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Influence of Dispersal Processes on the Global Dynamics of Emperor

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Appendices: Influence of dispersal processes on the global dynamics of Emperor penguin, a species threatened by climate change. Contents A Information about the known colonies of the emperor penguin in Antarctica. 2 B Description of the metapopulation model 5 B.1 Construction of the reproduction matrix F .......................5 B.2 The dispersal model . .9 C Global sensitivity analysis 13 D Baby models 15 D.1 Case 1 and 2: dispersion to the good patch is not always optimal . 15 D.1.1 Description of local and global dynamics . 15 D.1.2 Close to the equilibrium: analytical results. 16 D.1.3 Far away from the equilibrium: numerical results. 18 D.2 Case 3: Random dispersion between poor quality habitats . 20 D.3 Implications of theoretical results for the emperor penguin . 21 E Local and regional population dynamics 23 E.1 Population size of each colony . 23 E.2 Regional population size . 26 F Isolating the colonies on the Ross Sea 31 G Random departure and random search dispersal 34 1 A Information about the known colonies of the emperor penguin in Antarctica. Table 1: Information about the known colonies of the emperor penguin in Antarctica, modified from Fretwell et al. (2012) { see the figure A.1 for a spatial repartition of the known colonies in Antarctica. # is the index of the colony used in our figures; BE is the best estimate of the observed number of breeding pairs in 2009 used in our model simulations. # name longitude latitude BE 2009 1 Snowhill -57.44 -64.52 2164 2 Dolleman -60.43 -70.61 1620 3 Smith -60.83 -74.37 4018 4 Gould -47.68 -77.71 8242 5 Luitpold -33.6 -77.077 6498 6 Dawson -26.67 -76.02 2597 7 Halley -24.4 -75.54 22510 8 Stancomb -23.09 -74.12 5455 9 Drescher -17.4 -72.83 2469 10 Riiser -15.11 -72.12 4013 11 Atka -8.13 -70.61 9657 12 Sanae -1.42 -70 3193 13 Astrid 8.31 -69.95 1368 14 Lazarev 15.55 -69.75 821 15 Ragnhild 27.15 -69.9 6870 16 Gunnerus 34.38 -68.75 4652 17 Umbeashi 43.01 -68.05 146 18 Amundsen Bay 50.55 -66.78 88 19 Kloa Point 57.28 -66.64 3283 20 Fold Island 59.32 -67.32 213 21 Taylor Glacier 60.88 -67.45 519 22 Auster 63.98 -67.39 7855 23 Cape Darnley 69.7 -67.88 3465 24 Amanda Bay 76.83 -69.27 6831 25 Haswell Island 93.01 -66.52 3247 2 Table 1 continued. # name longitude latitude BE 2009 26 Shackleton Ice Shelf 96.02 -64.86 6471 27 Bowman Island 103.07 -65.16 1609 28 Peterson Bank 110.23 -65.92 1000 29 Dibble Glacier 134.79 -66.01 12476 30 Terre Ad´elie-Pointe Geologie 140.01 -66.67 3259 31 Mertz Glacier 146.62 -66.93 4781 32 Davis Bay 158.49 -69.35 1745 33 Cape Roget 170.59 -71.99 9505 34 Coulman Island 169.61 -73.35 25298 35 Cape Washington 165.37 -74.64 11808 36 Franklin Island 168.43 -76.18 7561 37 Beaufort Island 167.02 -76.93 1641 38 Cape Crozier 169.32 -77.46 303 39 Cape Colbeck Edward VII Peninsula -157.7 -77.14 11438 40 Rupert Coast -143.3 -75.38 1550 41 Thuston Glacier Mt Siple -125.621 -73.5 2989 42 Bear Peninsula -110.25 -74.35 9457 43 Brownson Islands -103.64 -74.35 5732 44 Noville Peninsula -98.45 -71.77 3568 45 Smyley -78.83 -72.3 6061 46 Dion Islands -68.7 -67.9 0 3 Figure A.1: Spatial repartition of known colonies of Emperor penguins in Antarctica (dots). The five regional of Antarctica are shown, as well as the annual mean change of sea ice concentrations (SIC) between the 20 and 21th centuries. Modified from Jenouvrier et al. 2014. 4 B Description of the metapopulation model In this supporting information, we detail the reproduction matrix (F) and dispersal matrix (D) for our metapopulation model. Both depend on the habitat characteristics, x(t), which can change in 1 2 3 1 time (due to climate change, for instance); x := (x ; x ; x ), with x (t) := r∗(t) the realized growth rate of the local patch, x2(t) := K the carrying capacities of the patch and x3 := (dist(i; j)) the distance between patch. The population vector n, which describes the population size in each patch, is model (1): n(t + 1) = D[x; n] F[x; n] n(t): (B.1) B.1 Construction of the reproduction matrix F The local population dynamics during the reproduction phase only depend on the sub-population size ni(t) inside patch i and the habitat characteristics of that patch. Each patch is characterized by its intrinsic population growth rate ri(t), which may vary in time, and its carrying capacity, Ki, which is set to be constant over the entire time period. We assume that negative density- dependence effects occur inside good quality patches (ri(t) > 0), and they are described by a Ricker model (Ricker, 1954). On the other hand, the population tends to go extinct inside poor quality patches (r (t) 0). Thus the realized growth rate r (t) takes the form i ≤ ∗ r (t)(1 n (t)=K ) e i − i i 1 if r (t) > 0; − i ri∗(t) = 8 (B.2) > <> eri(t) 1 if r (t) 0: − i ≤ > :> The reproduction matrix is diagonal, and for any time t is Fii[x(t); n(t)] := (1 + ri∗(t)) and Fij = 0: (B.3) Estimation of the carrying capacity K. Although no effect of negative density dependence has been detected in previous studies (Jenouvrier et al., 2012), breeding space and resources are likely limited for EPs at higher population densities than the ones observed. For instance, the 5 growth of the Beaufort Island colony is limited by available space on the fast ice plate next to the island (Kooyman et al., 2007). Because data on EP populations comprise sparse counts of chicks, we cannot calculate quantitative estimates of K for EP colonies (Wienecke, 2011). Therefore, we use the stochastic population trajectories projected by a sea-ice dependent population model without density dependence (Jenouvrier et al., 2014) to derive an estimate of K as it projects the maximum population growth rate in the absence of intra-specific competition for resources. Because the distribution of the population growth rates calculated from the stochastic popula- tion trajectories is skewed by a few realizations with high growth rates, the median of the intrinsic population growth rater ¯i is different from the growth rate of the median of population size r(¯ni). The skewness of the distribution is a mathematical descriptor of second order: it does not modify the mean but changes the variance. The carrying capacity K in the Ricker model has a similar property. It modifies the dynamics at the second order because it impacts the growth rate only when the density ni is high. For each colony i and s stochastic population projections, the median of the intrinsic population growth rate is defined by n~ (t + 1) n~ (t) r¯ (t) := median i;s − i;s : i n~ (t) i;s wheren ~i;s is the population size for the s stochastic simulation for colony i. The median of the population sizen ¯i is then n¯i(t) := median n~i;s(t) : Inverting equation (B.2) in Ki and substituting ri∗ for the `observed' change in population sizes between t and t + 1, we then define the maximal carrying capacity K := max median( K r¯ (t) > 0 ); n (0) : i f i;tj i g i This estimation provides carrying capacities K which satisfy K 2n (0) on average. Figure B.1 i i ' i shows the projected global population size obtained from our metapopulation model without dis- persion using equation (B.1) withn ¯i(t) and K = 2n(0) (gray line). It agrees well with the trajectory 6 of the global population size estimated as the sum of the median of population size in each patch ¯ N(t) = i n¯i(t) obtained from the stochastic model without density dependence from Jenouvrier et al. (2014).P We can thus assume that the carrying capacities are constant over time and equal twice the number of individuals in each colony. To test the sensitivity of our results to K, Figure B.2 shows the projected global population size obtained from our metapopulation model with K = [2n(0); 3n(0); 4n(0)] for different dispersal scenarios. The case K = 4 n(0) corresponds to the maximum population size ever observed for an EP colony (see Barber-Meyer et al. (2008)). For any scenario, the global population size projected by the model have similar dynamic pattern, only the magnitude of the population size changes. x 105 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 2020 2040 2060 2080 2100 Figure B.1: Comparison of the global population size trajectory projected by a model without density dependence (Jenouvrier et al., 2014, blue dots) and our metapopulation including the carrying capacity of each patch (gray line), for a case without dispersion. 7 x 105 x 105 3 3 2.5 2.5 2 2 1.5 1.5 total population size total population size 1 1 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 time (t) time (t) (a) Short distance, K=2 (b) Long distance, K=2 x 105 x 105 3 3 2.5 2.5 2 2 1.5 1.5 total population size total population size 1 1 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 time (t) time (t) (c) Short distance, K=3 (d) Long distance, K=3 x 105 x 105 3 3 2.5 2.5 2 2 1.5 1.5 total population size total population size 1 1 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 time (t) time (t) (e) Short distance, K=4 (f) Long distance,K=4 Figure B.2: Global number of breeding pairs of emperor penguins from 2010 to 2100 for various dispersal scenarios and various carrying capacity: (a)-(b) carrying capacity K = 2n(0) that matches the population projection of a model without density-dependence (Jenouvrier et al.
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