Avenue effect

In population biology and ecology , one speaks of the alley effect when a higher population size and / or density of conspecifics has a positive influence on the fitness of an individual of the corresponding species. The effect is named by the influential American ecologist Eugene P. Odum after his compatriot Warder Clyde Allee , who first described it.

background

In the ecological sciences it is normal that it is always disadvantageous for an individual when it is surrounded by many other individuals of the same species. This is due to the fact that conspecifics are ecologically very similar and accordingly have similar needs and requirements for their habitat. Conspecifics need the same resources as e.g. B. Food or nesting places, if they are of the same sex, they are looking for the same mating partner. It says that individuals mutually competing make, in the case of competition from other dogs is called the intra-specific competition . In population ecology, the influence of competition is considered a key factor. It is represented mathematically by various models, the simplest and most common of which is the logistic equation .

The exceptions to this almost universally valid relationship are now described as the Allee effect. In natural or laboratory populations, it is not uncommon for the number of offspring of an individual not to decrease but to increase when it is surrounded by an increasing number of conspecifics. Various reasons have been identified for this, which are described below. Typically, this effect only occurs in small or very small populations and is reversed in the case of high population densities, in that the influence of competition prevails here again.

In mathematical population models, the influence of the Allee effect can be grasped with a term that is added to the normal population model as a correction term. The normal population model mainly takes into account the influence of competition and can usually depict reality quite well with medium and high population densities. The correction term, on the other hand, has an effect particularly at very low population densities. In uncorrected models, the average number of offspring of each individual, or, in other words, their fitness , decreases with increasing population density and finally reaches (at the carrying capacity threshold of the habitat, i.e. when the maximum viable population is reached) the minimum value necessary to maintain the population size. The population growth rate gradually decreases to zero and becomes even negative at even higher densities. This means that the density of conspecifics only, to a greater or lesser extent, has a negative effect on the growth rate (if one disregards the trivial case that at least one individual of each sex must be present in segregated species). If an Allee effect is active, this relationship is reversed in a certain parameter range. To emphasize the exceptional character, one speaks here of an "inverse" (i.e. reverse) density effect.

Strong and weak avenue effect

Clarifying Allees and Odum's approach, a group of British ecologists tried to define the effect more clearly. They differentiate between individual factors or components in the life of the individual being considered, each of which, viewed individually, has an advantage in the case of high or low population densities. For example, it can be beneficial for an ungulate like a gazelle to be surrounded by many conspecifics when it comes to the influence of predators (called "predators" in technical terms). Many gazelles can notice an approaching predator more easily, but if it strikes anyway, the probability is higher that it will hit another. At the same time, the high density of gazelles is also disadvantageous because everyone eats the same grass, which can now become scarce. A component avenue effect is now taken into account for those components for which an increased density has a positive effect. There are numerous components to the number of offspring as a whole, some of which have an avenue effect and some of which do not. In total, the effect of the components with an avenue effect can predominate. In this case, the number of offspring will also increase overall at a higher density. It is said that a demographic avenue effect is at work. A demographic avenue effect does not occur automatically if there are factors that favor a higher density, but only if these are stronger.

The components that can cause a demographic avenue effect can take on widely different values depending on the respective population density. It can be the case that at low densities the growth of the population is only slightly delayed or reduced compared to higher densities. If this is the case, one speaks of a “weak” avenue effect. The effects are far more dramatic if, from a certain, minimal, population threshold, growth drops to zero and finally to negative values. In this case one speaks of a “strong” avenue effect.

The effects of a strong avenue effect on a population can be dramatic and, intuitively, produce completely unexpected results. The lower threshold, at which growth just reaches zero, is an unstable equilibrium point (in contrast to the upper threshold with zero growth, the carrying capacity value, which is a stable equilibrium point). That means: A population cannot sustain itself permanently at this point. With every minimal increase it will inevitably (without further factors: up to the upper equilibrium point) increase. With every minimal decrease it becomes, with increasing acceleration, up to the population value zero, i. H. the extinction fall. This means: If a strong avenue effect is effective, the extinction of a population below a certain threshold value is inevitable, even if a certain remaining population is still alive for a while: its extinction is already sealed. Viewed from the other direction: A new immigration into a habitat, through natural colonization or through human displacement (see Neobiota ) by the species in question will fail if it occurs by too few individuals. Above the threshold, the same species will then be able to colonize the habitat successfully without anything else having changed. In the same way, infection by a parasite or pathogen may possibly be much more successful above a certain dose or threshold of the infection.

Factors

With careful observation of many populations, ecological research has found many cases in which the growth of the corresponding population has presumably been and is influenced by avenue effects. The causative reasons usually fall into one of the following categories:

lack of mating partners . This affects z. B. in marine species that fertilize themselves by releasing flagellated swarmers into the open water, or in plant species that are pollinated by the wind. Below a certain threshold, the probability of fertilization becomes very low.
Robber saturation (ger .: predator satiation). This effect occurs when the population size of a prey organism can change much faster than that of a predator, e.g. B. because the predator is much larger and therefore has a longer generation duration. If the density of prey increases, the relative influence of the (relatively few) predators decreases.
Spread (Engl. Dispersal). An avenue effect triggered by dispersal processes occurs when individuals from small populations are more likely to leave their habitat than individuals from large ones, or when immigrants prefer already populated habitats to empty ones. In both cases, the probability that an initially small start-up population will develop and establish itself decreases. (At the same time, however, the speciation rate in small local populations could even increase in the long term through population-supporting immigration). The effect has been proven especially in insect species.
Habitat change . If a species changes its habitat favorably for itself, all individuals benefit more and more as the density increases.
lack of cooperation . In the case of species that live together in groups or in breeding colonies, small peoples, colonies or herds are often generally disadvantaged compared to large ones because the individuals can share tasks (e.g. stand guard to warn of approaching predators). The same effect occurs with predators hunting in groups (e.g. African wild dog ).

Theoretically very plausible, but more difficult to prove directly, are further factors whose actual influence is possibly even greater:

Inbreeding depression . In very small populations, the number of alleles and the degree of heterozygosity necessarily decrease. As a result, the population loses plasticity when adapting to changing environmental conditions and becomes more susceptible to infections and parasites.
stochastic population effects . In very small populations, the proportion of males or females can drop sharply due to minor coincidences. This can lead to further adverse effects (e.g. greater nuisance to females or more violent territorial fights). In addition, small populations with a high fluctuation rate often die out by chance if their size drops to zero due to a random fluctuation.

Mathematical modeling

A simple model for a population in which a demographic alley effect is at work could look like this:

{\ displaystyle {\ frac {dN} {dt}} = rN \ left (1 - {\ frac {N} {K}} \ right) \ left ({\ frac {N} {K '}} - 1 \ right)}

Here N is the population size, t is the time, K is the capacity of the habitat, i.e. H. the carrying capacity value for the maximum stable population size, r the intrinsic growth rate of the population, K ' the critical lower threshold below which population growth becomes negative. (For the factor r see article Logistic equation ).

The equation up to the second term in brackets is simply a notation of the logistic equation. The growth rate of the population per capita is simply proportional to its biological growth rate r, which is assumed to be constant, without density-dependent factors. Due to the influence of competition, it reaches a positive value below the load-bearing capacity threshold K and becomes negative above it. A population that can be described in this way grows (per capita) the faster the smaller it is. With the minimum population size, the term in brackets approaches the value one, so it no longer has any effect. ${\ displaystyle {\ tfrac {dN} {dt}}}$

The second term in brackets summarizes the influence of the Allee effect. If the population size N becomes smaller than the lower threshold value K ', the term becomes negative. This reduces the population size. If the population is much larger than K ', K' has almost no effect at all.

literature

Warder Clyde Allee: Animal Aggregations. A study in General Sociology. University of Chicago Press, Chicago (Illinois) 1931. ( digitized version )
Franck Courchamp, Tim Clutton-Brock, Bryan Grenfell (1999) Inverse density dependence and the Allee effect. Trends in ecology and evolution 14 (10): 405-410.

Individual evidence

^ PA Stephens, WJ Sutherland, RP Freckleton (1999): What Is the Allee Effect? Oikos, vol. 87, no. 1: 185-190.
↑ on use in the artificial reintroduction of species by humans: Anne Deredec & Frank Courchamp (2007): Importance of the Allee effect on reintroductions. Ecoscience 14 (4): 440-451.
↑ Roland R. Regoes, Dieter Ebert, Sebastian Bonhoeffer (2002): Dose-dependent infection rates of parasites produce the Allee effect in epidemiology. Proceedings of the Royal Society London Series B269: 271-279. doi : 10.1098 / rspb.2001.1816
↑ an overview: Andrew M. Kramer, Brian Dennis, Andrew M. Liebhold, John M. Drake (2009): The evidence for Allee effects. Population Ecology 51: 341-354. doi : 10.1007 / s10144-009-0152-6
^ Robert D. Holt, Tiffany M. Knight, Michael Barfield (2004): Allee Effects, Immigration, and the Evolution of Species' Niches. American Naturalist 163 (2): 253-262.

[1] PA Stephens, WJ Sutherland, RP Freckleton (1999): What Is the Allee Effect? Oikos, vol. 87, no. 1: 185-190.

[2] use in the artificial reintroduction of species by humans: Anne Deredec & Frank Courchamp (2007): Importance of the Allee effect on reintroductions. Ecoscience 14 (4): 440-451.

[3] Roland R. Regoes, Dieter Ebert, Sebastian Bonhoeffer (2002): Dose-dependent infection rates of parasites produce the Allee effect in epidemiology. Proceedings of the Royal Society London Series B269: 271-279. doi : 10.1098 / rspb.2001.1816

[4] verview: Andrew M. Kramer, Brian Dennis, Andrew M. Liebhold, John M. Drake (2009): The evidence for Allee effects. Population Ecology 51: 341-354. doi : 10.1007 / s10144-009-0152-6

[5] Robert D. Holt, Tiffany M. Knight, Michael Barfield (2004): Allee Effects, Immigration, and the Evolution of Species' Niches. American Naturalist 163 (2): 253-262.