Population Biology - 03-55-324

Basic Information:Professor: M. WeisOffice: 202 BiologyContacts: phone: ext.2724

email: mweis@uwindsor.caOffice Hours: Tuesday & Thursday afternoons

~2-4PMLectures: Room 367 Dillon Hall

10 – 11:20 AMTextbook: Rockwood, L.L. (2006). Introduction to

Population Ecology. Blackwell, Malden, MA, USA. 339p

Prerequisites: 03-55-210 Ecology, 03-55-211 GeneticsExams: 2 midterms given (tentatively) on Oct. 13

and Nov. 17 - 30% of final grade each, final December 10, 12PM – 35% of final grade.5% of final grade for class participation, obvious improvement over the semester, and other factors that I deem valuable.

Exam format: combination of short answer questions (matching for terminology, multiple choice) and short essay questions

Course web site: accessed via “Class Notes” at www.uwindsor.calecture notes will be posted on the web site following each lecture.

Introduction to the subject

What is Ecology?

“The goal of ecology is to provide explanations that account for the occurrence of natural patterns as products of natural selection.” (Cody, 1974)

What is Population Biology?

The study of populations. (Duh!)

Better would be to modify the definition of ecology, substituting dynamics of species for ‘occurrence of natural patterns’ and adding at the end “and the forces that drive that selection.”

What is a population?

A population is a group of interbreeding individuals, i.e. members of a single species living in close enough proximity (i.e. are sympatric) to have a reasonable likelihood of mating with each other.

It would also be convenient if we were dealing with closed populations – those in which there is (theoretically) no immigration or emigration. Except for isolated island or mountaintop populations, that is unlikely.

We can retain this simplification if we slightly complicate the definition using one presented by Turchin (2002):

“[A population is] a group of individuals of the same species that live together in an area of sufficient size to permit normal dispersal and migration behaviour, and in which population changes are largely determined by birth and death processes.”

Ecology also usually makes a number of simplifying assumptions about the internal structure and dynamics of populations. Individuals clearly differ genetically, phenotypically and ecologically, but effects of this variation are only incorporated in recent evolutionary and ecological theory.

Since a part of this course will be about the tools of demography, an alternate definition presented by Lamont Cole is also useful:

A population is "a biological unit at the level of ecological integration where it is meaningful to speak of a birth rate, a death rate, a sex ratio, and an age structure in describing the properties of the unit".

As with most of biology, population biology is a dynamic subject, with developments in models and theory occurring rapidly.

To understand where the subject is likely to go, you also need to know where it ‘came from’. To introduce the subject, we’ll first look at its history…

Population biology effectively began when data on births and deaths was used to assess population dynamics.

That began when John Graunt used Bills of Mortality and Christenings collected during the time of the Black Plague to measure population growth in London. Graunt organized the data into Observations on the Bills of Mortality (1662).

Graunt found there were more female than male babies, and that females had longer average lifespans. He found that the population of London was doubling every 56 years (though without estimating the effect of migration from the countryside into London).

The summary for London for one week during 1662. Note some of the interesting causes of death during this week, and also that there were no cases of plague during the week.

Graunt also ‘discovered’ a basic concept of exponential growth with limits:

Based on religious estimates of origin at 3948 BC…

And his measured doubling time of ~60 years…

The population of London should have doubled 87.7 times by 1662…

And the population size should have been 1026 or 100 x 106/cm2…

Ridiculous! He recognized that doubling (exponential growth) could not continue indefinitely, though he neither named the growth pattern or clearly stated the limitation.

Those basic aspects of population growth were named and described by Sir Matthew Hale, who coined the term 'geometric' in 1677 to describe population growth. Sir Matthew was, at the time, chief justice of the King's Bench, i.e. he was the highest ranking lawyer in England.

Graunt's friend, William Petty, originated the concept of a K, or maximum population size in Another Essay in Political Arithmetic in 1683.

Petty went further, and estimated how large a population the earth could support. His mapping guessed at twice our modern estimates of habitable area, and suggested a K of 20 billion, about 2x the modern estimate.

And Petty went even further, making the first steps in calculating growth rate from population structure…

He determined birth rate from the number of fertile females and the frequency with which they gave birth. He even corrected the initial estimate for infant mortality, frequency of miscarriage, etc.

From all this he came to an estimate of potential doubling time of 10 years, but recognized that actual growth fell far short of that. In fact, he estimated doubling time as ~360 years, and suggested that meant doubling time had slowed (lengthened) since biblical times. That is, of course, what should occur with logistic growth. Petty’s reason, however, was that when populations became dense the world would enter a period of "wars and great slaughter".

The next major development waited almost a century, and is found in the writings of Thomas Malthus, particularly in An Essay on the Principle of Population (1798). Even before Malthus, the adjustment of carrying capacity to agricultural productivity was widely recognized.

What Malthus accomplished was a focusing of diffuse arguments into this:

"Through the animal and vegetable kingdoms nature has scattered the seeds of life abroad with a most profuse and liberal hand. She has been comparatively sparing in the room and nourishment necessary to rear them. The germs of existence contained in this spot of earth [could] fill millions of worlds in the course of a few thousand years. Necessity, that imperious, all pervading law of nature, restrains them within prescribed bounds. The race of plants and the race of animals shrink under this great restrictive law..."

What Malthus said (and Darwin recognized 50 years later) was that:

1) Populations increase geometrically, while the resources needed to support them increase arithmetically (by which he meant linearly). His version:

"...by great exertion the whole produce of the Island (sic Great Britain) might be increased every 25 years...the first of the propositions (i.e. the geometrical tendency of population growth) I considered as proved the moment the American increase was related, and the second (i.e. the arithmetic tendency of increase of food) as soon as it was annunciated."

and

2) mankind has two basic drives, for food and for sex.

Charles Darwin was the next great force in ecology. He synthesized ideas from Malthus (the concept that the human population was growing exponentially), Georges Cuvier (that biological change was gradual and evident in the fossil record), James Hutton (that layers of sedimentary rock were laid down sequentially over time), and Charles Lyell (the concept of uniformatarianism).

Darwin’s Theory of Evolution driven by natural selection was only published when Alfred Russell Wallace sent him a manuscript describing an effectively identical theory he had developed during studies of insects in both the Amazon Basin and later in Indonesia.

In population biology the basic mathematical model of population growth is not exponential, but logistic growth. The mathematical equation for logistic growth was first published by Pierre Verhulst in the middle 1800s.

At first the logistic was not accepted. However, early in the 20th century Raymond Pearl and L.J. Reed published a study of human population growth in the U.S., and fit their data to a logistic model ["On the rate of growth of the population of the United States since 1790 and its mathematical representation." (PNAS, USA [1920] 6:275-288)].

Raymond Pearl

The expansion of the basic logistic equation into the realm of species interactions and their effects on population growth is traceable to two mathematicians, Alfred J.Lotka, an American, and Vito Volterra, an Italian.

Before we get ahead of ourselves, it’s time to explore the basic equations used to describe population growth…

Data collected from the 16th century onward all indicated that growth rates decline with increasing density. That fact can be represented mathematically in a generalized equation:

dN

dtf N ( )

We know the equation for exponential growth. This is a fit from a Taylor series using only one term:

dN

dtrN

Is the ‘f ’in this equation negative, i.e. does it give decreasing growth with increasing density? No!

So, we apply Taylor’s theorem from calculus to complicate the equation. Taylor’s theorem states that we can fit any arbitrary function with some indefinite polynomial series. The next simplest model (beginning with the complete Taylor series) uses an equation:

dN

dta bN cN 2

I hope you don’t believe in spontaneous generation, so there should be 0 growth when N = 0. That sets the constant a to 0.

Guess what? The first term, bN, gives the exponential growth equation. The first two terms of the equation, bN + cN2, gives the logistic equation. In the logistic, b = r and c = -r/K.

In the next lecture we’ll go back to exponential growth and consider what kinds of organisms, life histories and growth patterns correspond most closely to exponential growth.