Estudiante

20

METAPOPULATION DYNAMICS

Objectives
• Determine how extinction and colonization parameters
influence metapopulation dynamics.
• Determine how the number of patches in a system affects
the probability of local extinction and probability of regional
extinction.
• Compare “propagule rain” versus “internal colonization”
metapopulation dynamics.
• Evaluate how the “rescue effect”affects metapopulation
dynamics.

INTRODUCTION
Can you think of any species where the entire population is situated within one
patch, where all individuals potentially interact with each other? You will probably be hard pressed to come up with more than a few examples. Most species
have distributions that are discontinuous at some spatial scale. In some species,
subdivided populations may belinked to each other when individuals disperse
from one location to another. For example, butterflies may progress from egg to
larvae to pupa to adult on one patch, then disperse to other patches in search of
mates, linking the population on one patch to a population on another. This “population of populations” is often called a metapopulation, and in this exercise we
will explore the dynamics ofsuch interacting systems.
Metapopulation theory was first formalized by Richard Levins in 1969 (Levins
1969, 1970). In Levins’ model, a metapopulation exists in a network of habitat
patches, some occupied and some unoccupied by subpopulations of individuals.
The dynamics of metapopulations can be explored by examining patch occupancy
patterns over time. In the left-hand side of Figure 1, the100 squares represent 100
patches in a metapopulation at time t. The right-hand side of the figure shows
the pattern of patch occupancy at time t + 1.
In the traditional metapopulation model (Levins 1970), each subpopulation has
a finite lifetime and each subpopulation has the same probability of extinction. Additionally, all unoccupied patches have the same probability of being colonized. Atequilibrium, the proportion of patches that are occupied remains constant, although
the pattern of occupancy continually shifts as some subpopulations suffer extinction

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Exercise 20

Patches at time t

Patches at time t + 1

Figure 1 At time t, occupied habitat patches are represented with filled
circles; empty squares represent currently unoccupied patches. At time t +
1,some of the patches that were occupied in time t are vacant (open circles), some patches that were vacant at time t are now occupied (gray circles), and some patches maintain their “occupancy status” from time t to
time t + 1 (filled circles).

followed by recolonization. This is sometimes referred to as the “winking” nature of
metapopulations, as newly colonized patches “wink in” and extirpatedpatches “wink
out.” Thus, the classic metapopulation model (sensu Levins 1970) is a “presence-absence”
model that examines whether a population is present or absent on a given patch over time,
how presence and absence changes over time, and how the entire metapopulation system
can persist. In other words, metapopulation models explain and predict the distribution
of occupied and unoccupiedhabitat patches, factors that affect dispersal between patches,
and the persistence of the greater metapopulation (Hanski and Gilpin 1997).

Metapopulation Dynamics: Colonization and Extinction
Let’s begin our exploration of metapopulation dynamics by defining extinction and
colonization mathematically. Patches that are currently occupied in the system have a
probability of going extinct, pe,and a probability of persistence, 1 – pe. Patches that are
currently empty in the system have a probability of being recolonized, pi, and a probability of remaining vacant, 1 – pi. Since both pe and pi are probabilities, their values
range between 0 and 1.
Metapopulation dynamics focus on the occupancy patterns of patches over time. We
can think about the fate of a given patch over the...