A great myth of ecological theory is that the logistic equation is a suitable model for describing the growth of populations. In fact, there is little empirical evidence in support of this hypothesis. I have replotted the few time-series counts or estimates of population size that I have found in the literature for which logistic curves were “fitted.” Plots between near minimum size and maximum size, between which logistic growth should occur, did not resemble S-shaped curves at all. Populations essentially grew continuously upward (J-shaped) until the maximum size was reached, after which the populations fluctuated between an upper and lower boundary or declined. I thought this should be of interest to theoretical population ecologists, so I wrote a paper for publication, and it was rejected. So I ask - How do we know that population growth in any species is logistic?
To understand my thinking on this and other population biology questions, I have to provide a “crash course” about the practice of science in general because my colleagues and I differ considerably in what we accept as our background knowledge. For example, I take physics to be my model of what a scientific theory should be. This is contrary to the starting point of many of my colleagues who contend that the biological world is just too complex, especially when compared with the physical world, to accommodate universal laws from which predictions may be deduced.
Physics is characterized by laws and predictive theory. Laws are statements that are assumed to be universally true. Predictions are statements that are logically deduced from the laws and the initial conditions of the experiment or situation. The most famous and probably the easiest to understand is Newton’s Theory of Motion. Newton proposed three laws, including the First Law of motion, which states, “Every body continues in its state of rest, or of uniform motion in a right [straight] line, unless it is compelled to change that state by forces impressed upon it”. This law is an invention of Newton’s mind. There is no observation in the universe that even suggests that a body in motion should remain in motion forever until acted upon by an outside force. Newton had no justification for asserting that the First Law was universally true. He stated it as an axiom—a statement that he assumed to be universally true—of his theory. Nevertheless, with it, he worked out the “Moon problem”. Using his laws and his knowledge of the diameter and period of the Moon’s orbit (the initial conditions), he accurately predicted the acceleration of a body near the Earth’s surface, which could be measured. He and other physicists used his laws and other sets of initial conditions to predict or otherwise explain a wide range of physical phenomena, such as the shape of the earth (i.e. flattened at its poles), the daily cycle of two high and two low oceanic tides, the precession of the equinoxes, the orbits of comets, the position of an unknown planet, and much more.
Ecologists and evolutionary biologists (EEBs) do not have laws and predictive theory, and even argue that argue that “laws” can play no role in theoretical biology. Why should EEBs and physicists have such different approaches toward theoretical science? I think it is a matter of their training. As Dorothy Sayer’s Lord Peter Wimsey put it: “But you see, I can believe a thing without understanding it. It’s all a matter of training.” If this is so, we may ask, How are biologists trained regarding “theory.” The answer is given at the beginning of almost every biology textbook in a section often entitled, “The scientific method.” I happen to have at hand an old text, the second edition of Biological Science Keeton (1972) starts “Science cannot deal with anything that cannot be observed.” I wonder what Keeton meant by “observed.” As far as I know, protons, electrons, strong forces, weak forces, inertia, gravitation, and magnetism cannot be directly observed. What we observe are the effects of these hypothetical particles and processes, which is induction.
Einstein wrote “The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.” For reasons that I cannot explain, I think that I have always subscribed to that view. It seemed natural that I should be able to deduce my current observations from some sort of overriding principles. It seemed trivial to me to “deduce” that the next insect I saw would have three pairs of legs because all the insects I have seen so far have had three pairs of legs. So, I formalized this approach to explanation with the question, “What statements can I make from which I can deduce my data?” My theory of evolution, thus, starts with three laws (Murray, Population Dynamics: Alternative Models, 1979; Proc. 22 Int. Ornithol. Congr., 1999; Oikos, 2000; Biol. Rev., 2001). The deductions that I made from these three laws and appropriate initial conditions include (1) that the size of clutches of birds should increase with increasing latitude, (2) that clutch size should increase, not decrease, with increasing mortality of eggs and chicks in the nest (contrary to the conventional wisdom), and (3) that clutch size should become smaller as life expectancy gets longer. All of these predictions seem consistent with the empirical facts. Furthermore, from these same ideas, I predicted that the sex ratio of the polyandrous Spotted Sandpiper Actitis macularia should be >1, when Lew Oring, world’s authority on this species, believed that it was one. Also, using these ideas, Jehl and Murray (1986,Current Ornithology 3:1-86) explained the reversed sexual size dimorphism found in birds. My theory of evolution seems to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms (only three compared with the myriad of ad hoc hypotheses currently required to explain life history traits). Yet, my colleagues have completely ignored my theory: “What are they thinking?”; I wonder.
This book is about my speculations regarding what my colleagues have been thinking. Our approaches toward scientific research are strikingly different. The explanations of ecologists and evolutionary biologists are essentially ad hoc hypotheses, whereas my explanations take the form of deductive-nomological theories. I have been interested in developing a Newtonian-like universal theory, characterized by a small number of laws from which the many facts of biological diversity can be deduced. That sounds extraordinarily ambitious, but that is the goal I have set for myself.