Overview of Population Ecology - Basic Models
General objectives and questions addressed
Historical trends
Key people
Key terms
Some example data sets
Basics of exponential and geometric growth
Basics of limited growth and density dependence
Equilibrium concepts and stability
Survivorship and life histories
What regulates populations?
Survey of recent papers - topic coverage
Example paper - Akcakaya, H. R. 1992. Population cycles of mammals:
Evidence for a ratio-dependent predation hypothesis. Ecol. Monog. 62:
119-142.
General objectives of population ecology:
Deterrmine the relative impact of alternative factors (biotic, abiotic)
on the changes in size of populations.
Determine conditions under which populations maintain relatively
constant numbers of individuals - why are some populations highly
variable in size and others not
What are the relative effects of alternative life history patterns on
population dynamics
What are the effects of population structure (age, size, space, etc. )
on population dynamics
Provide basis for linking population dynamics of several species
Main historical trends:
A variety of paradigms have been described in the historical
development of population biology (den Boer and Reddingius, and see S.
Kingsland for alternative views):
Mechanistic view (Lotka, Volterra) - populations as differential
equations - treating them as made up of many, many individuals, each
with small effect on the aggregate - a mechanistic view that grew out
of physical models. In this view, one can still break down populations
(as Lotka did extensively for age structure) but maintain the same
assumptions about large sizes within each age group.
Regulation or engineering view (Nicholson) - population density was in
balance, e.g. adjusted to prevailing conditions, positing a
"controlling factor" or "density geoverning factor" (now thought of as
a density dependent factor) which produced a balance. There is an
inherent equilibrium, with a stabilizing feedback driving population
densities back to this equilibrium following perturbations - a
cybernetic view, in which population regulation is taken for granted.
Systems view (von Bertalanffy) - there are general principles, laws and
models that apply to systems with many components, irrespective of the
details of these components, which are applicable to the hierarchical
levels in ecology. These laws are not necessarily derivable from a
reductionist view.
Natural History view (Andrewartha and Birch) - population dynamics is
the result of a complex interplay between the properties of the
organisms themselves and the variables in the environment. A view of
populations made up of many small interaction groups, with which most
individauls interact across their lifespan. So distribution and
abundance determined by variations in localized environmental factors
which determine the organisms growth and survival in these localized
groups.
An Alternative (not in den Boer and Reddingius) Individual-Based View
- here we take the reductionist view that the properties of
populations can be derived from the complex of interactions between
individuals, environment, and other species. Thus it is not just
localized interaction groups which determine population dynamics, but
the entire complex of individual characteristics which vary through the
population. It is a view in which it is possible for rare individuals
to have significant impacts on population-level phenomena.
People (a few):
H. G. Andrewartha - density independent view of population
regulation
L. C. Birch - density independent view of population regulation
L. C. Cole - population cycles and randomness
G. F. Gause - early experiments for lab population growth
(Paramecia)
G. E. Hutchinson - Limnological examples, Diversity issues
P. H. Leslie - matrix age structured models
A. J. Lotka - mechanical view of populations, age structure
results
A. J. Nicholson - competition, classic blowflies population
data
M. Verhulst - logistic equation (also called Verhulst-Pearl,
but Verhulst was first)
V. Volterra - Harvesting populations - 2 species predator prey
models
L. Von Bertalanffy - systems view of populations
Some references:
Papers to read:
Akcakaya, H. R. 1992. Population cycles of mammals: Evidence for a
ratio-dependent predation hypothesis. Ecol. Monog. 62: 119-142.
Chitty, D. 1960. Population processes in the vole and their relevance
to general theory. Can. J. Zol. 38:99-113.
Ehrlich, P. R. and L. C. Birch. 1967. The "balance of nature" and
"population control". Am. Nat. 101:97-107
Hallam, T. G. 1986. Population Dynamics in a homogeneous environment.
Biomathematics 17:61-94.
Krebs, C. J., M. S. Gaines, B. L. Keller, J. H. Myers and R. H.
Tamarin. 1973. Population cycles in small rodents. Science 179:
35-41.
References:
Berryman, A. A. 1981. Population Systems: A General Introduction.
Plenum, NY.
Den Boer, P. J. and J. Reddingius. 1996. Regulation and Stabilization
Paradigms in Population Ecology. Chapman and Hall, London.
Gotelli, N. J. 1995. A Primer of Ecology. Sinauer, Sunderland, MA
Gutierrez, A. P. 1996. Applied Population Ecology: A Supply-Demand
Approach. Wiley, NY.
Hastings, A. 1997. Population Biology: Concepts and Models. Springer,
NY.
Hutchinson, G. E. 1978. An Introduction to Population Ecology. Yale,
New Haven.
Kingsland, S. E. 1985. Modeling Nature: Episodes in the History of
Population Ecology. Univ. of Chicago, Chicago.
Roughgarden, J. 1998. A Primer of Theoretical Ecology. Prentice Hall,
NY.
Tanner, J. T. 1978. A Guide to the Study of Animal Populations. Univ.
of Tennessee, Knoxville.
Wilson, E. O. and W. H. Bossert. 1971. A Primer of Population Biology.
Sinauer, Sunderland, MA.
Some Terms:
Allee effect - negative growth rate of a population at low population
densities
Carrying capacity - population density at which the population per
capita growth rate is zero
Density dependence - in general, any limitation on a process due to the
density of the population, so a density dependent growth rate would
correspond to the case in which per capita growth rate was a function
of density
Density independence - in general, the process of concern is not
affected by population density, so a density independent grwoth rate
would correspond to the case in which per capita growth rate was not a
function of density.
Equilibrium - situation in which the growth rate = 0
Functional response - the rate of prey capture per predator as a
function of prey density
Life history - the pattern of births and deaths for a population
Linearization - approximating a general non-linear function in a small
region by a linear function
Numerical response - the per capita growth rate of the predator
population as a function of prey density
Resilience - time constant for return to equilibrium following a
perturbation
Stable equilibrium (Local asymptotic stability) - following a small
perturbation in population density from an equilibrium, the population
moves back towrads equilibrium density.
Exponential growth
Unlimited growth - during early phases of epidemic, introduction to a
new habitat, per capita growth rate is constant
Geometric growth - discrete time analog of exponential growth
Logistic growth
Simplest density dependent growth in which per capita growth rate is
linear in population density
Appropriate discrete analog is not what is typically called the
discrete logistic, but rather is the hyperbolic form
x(n+1)=aX(n)/(b+x(n))
Discrete logistic x(n+1)= rx(n) (1-x(n)) exhibits diverse dynamical
characteristics not possible in continuous logistic
Equilibrium concepts
Locally stable equilibrium is only one possibility. Also have global
stability (approach the equilibrium from any initial condition),
dynamic stability (limit cycles), resilience, persistence, structural
stability
Population regulation
Major controversies arose between those with a view in which nature is
in balance (e.g. there are density dependent regulating factors) and
those with a view that it is density independent factors which govern
population regulation. Thus some view populations as persistyent, and
others view them as winking in and out on a regular basis. This was
also driven by different views of what was trying to be explained:
balance or fluctuations in populations. Much of this arose before there
was a large theoretical literature on spatial effects on populations,
in particular the effect of underlying spatial heterogeneity in
habitats and the effect on population persistence over larger spatial
extents (the metapopulation view)
Topics from 1990's search on population dynamics, and animal population
dynamics in 4 ecology journals: Summary:
Reintroduction 1
Food effects 3
Spatial effects 5
Soil populations 1
Landscape effects 2
Cannibalism 1
Social effects 1
Models and theory 4
Clonal aspects 1
Mark-recapture 2
Immigration effects 1
Density dependence 1
Total: 22