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Beyond the limit: carrying capacity (K) and the holism/reductionism debate

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Abstract

As the debate about holism and reductionism in ecology has ebbed in the last twenty years, this article aims to reassess the traditional opposition between holistic and reductionist epistemologies during the development of population biology. The history of the notion of carrying capacity, the upper demographic limit of a viable population, will be analyzed as a paradigmatic case of the progressive imposition of reductionist strategies, from both an epistemological and a semantic point of view, since the middle of the twentieth century. Then, Richard Looijen’s reduction of the carrying capacity concept to the niche partitioning theory will be assessed and rebuked for both empirical and logical reasons. Eventually, some recent “weak” and “hard” emergent conceptualizations of the notion of carrying capacity, in logistic map models or in coupled niche-population systems, will be presented in order to show how they call into question the nature and the use of the notion of carrying capacity as a predefined ecological limit.

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Notes

  1. Since the founding book of this debate pertained to ecology and evolution (Smuts, 1926).

  2. According to Kirchhoff (this volume), despite the “superorganism” vocable, Clements’ position should not be considered as “superholistic” as he was not supporting a mutualistic theory of the organisation of communities, but rather a “control-hierarchical theory” that could today fit somewhere in the box of emergent organicism.

  3. Bergandi shows that the Odum brothers, despite many claims about the holistic nature of ecosystems, relied almost exclusively on reductionist methodologies like the measurement of energy and material flows. Concluding that ecosystems exhibit holistic properties from the study of their energy balance is more a rhetorical trick than a real epistemological argument; hence, the “crypto-reductionist” label that they are awarded by Bergandi. More recent approaches in ecosystem science, such as those of Bernard Patten (1982) based on the notion of environ or Sven Jørgensen (Jørgensen et al., 2011) on ecological systems analysis, claim a clear emergent-oriented agenda, which should be carefully assessed.

  4. More precisely I will show below that Lotka had an analogical approach to population models, less reductionist in its spirit than the mechanical approach of Volterra. With reference to contemporary discussions on group selection, it is notable that Elliott Sober and David S. Wilson (2003) as well as Edward O. Wilson and his colleagues (Nowak et al., 2010) have forcefully argued for group selection as a multilevel process, even dismissing Hamilton’s theory.

  5. Aside from passing comments in works dedicated to the history or philosophy of ecology, few works were specifically dedicated to the holism/reductionism debate applied to population ecology: cf. Mitman (1988), Looijen (1998) and Odenbaugh (2005).

  6. See below for a presentation and analysis of this concept in Allee’s work.

  7. Allee’s loose use of the notion of emergence (as he does not specify what exactly he means by it) is nonetheless very significant as an epistemological marker. A philosophically informed (and heated) debate about the opposition between emergent and collective (or aggregative) properties in population biology will only “emerge” during the 70s (Cf. Edson et al., 1981; Salt,, 1979) for instance).

  8. Lotka’s researches were strongly encouraged by Pearl.

  9. Lotka’s quote brings to mind what we call today the ecological footprint (Wackernagel and Rees, 1996) of humanity, which encompasses much more than the minimal conditions for the survival and reproduction of the human bodies, and which changes too rapidly to make any valuable prediction as to the value of the maximum size of the population. Indeed, the sheer number of human individuals on a particular territory does not say much of the underlying ecological mechanisms. More disturbing from an anthropological point of view, one must choose between two options: human populations obey ecological laws like any other ecological engineer species (apart from quantitative considerations) and hence are submitted to the traditional pattern of the carrying capacity; or there is a strange (cultural) feedback loop between our ecological knowledge and our ecological footprint that should make us exceptional from an ecological point of view.

  10. Leopold’s term for “Native American Peoples.”

  11. The flour is of organic nature of course, as it comes from wheat. Howewer, from an ecological point of view, it can be considered as “abiotic” because it does not depend on the activity of living organisms inside Chapman’s experiment bottles.Thus, its food value food can be reduced to its chemical composition: starch, proteins, etc.. On the contrary, eggs and puppae are living entities whose fate (being eaten or not, and at what stage) directly modify the structure and dynamics of the population.

  12. Malthus does not mention a “resistance” per se to the growth of a population. He uses the term “checks.”

  13. Equating m/n with K and replacing p by N, one easily finds the modern differential expression of the logistic equation.

  14. Original in French: “La loi de la population nous est inconnue, parce qu’on ignore la nature de la fonction qui sert de mesure aux obstacles, tant préventifs que destructifs, qui s’opposent à la multiplication indéfinie de l’espèce humaine.”

  15. Italics in the original: “si l’on suppose que ces obstacles croissent exactement dans la même proportion que la population surabondante, on obtient la solution complète du problème, sous le point de vue mathématique.”

  16. From an epistemological point of view, Delmas considers that Verhulst and Quételet were the forerunners of Alfred Lotka and Vito Volterra in setting the stage, almost a century earlier, for a similar epistemological opposition in population biology. Delmas follows Giorgio Israel’s analysis (1996) who argues that Volterra had a strictly mechanistic and deterministic view of the predator–prey dynamic that could univocally be represented in mathematical terms (the mechanical model in Israel’s terms). On the contrary, Lotka considered his mathematical model as a mere analogy, a free axiomatisation of the predator–prey relationship from a given perspective (the mathematical model).

  17. The general logistic formula of Richard’s curve is: \(l_{t} = L_{\infty } \left[ {1 + (\delta - 1)e^{{ - k(t - \gamma )}} } \right]^{{1/(1 - \delta )}}\).

  18. Italics are in original. Bold characters are mine.

  19. Eugene Odum (as well as his brother Howard) assumes that the oscillations (or pulses) of ecosystems due to internal or external constraints are a general feature of their dynamics. On the conrary, ecosystems in equilibrium should be understood as ecosystems maintaining a temporarily steady state.

  20. Looijen considers the Lotka-Volterra model of competition to be a “holistic” (i.e. emergent) theory because of its “phenomenological” nature: the model assumes that the populations of different species influence each other through competition or predation but does not say how they do so at the lowest level (that of the individual). For the sake of generality and simplicity, the Lotka-Volterra models use only population-level parameters, such as fertility rates or predation rates, for instance.

  21. A short semantic precision: B. Wimsatt’s epistemological notion of aggregativity refers to the fact that low level parts and properties of a system can be added independently; for Wimsatt, aggregativity’s antonym is “non-independence” under the system’s properties. For his part, W. C. Allee refers to aggregation as a descriptive property of animal populations that implies emergent effects. Aggregation’s antonym is “dispersion” or “scattering.”

  22. Suppose a rectangular forest habitat 20 × 10 km with a border effect represented by a 1 km strip all around the forest where a given bird species will not be able to feed because of the competition of non-forest species. Its effective habitat is thus 18 × 8 = 144 km2. Now suppose that the forest is reduced 10 times (4 × 5 km). The remaining effective habitat of the bird species is only 2 × 3 = 6 km2. The effective habitat or niche of the species is thus reduced by a factor 24. Even worse, if the reduced forest is now a 10 × 2 km rectangle, the effective habitat becomes 0 as the entire forest is subject to border effects.

  23. The debate is still open whether Gleason used randomness simply as a heuristic tool or as an explanatory feature of community assembly rules excluding interactions between species (Nicolson and McIntosh 2002).

  24. Here, I set aside the discussion about the neutral theory of biodiversity that eliminates the notion of niche (see Hubbell, 2001). Moreover, even in the neutral theory, competition for space between individuals of different species remains a major ecological factor.

  25. The idea that the carrying capacity of the human population is dependent on its action on the environment (positive at the beginning thanks to niche construction and ecological engineering—what can be called “downward facilitation”—then negative due to growing environmental constraints such as pollution) has been forcefully advocated for a long time by some ecologists (Ehrlich and Ehrlich 1970) and human ecologists (Boughey, 1968; Catton, 1980; Wisniewski, 1980), unfortunately with little effects on “mainstream” population biologists and demographers. Some models of Meadows’ Limits to growth report also considered a variable carrying capacity, but were not developed analytically.

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Acknowledgements

“I would like to thank Alice Everly for editing of the manuscript. Broder Breckling and the guest editors Thomas Potthast and Antoine Dussault were very valuable for their detailed comments that helped me to signifcantly improve this article”.

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Delord, J. Beyond the limit: carrying capacity (K) and the holism/reductionism debate. HPLS 43, 90 (2021). https://doi.org/10.1007/s40656-021-00440-4

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