ecology of phasmids - KLUEDO - Universität Kaiserslautern
ecology of phasmids - KLUEDO - Universität Kaiserslautern
ecology of phasmids - KLUEDO - Universität Kaiserslautern
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Life history & potential population growth 35<br />
abdomen, marked individually with a four-color code (permanent ink) on the pronotum, and transferred<br />
to an extra cage only containing adults. Emergence date and time <strong>of</strong> death were recorded individually.<br />
3.2.2 Modeling potential population growth and the effect <strong>of</strong> limited<br />
hatching success<br />
The above described parameters are a reflection <strong>of</strong> the life cycle <strong>of</strong> M. diocles (i.e., patterns <strong>of</strong> birth,<br />
death and growth) and can serve as the basis for a mathematical model <strong>of</strong> population growth.<br />
For modeling population growth <strong>of</strong> M. diocles, I assumed (1) that generations do not overlap, (2) that<br />
the population increases competition-free, and (3) that all individuals complete their life cycle (i.e., all<br />
individuals complete their mean expected lifetime and reproduce).<br />
Generations in M. diocles populations will not overlap if mean developmental time <strong>of</strong> egg and nymphal<br />
stage together exceed mean adult lifetime. Population growth will then be best described by models <strong>of</strong><br />
discrete stepwise growth (Begon et al. 1996):<br />
Equation 3-1<br />
NT = N 0<br />
where NT = Population size N at generation T<br />
R = Fundamental net per capita rate <strong>of</strong> increase<br />
R<br />
T<br />
This model describes the exponential growth <strong>of</strong> a competition-free population with discrete generations<br />
and constant R. If R > 1 the population will grow exponentially.<br />
R usually combines the birth <strong>of</strong> new individuals with the survival <strong>of</strong> existing individuals (like in<br />
organisms with overlapping generations). When generations are discrete R describes only the birth <strong>of</strong><br />
new individuals and is equivalent to the basic reproductive rate R0:<br />
Equation 3-2<br />
R<br />
0<br />
∑<br />
where R0 = Basic reproductive rate<br />
=<br />
a<br />
F<br />
0<br />
x<br />
Fx = Total number <strong>of</strong> fertilized eggs produced during one generation<br />
a0 = Original number <strong>of</strong> individuals<br />
The natural logarithm <strong>of</strong> R0 describes the intrinsic rate <strong>of</strong> natural increase r. This is the change<br />
in population size per individual per unit time, which is one generation in the presented study.<br />
R0 is usually derived from cohort life tables that describe mortality and survivorship in particular life<br />
stages during the life cycle <strong>of</strong> organisms with discrete generations (e.g., Begon et al. 1996). Therefore<br />
the initial number <strong>of</strong> individuals a0 (here eggs) differs to some extent from individuals alive in the last<br />
life stage ax, which is for insects the reproductive adult phase. In this study, I wanted to model potential<br />
population growth and as a consequence I assumed that all individuals survive until the reproductive<br />
phase; thus a0 = ax.<br />
The total number <strong>of</strong> fertilized eggs produced during one generation (ΣFx) <strong>of</strong> M. diocles can be<br />
calculated on the base <strong>of</strong> the assessed average values for life history parameters by: