The effect of transient dynamics on future population sizes: A case study on Acyrthosyphon pisum

Background/Question/Methods Ecologists are increasingly interested in short-term dynamics in populations that have not yet reached the stable stage distribution. Projections based on long-term population growth (λ) will underestimate future population size if, on average, transient population growth exceeds λ. Deviations from the stable stage distribution are expected in populations prone to large disturbances like fire or drought (survival of only few life history stages). Furthermore transient dynamics may dominate in the early phase of population establishment following a dispersal event because dispersal is typically restricted to one or few life history stages like seeds in plants or young adults in many animal species. Our previous work on matrix projection models of the aphid species, Acyrthosyphon pisum, showed a large discrepancy in empirically measured transient dynamics and model predictions; however, the larger the number of life history stages the closer was the match between experimental results and model predictions. This could be due to discretization inherent in matrix models, or to parameter estimation error. I developed a Partial Differential Equation (PDE) Model and solved it using the numerical Escalator Boxcar Train approximation developed by Anderé deRoos (1988).

Results/Conclusions The PDE model and the best fitting matrix model of our previous work resulted in similar predictions; none matched the empirically measured transient dynamics. There are two possibilities for parameter estimation error: (1) The temperature during the parameter estimation experiments was about 2^oC lower than during the experiment measuring the transient dynamics. (2) The parameter estimation was conducted on single feeding aphids, and it is possible that aphids benefit from feeding in small groups (Allee effect). Both a higher temperature and an Allee effect generally reduce developmental time and shift reproduction to earlier ages. Increasing the fecundity of the youngest adults from 4.8 to 5.5, followed by a drop in fecundity to keep the total fecundity the same, and decreasing developmental time from 10 to 8 days resulted in a perfect match of empirical results and model predictions. I used my model to predict population dynamics following the arrival of a single adult migrant. The predicted total population size after 20 days assuming transient dynamics was 6 times as high as predicted assuming asymptotic growth. In contrast, using the original parameter estimates the transient amplification caused population size to triple. Conclusion: Transient dynamics can be ecologically significant and high temperatures are likely to magnify the effect of transient dynamics.