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In-Depth Information
small lake. The questions to be answered by the model are: If zebra mussels are in-
troduced into the lake, how will the population grow over time? What are the critical
parameters that influence the size of the population? How significant an impact will
the equilibrium mussel population have on the lake's ecosystem?
In order to enhance the understanding of the model, we split it up into three
parts, or modules, that are interrelated and together comprise the critical dynamic
aspects of the questions being addressed. Partitioning a model into individual, easily
comprehensible parts is always helpful in making the model structure transparent.
In the model of the zebra mussel, the growth module captures the growth processes
of the zebra mussel population. The sustainability module determines the long-term,
sustainable level of the population by incorporating some key physical parameters.
The filtration module yields a relative indication of the impact of the population on
the lake by computing the frequency with which the total population filters the entire
water volume of the lake. An explanation of the structure of each of these modules
and the data and assumptions that were used to construct them follows.
The growth module in Figure 10.1 is made up of four population cohorts (one
juvenile and three adult). The average life span of a zebra mussel appears to vary
between populations in different areas. We chose a life span of four years, which
seemed most appropriate for the analysis. Zebra mussel populations typically re-
produce once a year (usually sometime during the summer) according to a mass
synchronous spawning behavior. Therefore, each cohort represents one generation
of mussels. The juvenile cohort represents all those mussels that have successfully
attached to some suitable substrate and have grown to a certain average size by the
end of the first year. These individuals are not yet sexually mature. The three adult
cohorts are the populations of each generation that has reached sexual maturity and
survived to the end of years two, three, and four.
The number of individual mussels that enter the juvenile cohort in a certain year
is a function of the number of adult female zebra mussels and their fecundities.
Although fecundities are high (30,000-40,000 larvae per female), larval mortality
rates are fairly high as well. The survival rate (.008) represents the percent of larvae
that attach to a substrate and grow to a certain size by the end of the year.
The survival potential is then the number of mussels that reach the juvenile cohort
under normal circumstances (no limiting conditions). However, the actual number of
mussels that survive the first year depends on whether or not the overall population is
close to or above the sustainable population of the lake. The sustainable population
is determined in the sustainability module described in detail below. So, the actual
number that survive is calculated as follows: if the total population is less than the
sustainable population in any year, then SURVIVE equals the smaller of the survival
potential, SURVIVE POT, and the difference between SUSTAINABLE POPULA-
TION and TOTAL POPULATION. If the total population is greater than or equal
to the sustainable population, then SURVIVE equals SURVIVE POT times a factor
that is less than one and decreases exponentially as total population gets larger. The
result is that the more the total population exceeds the sustainable population, the
smaller the number of juveniles that survive during that year.
