Allee effect

From the Allee effect is referred to in the population biology and ecology, if a higher population size and / or density of conspecifics has a positive influence on the fitness of an individual of the appropriate type. The effect is named by the influential American ecologist Eugene P. Odum after his compatriot Warder Clyde Allee, who has described it for the first time.

Background

In the ecological sciences, it is considered normal case, that it is always detrimental to an individual usually when it is surrounded by many other individuals of the same species. This is because conspecifics are ecologically very similar and therefore have similar needs and make demands on their habitat. Conspecifics need the same resources, such as Food or nesting sites, they are of the same gender, they are on the same mating partner. We say that the individuals do compete with each other, in the case of competition from conspecifics this is called intra -specific competition. In the population ecology of the effect of competition is considered to be a key factor. It is mathematically modeled by several models whose simplest and verbreitetstes the logistic equation.

As Allee effect you now describes the exceptions to this almost universal context. In natural or laboratory populations it not infrequently happens that the number of offspring of an individual does not decrease, but increases when it is surrounded by an increasing number of conspecifics. Various reasons have been identified, which are described below. Typically, this effect occurs only in small or very small populations and is reversed at high population densities in the opposite by here again outweighs the effect of competition.

In mathematical population models can be the influence of the Allee effect with a term hold, is added to the normal population model as a correction term. The normal population model focuses primarily on the impact of competition and can usually reflect the reality quite well at medium and high population densities. The correction term, however, affects especially at very low population densities. In uncorrected models, the average number of offspring of each individual drops, or, in other words, his fitness, with increasing population density decreases and eventually reaches ( as to the viability threshold of habitat, ie when the maximum viable population ) the energy required to keep the population size minimum value. The growth rate of the population thus decreases gradually to zero and at even higher densities even negative. This means that the density of conspecifics exclusively, more or less strong, negative effect on the growth rate effect (apart from the trivial case that in dioecious species, at least one individual of any gender should be there). If an Allee effect effectively, this relationship is reversed in a certain parameter range. To emphasize the exceptional nature, one speaks of an " inverse " (ie inverse ) density effect.

In a clarification of Allees and Odum's approach a group of British ecologists have attempted to define the effect more clearly. They are different individual factors or components in the life of the considered individual, considered individually cause an advantage at high or at low population densities. For example, it may be beneficial for a hoofed animal like a gazelle to be surrounded by many other dogs when it ( called in the jargon " predators " ) to study the influence of predators goes. Many gazelles may notice an approaching predators more easily, this still strikes, the probability is higher that it catches another. At the same time the high gazelle density but is also disadvantageous because all eat the same grass that may be just now. For those components for which there was an increased density has a positive effect, a component Allee effect will be taken into account. For the number of offspring as a whole, there are many components, some of which have an Allee effect, others do not. In sum, the effect of the components may predominate with an Allee effect. In this case, the number of offspring will grow at a higher overall density. We say that a demographic Allee effect is effective. A demographic Allee effect therefore occurs automatically when there is increased density of favorable factors, but only if they are stronger.

The components that can cause a demographic Allee effect, can take depending on the particular population density greatly different values. It may be that the growth of the population towards higher densities only delayed or decreased slightly at low density. If this is the case, one speaks of a "weak" Allee effect. By far more dramatic are the effects if the growth to zero and finally drops to negative values ​​from a certain, minimal population threshold. In this case one speaks of a 'strong' Allee effect.

The effects of a strong Allee effect on a population can be dramatic and cause intuitively unexpected results. The lower threshold value, wherein the growth reaches exactly zero, is an unstable equilibrium point (as opposed to the upper threshold of growth to zero, the load capacity value, it is a stable equilibrium point ). This means that a population can not rely on this point keep permanently. For each minimal improvement they will inevitably ( without further factors: to the upper equilibrium point ) increase. Each minimal decrease will, with ever greater acceleration, to population zero, ie extinction, fall. This means that if a strong Allee effect effectively, the extinction of a population below a certain threshold is inevitable, even though there are still some residual population for some time alive: their extinction is already sealed. From the other direction considered: A Neueinwanderung in a habitat through natural colonization or human abduction (see invasive species ) by the species concerned will fail unless it is carried by too few individuals. Above the threshold value in the same way is then able to colonize the successful habitat without otherwise something had changed. In the same way, may be much more successful at a certain dose or threshold of infection, the infection caused by a parasite or pathogen.

Factors

The ecological research has found in the careful observation of many populations of many cases in which the growth of the corresponding population has been affected by Allee effects and probably will. The causative reasons usually fall into one of the following categories:

  • Lack of breeding partners. This affects, for example, to in marine species from which cross-fertilize into the open waters by releasing flagellated swarmers, or plant species that are pollinated by the wind. Below a certain threshold, the probability of fertilization is very low.
  • " Predator saturation " ( engl: predator satiation ). This effect occurs even when the population size of a prey organism can change much faster than that of a robber, for example, because the predator is much larger and therefore has a longer generation time. Increases the prey density, the relative influence of the ( relatively few) robber is getting smaller.
  • Propagation (English dispersal ). A triggered by propagation processes Allee effect occurs when individuals from small populations more likely to leave their habitat as individuals from large, or if immigrants prefer already populated habitats compared to empty. In both cases, the likelihood of building up a first small founding population and established drops decreases. ( At the same time Artbildungsrate could but this in small local populations by supporting immigration population in the long term even increase ). The effect was mainly detected in insects.
  • Habitat change. Modifies a kind of habitat for them cheap, all individuals benefit with increasing density is always more of it.
  • Lack of cooperation. In social or living together in groups or breeding colonies kinds of small nations, colonies or herds are generally at a disadvantage compared to large often because individuals of labor can distribute tasks (eg standing guard to warn of approaching predators ). The same effect occurs when hunting in groups vertebrate predators (eg African wild dog).

In theory very plausible, but heavier directly detectable, are other factors whose actual influence may be even bigger:

  • Inbreeding depression. In very small populations, the number of alleles and the heterozygosity decreases necessarily. Thus, the population loses plasticity in adapting to changing environmental conditions and is more susceptible to infections and parasites.
  • Stochastic population effects. In very small populations may drop sharply due to low chances of the proportion of males or females. This can occur ( eg stronger harassment of females or violent turf wars ) other adverse effects. In addition, small populations die at a high turnover rate generally often randomly from when drops by a random fluctuation in their size to zero.

Mathematical modeling

A simple model for a population in which a demographic Allee effect is effective, could look like this:

Here N is the population size, t is time, K is the capacity of the environment, ie the carrying capacity value for the maximum stable population size, r is the intrinsic growth rate of the population, K ' the critical lower threshold below which the population growth will be negative. ( to a factor of r see Article Logistic equation).

The equation to the second bracket term is simply a notation of the logistic equation. The growth rate of population per capita is no density-dependent factors simply proportional to the biological growth rate r, which is assumed to be constant. Through the influence of the competition it reaches a positive value below the carrying capacity K threshold and above it is negative. A population that can be described as growing (per capita considered ) the faster, the smaller it is. At minimum population size, the bracket term approaches the value one, so it has no effect.

The second bracket term summarizes the influence of the Allee effect. Is the population size N is less than the lower threshold value K ', the expression is negative. Thus the population size decreases. If the population is much larger than K ', it affects K' as good as ever any more.

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