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[2] [3] Subsequent work has derived the model under other assumptions such as scramble competition, [4] within-year resource limited competition [5] or even as the outcome of source-sink Malthusian patches linked by density-dependent dispersal. [6] [7] The Ricker model is a limiting case of the Hassell model [5] which takes the form
Density-dependent mortality can be overcompensating, undercompensating or exactly compensating. [ citation needed ] There also exists density-independent inhibition , where other factors such as weather or environmental conditions and disturbances may affect a population's carrying capacity .
The generally accepted definition of Allee effect is positive density dependence, or the positive correlation between population density and individual fitness. It is sometimes referred to as "undercrowding" and it is analogous (or even considered synonymous by some) to "depensation" in the field of fishery sciences.
Above this point, density dependent factors increasingly limit breeding until the population reaches carrying capacity. At this point, there are no surplus individuals to be harvested and yield drops to zero. The maximum sustainable yield is usually higher than the optimum sustainable yield and maximum economic yield.
In microeconomics, economies of density are cost savings resulting from spatial proximity of suppliers or providers. Typically higher population densities allow synergies in service provision leading to lower unit costs. [1] If large economies of density exist there is an incentive for firms to concentrate and agglomerate. [2]
Subsequent work has derived the model under other assumptions such as contest competition (Brännström & Sumpter 2005), within-year resource limited competition (Geritz & Kisdi 2004) or even as the outcome of a source-sink Malthusian patches linked by density-dependent dispersal (Bravo de la Parra et al. 2013).
If the dependent variable is referred to as an "explained variable" then the term "predictor variable" is preferred by some authors for the independent variable. [22] An example is provided by the analysis of trend in sea level by Woodworth (1987). Here the dependent variable (and variable of most interest) was the annual mean sea level at a ...
The causes of delayed density dependence vary in each situation. In lemmings, food supply and predation are the most important factors that lead to delayed density dependence. [3] Competition between life stages is another cause. In some species of moth the practice of egg cannibalism takes place where older moths eat eggs of their own species. [6]