4. The third principle, competition
Alan Berryman
Monday, 11 May 2009 17:11 UTC
When the third principle is in operation, competitive interactions between organisms in a population dominate the R-function; i.e., aggressive social behavior such as dominance hierarchies and territoriality (i.e., contest competition), and the random negative interaction between individuals using the same resources or trying to escape from their enemies (often called scramble competition). Thus, R decreases directly with population density and, if it crosses R=0, then an equilibrium is formed which is stable, because when R is above it the population declines and when R is below it grows.
Natural populations are often seen to fluctuate in the vicinity of competitive equilibria in systems which vary considerably with time (c.f., with cooperative equilibria). For this reason, competition seems to dominate ecological research and theory. Most textbooks deal with it in great detail, while cooperation is hardly mentioned. Competition can be traced back at least to Thomas Malthus’ notion of a “struggle for existence” (Malthus 1798), an idea that subsequently became one of the cornerstones of Charles Darwin’s theory of evolution. It is covered in detail by all major textbooks and monographs. Pearl (1924) and Lotka (1925) considered it to be a fundamental “law of population dynamics” while others think of it as one of the founding principles of ecology (Allee and Park 1939, Berryman 1999, Turchin 2003). Despite this, some ecologists still question the value and/or validity of the concept (Andrewartha and Birch 1984, Murray 1999, White 2001). There has also been considerable confusion about the meaning (definition) of the word “competition”. As stated above, however, it is merely a descriptive term for any ecological interaction between individuals of the same species that causes a reduction in per-capita reproduction and/or survival as their numbers increase. Although some may find this definition a bit too broad, it is at least unambiguous at the operational level.
The competitive process can be defined as follows:
Competition operates whenever interactions between individuals, whether purposeful or accidental, give rise to an inverse (negative) effect of population density on the average per-capita rate of change, the maximum being set by the genetics of the species and environmental conditions.
The two principles (cooperation and competition) occur between members of a species. They are therefore internal (intrinsic) to the species in question. Because of this they operate quickly, within the generation span of the species, and therefore are usually regarded as first order regulatory processes. Our next topic, the fourth principle, will deal with negative feedback between different species (e.g., predators and their prey), and this feedback occurs with a longer time frame.
Note: The two principles (cooperation and competition) are similar in practical terms to the laws of increasing and diminishing returns in economics.
Allee, W. C. and Park, T. 1939. Concerning ecological principles. Science 2304: 166-169.
Andrewartha, H. G. and Birch, L. C. 1984. The ecological web: more on the distribution and abundance of animals. Univ. Chicago Press.
Berryman, A. A. 1999. Principles of population dynamics and their application. Stanley Thornes (Garland Science, Taylor & Francis).
Lotka, A. J. 1925. Elements of physical biology, Williams and Wilkins. Reprinted as Elements of mathematical biology, Dover (1956).
Malthus, T. R. 1789. An essay on the principle of population. Johnson, London.
Murray, B. G. 1999. Can the population regulation controversy be buried and forgotten? Oikos 84: 148-152.
Pearl, R. 1924. Studies in human biology. Williams and Wilkins.
Royama, T. 1992. Analytical Population Dynamics. Chapman & Hall.
Turchin, P. 2003. Complex Population Dynamics: A Theoretical/Empirical Synthesis. Princeton University Press.
White, T. C. R. 2001. Opposing paradigms: regulation or limitation of populations? Oikos 93: 148-152.
Updated 30 May 2009 15:40 UTC
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Replies
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As for Berryman’s first and second principle – I must also here for the third – make the point that the traditional notion that R is a monotonic declining function of density under intra specific competition is only true for the special – non natural – case where there are no heritable variation between the individuals in the population. With heritable variation present – the traditional monotonic density regulation function is evolving over time and R is no longer a monotonic declining function of N. In fact – in many cases – R may take both positive and negative values (increasing or declining population) at any given N and the resulting population dynamics is likely damped cyclic (known as inertial dynamics) instead of monotonic.
One easy way to get a feel for inertial dynamics is to think of a traditional density regulation function R_t = R(max) f (N_t), but now with R(max) evolving so that R_t = R_t(max) f(N_t) with R(max) declining whenever the population is above its equilibrium level, and R(max) increasing whenever the population is below the equilibrium density. And as the evolving R(max) is responding with a time-delay of one generation (genetic and epigenetic evolutionary changes occur between generations) there is now both a direct and a one generation delayed form of density dependence and the dynamics becomes inherently cyclic, probably damped cyclic in most natural cases.
For more detailed treatments of inertial dynamics see, e.g.,
Ginzburg, L. R. and Colyvan, M. 2004. Ecological orbits. How planets move and populations grow. Oxford University Press, Oxford.
Witting, L. 2000. Population cycles caused by selection by density dependent competitive interactions. Bull. Math. Biol., 62: 1109-1136
Witting, L. 2002. Evolutionary dynamics of exploited populations selected by density dependent competitive interactions. Ecological Modelling 157: 51-68
Witting, L. 2003. Reconstructing the population dynamics of eastern Pacific gray whales over the past 150 to 400 years. J. Cetacean Res. Manag., 5: 45-54
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To Lars: I’m glad you got into this debate. I entirely agree with your analysis. Sidney Holt
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I’m glad you got into this debate, Lars. I think this matter is veryimportant. I agree with your analysis and think this forum has to get away from simplistic assumptions about exponential growth and the logistic.
I also do feel it is a mistake to exclude individual growth from the basic principles. For all sorts of reasons. Biomass matters as much as numbers in population dynamics. It is also necessary to pay proper attention to the structure of the population, not merely its numerical size – especially age/size and sex. A one-dimensional population dynamics theory that take account only of numbers is, I think, useless. And genetic history must be taken properly into account – possibly in matters also other than the issues you have dealt with so elegantly. Sidney Holt
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