Skip to main content
Biology LibreTexts

7.2: Depicting population growth

  • Page ID
    25457
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    population growth.JPG
    Figure \(\PageIndex{1}\). Population growth viewed four ways. (A,B) Phenomenological. (C,D) Mechanistic.

    Figure \(\PageIndex{1}\) shows four approaches to depicting populations. While not all equally helpful, each has its use. Let’s start with phenomenological graphs for a single species: graphs that merely depict the population phenomena observed without attempting to describe the mechanisms causing the phenomena. Observations might come from successive bacterial plate counts or censuses of people or, in this case, successive insect censuses. Part A in the figure represents the whole population N over time, and is a starting place to view population change. Similarly, Part B represents the whole population’s rate of growth, dN/dt, over time, also phenomenological.

    A touch of biology is introduced in Part C by transforming the vertical axis to per-capita growth, 1/N dN/dt. This transformation recognizes the growth rate that an individual organism achieves in a unit of time—say in a year or a week—under prevailing conditions. There is a nominal biological limit on the number of offspring produced by an individual in each unit of time—one new bacterium per individual bacterium in twenty minutes, say, or four goslings per family of geese in a year, or one infant per human family each year. This subtle amount of biology can reveal patterns not evident in the phenomenological approaches of Parts A and B—that the number of surviving offspring per individual increases with time for orthologistic growth, does not change for exponential growth, and decreases with time for logistic growth.

    Finally, in Part D, a touch of ecology is added to the biology of Part C by considering, on the horizontal axis, interactions among organisms. This shows per-capita growth rate versus population density N, rather than versus time t. And it reveals even more clearly the ecological mechanism behind the phenomena and the distinct nature of the three kinds of population growth—orthologistic growth appears as a straight line slanted upward (as in Figure 6.2.1), exponential growth as a straight horizontal line, and logistic growth as a straight line slanted downward (as in Figure 6.3.1). Population density N acts a proxy for space, food, or other resources or limits.


    This page titled 7.2: Depicting population growth is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Clarence Lehman, Shelby Loberg, & Adam Clark (University of Minnesota Libraries Publishing) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.