Appendix A. Numerical solutions by the finite element method.

Numerical solutions by the finite element method

Appendix C. Details of the diatom case study.

Details of the diatom case study

Evaluating the performance of different models in estimating total population size.

The panels show the true and estimated population sizes for each year and replicate (gray dots), their means (black squares), fitted regression lines (solid black), and identity lines that would correspond to ideal fits (dashed black lines). The models are the Formozov–Malyshev–Pereleshin estimator (FMP), and the spatio-temporal (ST) and temporal (T; with priors 1 and 2) models. Note the log-scale. The figure is shown for Scenario A. Similar figures all Scenarios are shown in S1–S4 Figs.</p

LIST OF PUBLICATIONS BY ILKKA HANSKI from Ilkka Aulis Hanski. 14 February 1953—10 May 2016

Professor Ilkka Hanski made seminal contributions to both empirical and theoretical ecology and evolutionary biology, in particular metapopulation biology, throughout his scientific career. He started his career with dung beetle ecology, earning his doctorate at University of Oxford in 1979. He developed the rest of his career at University of Helsinki, where he was appointed professor in ecology in 1993 and academy professor in 2006. Hanski's most influential research was based on empirical work on the Glanville fritillary metapopulation in the Åland Islands, started in 1991, and continued until his death. His early research focused on ecological aspects of metapopulation biology, such as how the spatial structure of a landscape influences extinction thresholds, whereas his later work focused on genetic and evolutionary processes, such as maintenance of genetic variation by selection pressures varying with landscape structure. During the last years of his career, Hanski was a pioneer in the field of eco-evolutionary dynamics, showing how molecular-level underpinnings of trait variation can explain rapid evolutionary changes in natural populations. Hanski actively applied his research findings to conservation biology, involving himself in debates ranging from forest conservation in Finland to the links between human health and biodiversity. He was an exceptionally devoted group leader and mentor of younger researchers. His Metapopulation Research Centre grew gradually from a group consisting of Hanski and a few PhD students into a centre of 70 researchers

Appendix B. Bayesian estimation schemes.

Bayesian estimation schemes

The performance of the spatio-temporal (ST) model in estimating spatial variation in population size.

<p>The dots show Pearson’s rank correlation between the true and estimated population sizes, computed for each year and each replicate from the regular grid shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162447#pone.0162447.g002" target="_blank">Fig 2b</a>. The gray horizontal lines indicate no correlation. The panels correspond to the Scenarios A–F.</p

The performance of different models in estimating total population size.

<p>The panel (a) shows the means and 95% quantiles for the log-transformed ratio of estimated population size + 1 and true population size + 1 (<i>α</i>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162447#pone.0162447.e014" target="_blank">Eq 7</a>). The panels (b) and (c) show respectively the slope (<i>β</i>) and the variance explained (<i>R</i>²) in the regressions of estimated versus true population sizes (illustrated in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162447#pone.0162447.g003" target="_blank">Fig 3</a> for Scenario A). The panel (d) shows the percentage of estimates considered technically not valid (Failed) due to convergence issues during the estimation of the parameters. The different models (FMP, ST, T1, T2) are shown by different symbols, and the data are shown for Scenarios A–F. Numerical values are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162447#pone.0162447.s007" target="_blank">S1 Table</a>.</p

Illustration of density maps generated by the spatio-temporal (ST) model fitted to data generated by Scenarios A–F.

<p>(a) True locations of the simulated non-observed agents (grey dots), observed agents (black dots), and estimated densities from the ST model (contour lines with scale specific to each Scenario and colors with common scale). Densities in Scenarios E–F have been weighted with the habitat preferences. (b) A snapshot of survey transect locations without observations (grey dots) and with one or more observations (black dots). The rectangular grid is used to assess the ability of the spatio-temporal model to capture spatial variation (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162447#pone.0162447.g005" target="_blank">Fig 5</a>). The data are from the 30^th day of the 60-day long survey period on the 10^th year of the 20 years. For a description of the ST model and the Scenarios A-F, see text.</p

Illustration of simulated data generated by Scenarios A–F.

<p>The panels show a snapshot of movement tracks of the agents simulated for 60 days (gray lines) with the movements during counting day highlighted (black lines). The blue triangles show the survey transects. The background maps in Scenarios E–F show the different habitat types influencing movement behavior of the agents. For a description of the Scenarios A-F, see text.</p

The validity of interval estimates for total population size.

<p>The symbols show the proportions of true population sizes falling within 95% (black symbols) and 50% (gray symbols) credible intervals (CrI) for the Bayesian models (spatio-temporal ST; temporal with default prior T1; temporal with custom prior T2) and confidence intervals (CI) for the FMP model in the Scenarios A–F. Ideal proportions are marked with grey horizontal lines at 0.95 and 0.50.</p