simple mathematical example of an Allee effect is given by the cubic growth model.\nwhere the population has a negative growth rate for 0< N < A, and\na positive growth rate for A < N < K (assuming 0 < A < K).\nThis is a departure from the [logistic growth equation](https://bliptext.com/articles/logistic-function)\nwhere\nAfter dividing both sides of the equation by the population size N, in the logistic growth the left hand side of the equation represents the per capita population growth rate, which is dependent on the population size N, and decreases with increasing N throughout the entire range of population sizes.\nIn contrast, when there is an Allee effect the per-capita growth rate increases with increasing N over some range of population sizes [0, N].\nSpatio-temporal models can take Allee effect into account as well.\nA simple example is given by the reaction-diffusion model\nwhere\nWhen a population is made up of small sub-populations additional factors to the Allee effect arise.\nIf the sub-populations are subject to different environmental variations (i.e. separated enough that a disaster could occur at one sub-population site without affecting the other sub-populations) but still allow individuals to travel between sub-populations, then the individual sub-populations are more likely to go extinct than the total population.\nIn the case of a catastrophic event decreasing numbers at a sub-population, individuals from another sub-population site may be able to repopulate the area.\nIf all sub-populations are subject to the same environmental variations (i.e. if a disaster affected one, it would affect them all) then [fragmentation](https://bliptext.com/articles/population-fragmentation) of the population is detrimental to the population and increases extinction risk for the total population.\nIn this case, the species receives none of the benefits of a small sub-population (loss of the sub-population is not catastrophic to the species as a whole) and all of the disadvantages ([inbreeding](https://bliptext.com/articles/inbreeding) depression, loss of [genetic diversity](https://bliptext.com/articles/genetic-diversity) and increased vulnerability to environmental instability) and the population would survive better unfragmented.\n\n# Allee principles of aggregation\nClumping results due to individuals aggregating in response to: local habitat or landscape differences, daily and seasonal weather changes, reproductive processes, or as the result of social attractions.","revisionCount":0},"hasMore":false,"nextCursor":null}