Transcript Introduction – History of the subject

Population Biology - 03-55-324
Basic Information:
Professor: M. Weis
Office:
202 Biology
Contacts: phone: ext.2724
email: [email protected]
Office Hours: Tuesday & Thursday afternoons
~2-4PM
Lectures: Room 367 Dillon Hall
10 – 11:20 AM
Textbook: Rockwood, L.L. (2006). Introduction to
Population Ecology. Blackwell, Malden,
MA, USA. 339p
Prerequisites:
Exams:
Exam format:
Course web site:
03-55-210 Ecology, 03-55-211 Genetics
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.
combination of short answer questions
(matching for terminology, multiple
choice) and short essay questions
accessed via “Class Notes” at
www.uwindsor.ca
lecture 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
 f (N)
dt
We know the equation for exponential growth. This is a fit
from a Taylor series using only one term:
dN
 rN
dt
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
2
 a  bN  cN
dt
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.