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

October 12, 2017
114 (43) E8955-E8956
Research Article
Black-swan events in animal populations
Sean C. Anderson, Trevor A. Branch [...] Nicholas K. Dulvy
Letter
Black-swan events: Population crashes or temporary emigration?
Casey Youngflesh, Heather J. Lynch
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 ρ (3), r>ρ], and hence may be driven by migration. However, they estimate the greatest realized r without accounting for observation error (uncertainty in measuring population abundance); consequently, there will be false-positive cases of apparent high r (Fig. 1 AC). If we calculate 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(r > ρ) >0.5 and the 95% credible interval excludes ρ in only two cases (Fig. 1D). These two populations include lesser spotted dogfish (Scyliorhinuscaniculus) in the North Sea, which may indeed be an example of immigration from the English Channel due to thermal habitat expansion (4). In contrast, 18 of 26 populations with high probability of black-swan events in our original analysis were robust to allowing observation error (CV = 0.2).
Fig. 1.
(AC) We simulated populations with a constant population growth rate: logN(t+1)=r+logN(t), where N represents abundance, t represents a year from 1 to 25, and r represents the population growth rate. We added multiplicative observation error with CVs of 0.05, 0.1, 0.2, and 0.4. The vertical axis represents the ratio between the maximum observed growth rate and true r. Violin plots show the probability density across 2,000 simulations, and panels show three true population growth rates. (D) Populations featured by Youngflesh and Lynch (1), with r calculated allowing for observation error [CV = 0.2; median = solid circles (●), line segments = 95% credible interval]. Open circles (○) represent maximum r from Youngflesh and Lynch (1), and red crosses indicate Cole’s ρ (3). We accounted for observation error by fitting a state-space random walk to the log abundances: U(t+1)=Normal(U(t),σproc2), logN(t)=Normal(U(t),σobs2), where U(t) represents the unobserved true log abundance at time t, N(t) represents the observed abundance, and σproc2 and σobs2 represent process and observation variance. Numbers in parentheses indicate Global Population Dynamics Database IDs. Red crosses for bottom three populations are off the right side of the truncated axis. obs., observation; pop., population.
In our paper, we examined the root cause of black-swan events wherever possible (2). The population of red grouse (Lagopuslagopusscoticus) flagged by Youngflesh and Lynch (1) is one of three red grouse populations in the dataset and has been intensely studied. The parasitic nematode Trichostrongylustenuis, not emigration, is known to cause periodic population crashes for these populations (5, 6), and sampling error due to the time series being based on hunting records, not immigration, may be responsible for the high apparent maximum rates of population increase (6).
In addition, immigration and emigration should, on average, be equally likely, yet the observed black-swan events are nearly all downward. This either means that most such events are caused by population die-offs or that migration is surprisingly one-sided, involving rapid emigration from stable populations and large but slower immigration to restore populations. Naturally, emigration and population die-offs followed by immigration are not mutually exclusive: Die-offs can open excellent habitat that attracts individuals from other areas.
Migration is one of many possible causes of apparent black-swan events in animal populations. We agree that migration likely affects some of the populations in our analysis and agree with the need for caution when fitting models to data from open populations. On a case-by-case basis, modeling factors, such as migration and disease dynamics, yield more realistic predictions of population abundance and can explain events that would otherwise be considered black swans. However, we rarely, if ever, model all factors affecting a population, and we therefore maintain that allowing for heavy-tailed process error is an important step toward allowing for ecological surprises.
Code and data for these analyses can be found at https://github.com/seananderson/heavy-tails-response and Zenodo at https://doi.org/10.5281/zenodo.998224.

Acknowledgments

Funding was provided by a Simon Fraser University Graduate Fellowship and David H. Smith Conservation Research Fellowship (to S.C.A.), the Natural Sciences and Engineering Research Council of Canada (S.C.A., A.B.C., and N.K.D.), and the Canada Research Chairs Program (N.K.D.). T.A.B. was funded in part by the Richard C. and Lois M. Worthington Endowed Professor in Fisheries Management.

References

1
C Youngflesh, HJ Lynch, Black-swan events: Population crashes or temporary emigration? Proc Natl Acad Sci USA 114, E8953–E8954 (2017).
2
SC Anderson, TA Branch, AB Cooper, NK Dulvy, Black-swan events in animal populations. Proc Natl Acad Sci USA 114, 3252–3257 (2017).
3
LC Cole, The population consequences of life history phenomena. Q Rev Biol 29, 103–137 (1954).
4
C Sguotti, CP Lynam, B García-Carreras, JR Ellis, GH Engelhard, Distribution of skates and sharks in the North Sea: 112 years of change. Glob Change Biol 22, 2729–2743 (2016).
5
GR Potts, SC Tapper, PJ Hudson, Population fluctuations in red grouse: Analysis of bag records and a simulation model. J Anim Ecol 53, 21–36 (1984).
6
PJ Hudson, AP Dobson, D Newborn, Prevention of population cycles by parasite removal. Science 282, 2256–2258 (1998).

Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 114 | No. 43
October 24, 2017
PubMed: 29073091

Classifications

Submission history

Published online: October 12, 2017
Published in issue: October 24, 2017

Acknowledgments

Funding was provided by a Simon Fraser University Graduate Fellowship and David H. Smith Conservation Research Fellowship (to S.C.A.), the Natural Sciences and Engineering Research Council of Canada (S.C.A., A.B.C., and N.K.D.), and the Canada Research Chairs Program (N.K.D.). T.A.B. was funded in part by the Richard C. and Lois M. Worthington Endowed Professor in Fisheries Management.

Authors

Affiliations

Sean C. Anderson2 [email protected]
Earth to Ocean Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;
School of Aquatic and Fishery Sciences, University of Washington, Seattle, WA 98195;
Present address: Pacific Biological Station, Fisheries and Oceans Canada, Nanaimo, BC, V6T 6N7, Canada.
Trevor A. Branch
School of Aquatic and Fishery Sciences, University of Washington, Seattle, WA 98195;
Andrew B. Cooper
School of Resource and Environmental Management, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
Nicholas K. Dulvy
Earth to Ocean Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;

Notes

2
To whom correspondence should be addressed. Email: [email protected].
Author contributions: S.C.A., T.A.B., and N.K.D. designed research; S.C.A. analyzed data; and S.C.A., T.A.B., A.B.C., and N.K.D. wrote the paper.

Competing Interests

The authors declare no conflict of interest.

Metrics & Citations

Metrics

Note: The article usage is presented with a three- to four-day delay and will update daily once available. Due to ths delay, usage data will not appear immediately following publication. Citation information is sourced from Crossref Cited-by service.


Citation statements




Altmetrics

Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

    Loading...

    View Options

    View options

    PDF format

    Download this article as a PDF file

    DOWNLOAD PDF

    Get Access

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Personal login Institutional Login

    Recommend to a librarian

    Recommend PNAS to a Librarian

    Purchase options

    Purchase this article to access the full text.

    Single Article Purchase

    Reply to Youngflesh and Lynch: Migration and population growth rate in animal black-swan events
    Proceedings of the National Academy of Sciences
    • Vol. 114
    • No. 43
    • pp. 11259-E9182

    Media

    Figures

    Tables

    Other

    Share

    Share

    Share article link

    Share on social media