Matrix models population growth rate

It can be shown that the population s long-term growth rate only depends on the transition matrix, not on the initial state of the population. If all elements of the matrix are constant, the growth rate can be calculated as the first eigenvalue of the matrix (i.e., the constant that is obtained by solving Equation 3.1). If restricted to constant demographic rates, matrix models do not require any modeling at all, because... 

The simple matrix model depicted earlier is an example of a deterministic matrix model. Deterministic matrix models have no measure of randomness (stochastic-ity), assume constant demographic parameters, and ignore density dependence. Moreover, estimated growth rate and stable stage or age structure refer to an exponentially increasing (or decreasing) population. 

The growth rates (k) for these species were determined to be 2.7484,1.6897, and 1.5992/week for the oriental, melon, and Mediterranean fly, respectively (modified from Vargas et al. 1984). Matrix models were developed for each species (controls) and with the predicted mortalities resulting from exposure to acephate (Figures 5.5 and 5.6). The recovery time interval was the endpoint of interest here. The Mediterranean fly was unaffected by 1% mortality, and therefore no graph is presented. However, the melon fly population had a recovery period of 2 weeks (Figure 5.6), while the oriental fruit fly had a recovery period of 7 weeks (Figure 5.5). 

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