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Reply to Youngflesh and Lynch: Migration and population growth rate in animal black-swan events

  1. Nicholas K. Dulvya
  1. aEarth to Ocean Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;
  2. bSchool of Aquatic and Fishery Sciences, University of Washington, Seattle, WA 98195;
  3. cSchool of Resource and Environmental Management, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

We thank Youngflesh and Lynch (1) for their thoughtful comments on our paper (2). As they note, we should have mentioned immigration and emigration alongside the intrinsic population properties (e.g., population birth rate, mortality, and age at maturity) and extrinsic causes of black-swan events (e.g., extreme climate, disease, predation, competition, exploitation, and habitat destruction). After all, immigration and observation error are the only possible explanations for sudden abundance increases above those possible from the maximum biological rate of increase.

Youngflesh and Lynch (1) use a simple approach to flag which time series have population increases (r) that are greater than the demographic maximum [Cole’s <mml:math><mml:mi>ρ</mml:mi></mml:math>ρ (3), <mml:math><mml:mrow><mml:mi>r</mml:mi><mml:mo>></mml:mo><mml:mi>ρ</mml:mi></mml:mrow></mml:math>r>ρ], and hence may be driven by migration. However, they estimate the greatest realized <mml:math><mml:mi>r</mml:mi></mml:math>r without accounting for observation error (uncertainty in measuring population abundance); consequently, there will be false-positive cases of apparent high <mml:math><mml:mi>r</mml:mi></mml:math>r (Fig. 1 AC). If we calculate <mml:math><mml:mi>r</mml:mi></mml:math>r for the populations referenced by Youngflesh and Lynch (1) while accounting for moderate observation error [coefficient of variation (CV) = 0.2], only six populations remain with probability Pr(<mml:math><mml:mi>r</mml:mi></mml:math>r > <mml:math><mml:mi>ρ</mml:mi></mml:math>ρ) <mml:math><mml:mrow><mml:mo>></mml:mo><mml:mo>?</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math>>?0.5 and the 95% credible interval excludes <mml:math><mml:mi>ρ</mml:mi></mml:math>ρ in only …

?2To whom correspondence should be addressed. Email: sean.anderson{at}dfo-mpo.gc.ca.

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