Biology Reference
In-Depth Information
CHAPTER
7
Predicting Population
Growth: Modeling with
Projection Matrices
Janet Steven and James Kirkwood
Department of Biology, Sweet Briar College, Sweet Briar, VA 24595, USA
Department of Mathematical Sciences, Sweet Briar College, Sweet Briar, VA 24595, USA
7.1 INTRODUCTION
Biologists studying an organism in its natural environment often start with a descrip-
tion of a population's size and demographic structure. How many individuals are in
the population? What major life stages does each individual pass through? Howmany
offspring are generated?Once this initial description is complete, biologists frequently
move on to examine the causes and consequences of the observed size and structure.
Is the population shrinking or growing? Which demographic stage experiences the
greatest mortality? How does survival at a particular stage affect overall growth?
Matrix population models that utilize projection matrices function to bridge the gap
between population structure and population dynamics by providing a mathematical
framework that both summarizes and models a population [ 1 ].
A matrix-based model can incorporate the different stages an organism goes
through during its life, and then predict both the overall growth of the population
and the distribution of individuals across these life stages. A projection matrix gener-
ated from data collected in a natural population models transitions between stages for
a given time interval and allows us to predict how many individuals will be in each
stage at any point in the future, assuming that transition probabilities and reproduction
rates do not change.
Projectionmatrices are widely used in ecology and conservation biology to address
both theoretical and practical questions. They can reveal the life stages that have the
greatest influence on population growth and are therefore potentially shaped most
strongly by natural selection [ 2 ]. They have been used to examine the impact of her-
bivory on plant populations [ 3 , 4 ] and the relative importance of alternative mating
systems [ 5 ]. But perhaps their greatest impact is in providing quantitative predictions
for conservation management decisions; because projection matrices can use the cur-
rent structure and size of a population to predict future growth, they are often used
to assess extinction risk of the population [ 6 , 7 ]. Moreover, because the models can
inform the relative importance of each life stage to growth, they are used in guiding
decisions about hunting limits and choosing key life stages to target during conserva-
tion [ 8 ]. Projection matrices in combination with some knowledge of available habitat
 
 
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