Chapter 4. Limiting Factors

We have seen that the Theory of Island Biogeography can explain in general terms how the immigration and extinction of species to (on) an island, whether a true island surrounded by water or a conceptual island surrounded by patches of differing communities, produces a dynamic equilibrium of species diversity on the island. In the remaining chapters, we shall explore in more detail the mechanisms by which natural communities maintain this dynamic equilibrium over short-term geologic time. Over long-term geologic time, mass extinctions occur and the mechanisms for the communities to maintain their equilibrium may change in ways that are beyond the scope of this text.

Law [hypothesis] of Tolerance:

Originally, the Law of the Minimum (Leibig, 1840) suggested that plant yield is always limited to that environmental factor which is in most limited supply, and supplying fertilizers to increase that factor will increase yield, but will cause another factor to become the limiting factor. This was later generalized as the Law of Tolerance (Shelford, 1913) which suggested that the presence or absence of any species is controlled by the range of values for the environmental factors under which the species can thrive.
    When plants are grown under laboratory (or greenhouse) conditions, their growth (and other measures of response to varying environmental conditions) tend to follow a bell-shaped (Normal distribution) physiological response curves, with mean, µ and variance, σ². There exists a set of environmental factor levels which are “optimal” for each species. In statistical terms, the optimal value is the mode (highest point) on the physiological response curve. On either side of the optimum point, there is an “optimum” range, in which the species response is near its optimal value.

Beyond the optimum range, there are sub-optimal ranges in which the species response curve drops off, so the species response is below its optimum, yet sufficient for the species to persist. Beyond the the sub-optimum ranges there are “marginal” ranges in which the species, although present, has much lower growth, reproduction, or any other estimate of response. Finally, beyond the marginal ranges, are the “lethal” ranges, where the species response is approximately zero. For the purposes of plant community ecology, we use population density as our estimate of species response. In this view, the population density will be highest within its optimum range, and will decline across the sub-optimum and marginal ranges. The species can be expected to become too rare locally to appear in the sample data in the lethal range. [In a graduate seminar class, my colleagues and I had a rather lengthy discussion of a concept of “quantative absence” (which we came up with ourselves) in which we imagined that the probability of seeing the species was too low to encounter individuals in the sample data, but remained above zero. We, of course, thought our concept had merit; our professor did not agree.] The terms ‘incidental’ and ‘accidental’ have been used to describe the occasional appearance of a single individual in sample data beyond its usual environmental tolerance range. Both terms imply that the incidental individual can be ignored, and that the population functions only between (B/T) the upper & lower limits of its environment tolerance range. I remain unconvinced that this is completely valid.

Shifts in tolerance:

A species tolerance range may shift under certain (unusual) conditions. Some species (mostly Animals) may exhibit seasonal changes in population response, often associated with the end of the reproductive season, or even as a migration from its summer range to its wintering range. Another event which is expected to drive a shift in tolerance range is a climatic change in the environment. For example, the sunspot cycle (approximately 11 years) because the solar ‘constant’ varies with sunspot number. There is slightly more solar energy at the top of the Earth's atmosphere during active sunspots (yes, sunspots are ‘dark’ because the sunlight is less strong in the visible wavelengths, but sunspots are much brighter in the extreme UV wavelengths. There have been numeroous references to a climate cycle associated with sunspot numbers. Using data for Peoria, IL, from 1856 to 1946, the precipitation exhibits a bimodal curve, with a dry climate, with 30.99 ± 3.78 inch annual precipitation, and a wet climate, with 35.75 ± 6.12 inch annual precipitation. These two climate regimes cycle roughly following the sunspot cycle.
    A species tolerance range can also be expected to shift if the species becomes adapted to a different climatic (or other environmental) regime. Adaptation occurs when there is a change in the population genetics of the species. Any trait (a trait is defined as “an inheritable characteristic of the population”) which affects the physiological response of the population can undergo adaptation if the relative frequencies of the alleles for the trait change. The two primary causes for such a change are (a) avoidance of competition by adaptation, or (b) a long-term change in the underlying environmental factor (usually climatic) causing a gradual change in the population gene pool, if the change in gene pool increases ‘fitness’ in the changing environment (where fitness is a population genetics term for probability of physiological success on the site; definition 3 of carrying capacity in the glossary). When we are being more rigorous in usage of our jargon, we would restate this to match definition 1 of carrying capacity in the glossary.

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