Influence of Dispersal Processes on the Global Dynamics of Emperor

Home , Amanda Bay, Cape Colbeck, Cape Roget, Cape Washington, Dibble Glacier, Mertz Glacier

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) =  (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 population 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 { i,t| i } 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 dispersion 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

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. 2014, Fig. S1), putative larger carrying capacities of (c)-(d) K = 3n(0) and (e)-(f) K = 4n(0). Light gray thick line is the population trajectory without dispersion. Colored solid lines are population trajectories under 1 1 high dispersion rates (m (rc) = 0.9), while dashed lines show low dispersion rates (m (rc) = 0.1). Green lines are trajectories under informed search, while red lines show the random search.

8 B.2 The dispersal model

In our metapopulation model, the dispersion phase D during each annual projection is a series of dispersal events. If the dispersion phase is composed of p events, then the dispersal matrix De projects the population from dispersal event e to e + 1 with e [1 p], and Dp projected from ∈ dispersal event p to the ﬁrst event of the reproduction process F.

D := Dp... De+1DeD1.

In our case study, p = 2.

In addition, each dispersal event is composed of two successive behaviors: dispersion from the colony described by Me followed by a searching and habitat selection phase described by Se, such that

De = SeMe.

The dispersion matrix Me is a diagonal matrix that deﬁnes, for each patch, the probability that an individual leaves his resident patch. During the ﬁrst dispersal event D1, the proportion of individuals leaving their resident patch only depends on the quality of the resident patch measured by ri∗ and the sensitivity of individual to this quality, rc∗.

1 1 ri∗(t) 1 Mii := m and Mij := 0. rc∗

1 if r∗ < rc∗, 1  r∗ m (r∗/rc∗) :=  if rc∗ r < 0, (B.4)  rc∗ ≤  0 if r∗ > 0.   When the critical quality threshold rc∗ is close to 0, it corresponds to a high dispersion rate scenario, while when rc∗ is larger, it reﬂects low dispersion rate (see Figure B.3). For the EP, the growth rate r over the twenty-ﬁrst century is predicted to have a range of

( 0.2275, 0.0237) (Jenouvrier et al., 2014). Thus in our simulation, the critical threshold r en- − c∗

9 m1 r∗ rc∗ 1

0.5

0.3 rm∗ rc∗ 0.2 0.1 rc∗ 0 r∗ − − −

1 Figure B.3: Probability of leaving the resident patch m (r∗/rc∗) as function of the quality of the habitat measured by r∗ and the sensitivity parameter rc∗. Colored lines refer to the two scenarios: 1 1 high emigration rate (m (rc∗) = 0.9, red line) and low emigration (m (rc∗) = 0.1, blue line). compasses (r , 0) where r = 0.25 is the poorest quality patch, i.e. the minimum possible growth m∗ m∗ − 1 rate. We deﬁne the emigration rate m (rc∗) as follows

1 1 rc∗ 1 rc∗ rc∗ m (rc∗) := m m = 1 for all rc∗ (rm∗ , 0). (B.5) rc∗ − rm∗ − rm∗ ∈

During the second dispersal event, only the surplus of individuals in saturated patches will leave

(Fig. 1). The dispersion function M2 is described by

2 2 Ki 2 Mii = Mii[K, n] := max 1 , 0 and Mij := 0. (B.6) − ni where Ki is the carrying capacity of patch i.

The searching matrix Se includes the probability of selecting a patch given a speciﬁc habitat selection behavior and depends on an individual’s dispersal ability (i.e. mean distance an individual can travel, d). The searching matrices S[x] is

S [ x, d ] := (j i, x(t), d), for j = i and S [ x, d ] := S [ x, d ], ij S | 6 ii − ij j=i X6 indicating that the probability of settlement in a patch j depends on leaving patch i, the characteristics of the habitat in the patch j (x(t)), and the dispersal ability of the individuals d.

To account for various habitat selection processes, the search strategies are decomposed as S

10 follows: Ns w (i, x(t), d)S (j i, x(t), d) k k | (j i, x(t), d) := Xk=1 , S | Ns w (i, x(t), d)S (j i, x(t), d) k k | j=i k=1 X6 X where wk(i, x(t), d) corresponds to the weight of the searching behavior Sk, given that individuals were at patch i at time t and are moving across the habitat described by x(t). These weight functions sum to 1 over the possible search behaviors, Ns, for each resident patch i; that is

Ns wk(i, x(t), d) = 1. Xk=1

The term S (j i, x(t), d) describes the probability distribution of moving to the new patch j given k | that individuals left resident patch i at time t and are moving across habitat x(t) using the searching behavior k.

If a patch j is not reachable with any search behavior—that is w (i, x(t), d)S (j i, x(t), d) = 0 k k | for any k—then we set

(j i, x(t), d) := 0 if w (i, x(t), d)S (j i, x(t), d) = 0. S | k k |

In our case study, we focus on two search behaviors: the random searching behavior (SR) and the informed searching behavior (SI ) (see Fig. 1), which are extreme cases along a gradient of possible search behaviors. Moreover, we assume one searching behavior for each scenario. More precisely, we either assume that the weight function wR, associated to searching behavior SR, is always equal to 1 and the weight function wI , associated to SI is always equal to 0 (Random searching scenario) or conversely w 0 and w 1 (Informed searching scenario) R ≡ I ≡ The random searching behavior assumes that individuals can move randomly across landscape according to a dispersal kernel k(x) which describe the probability of traveling a distance x. This probability distribution can take various forms according to the dispersal ability of the species. In

11 our simulation, we use a uniform kernel:

1 k (x) := 1 (x), for all x [0, + ), unif d [0,d] ∈ ∞

1 where d represents the mean distance dispersal of the species and [0,d](x) is the characteristic function of the interval [0, d]. Thus under the random dispersal behavior, the probability S (j i, x(t), d) R | of moving to patch j given that individuals left its resident patch i at time t is deﬁned by

k(dist(i, j)) SR(j i, x(t), d) := . (B.7) | k(dist(i, j)) j=i X6 where dist(i, j) corresponds to the landscape topography, speciﬁcally the coastal distance between colonies in our case study. With the random behavior scenario, individuals may settle in a new habitat patch of lower quality than their resident patch.

The informed searching behavior assumes that individuals select their habitat using the

ﬁtness of conspeciﬁcs as a source of public information on patch quality. Thus the patch quality is described through the realized growth rate r (t). The probability S (j i, x(t), d) of moving to a ∗ I | new patch j given that an individual left its resident patch i at time t is

1 if rj∗(t) = max (r∗(t) dist(i, k) d), S (j i, x(t), d) := k | ≤ (B.8) I |   0 otherwise,

 where d represents the mean distance dispersal of the species. Unlike individuals using the random behavior, individuals will move to the most favorable habitat they can reach, i.e. max rk∗(t) such that dist(i, k) d. ≤

12 C Global sensitivity analysis

Since dispersal characteristics of the EPs can not be quantiﬁed yet, we performed our analysis using a wide range of parameters p := (p1, p2) for the mean distance dispersal p1 = d and the emigration

1 rate p2 := m (rc∗). Specifically, foraging studies have shown that EP adults travel more than 2000 km to their colonies in the western Ross Sea (Kooyman et al., 2004) and one juvenile covered more than 7000 km during the first 8 months after leaving his natal colony in Terre Adélie(Thiebot et al., 2013). In addition, populations around the Antarctic coast other than in the Ross Sea are panmictic (Younger et al., 2015), suggesting potentially large dispersal distance. Since the minimum coastal distance between colonies is 68.2 km and the maximum is 8220 km, we assume that the mean distance dispersal parameter d ranges from 250 Km to 6000 km. The emigration rate ranges between 0 and 1 because the critical quality threshold ranges from 0 to r = 0.25. m∗ − To quantify the effect of interactions among these dispersal characteristics and model structure uncertainty, we conduct two global sensitivity analyses for each year from 2010 to 2100: (1) variance-based sensitivity analysis and (2) a Partial Rank Correlation Coefficient (PRCC). These two analyses are performed on the global population size percentage difference relative to a scenario without dispersion, referred as N . This percentage difference which depends on dispersal 4 t parameters p = (p1, p2), is calculated as:

+ 0 Nt Nt Nt(p) = −0 4 Nt

+ 0 with Nt the global size population projected under diﬀerent dispersal scenario and Nt the size projected without dispersion.

Total eﬀect sensitivity index – sT . We ﬁrst run a variance-based sensitivity analysis with dispersal parameters generated by a Uniform Random Sampling. For each parameter, we compute the total sensitivity index sT , that measures the fractional variance accounted for by individual parameter and groups of parameters (Saltelli, 2004; Marino et al., 2008). We sample two set p1 and p2 of size q = 10, 000 each. For i either equal to 1 or 2, we use the following estimator to

13 compute the total sensitivity index (Saltelli, 2004)

2 Uˆ i Eˆ (p) sT i := 1 ∼ − , (C.1) − Vˆ (p) where Eˆ(p) := 1/q q N (p1) stands for the empirical mean of N (p1) and Vˆ (p) := 1/(q j=1 4 t 4 t − q 1 2 ˆ2 ˆ 1) j=1 Nt(p ) PE (p) corresponds to its empirical variance. The last term U i is covariance 4 − ∼ 1 2 ˆ whereP the parameter pi is replaced by pi . For instance, U 1 is deﬁned by ∼

q ˆ 1 1 1 2 1 U 1 := Nt((p1)j, (p2)j) Nt((p1)j, (p2)j) ∼ q 1 4 4 − Xj=1

This sensitivity index captures the total effect, that is the first and higher order effects (interactions), of dispersal parameters.

Partial Rank Correlation Coefficients – PRCC. We also calculate the Partial Rank Cor- relation Coefficients which provide a measure of monotonicity of all but one parameter, after the removal of the linear effects (Aiello-Lammens and Ak¸cakaya, 2016). They have been computed using the function partialcorr of Matlabr with the Spearman (rank) partial correlations.

14 D Baby models

We develop simpler “baby” models with only two patches to draw general conclusions about the complex dynamics arising from climate change in our case study. First, we develop a model with a ‘good’ patch in which the population intrinsic growth rate, r1, is positive and a ‘poor’ patch in which the population growth rate, r , is non-positive ( 1 r 0). Case 1 and 2 are described in 2 − ≤ 2 ≤ section D.1. In the good patch the population dynamics follow a Ricker model, while in the poor patch the local population faces extinction at an exponential rate. Individuals from the poor patch may move to the good patch with a probability α.

Second, we develop a model with two poor patches (Case 3 described in section D.2): 1 − ≤ r 0 and 1 r 0 but patch 1 is more favorable than patch 2, that is r < r 1. 1 ≤ − ≤ 2 ≤ | 1| | 2| ≤ Individuals move between these two patches, and the proportion of individuals that move during each time step is assumed to be constant. This movement probability is α1 for population 1 and

α2 for population 2.

The two local populations are described by the number of individuals n1 and n2. We will discuss the dynamics of the global population size N := n1 + n2.

D.1 Case 1 and 2: dispersion to the good patch is not always optimal

Case 1 and 2 correspond to r > 0 and 1 r 0. 1 − ≤ 2 ≤

D.1.1 Description of local and global dynamics

The ﬁrst model (r > 0 and r 0) is, for t > 0, 1 2 ≤

r1(1 n1(t)/K1) n1(t + 1) = n1(t) e − + α(1 + r2)n2(t)  (D.1)   n (t + 1) = (1 α)(1 + r )n (t) 2 − 2 2   where K1 is the carrying capacity of the patch 1. The particular case α = 0 corresponds to the dynamics without dispersion and is our reference for understanding the impact of dispersion on the global dynamics.

15 We ﬁrst observe that the dynamics of n2 can be explicitly computed as follows

n (t) = (1 α)t(1 + r )t n (0), for all t > 0, 2 − 2 2

where n2(0) > 0 is the initial population size of patch (2). We observe that the dispersion will accelerate the extinction of the population 2.

The system admits a globally stable equilibrium (n , n ) = (K , 0) for any α [0, 1]. It corre- 1∗ 2∗ 1 ∈ sponds to a saturated good quality patch (n1∗ = K1) and an empty poor patch (n2∗ = 0). To explore the eﬀect of dispersion we distinguish two cases: the system is initially close to the equilibrium (see section D.1.2) or it is initially far away from the equilibrium (see section D.1.3).

The ﬁrst case is treated analytically while the second case is analyzed numerically.

D.1.2 Close to the equilibrium: analytical results.

Since we are interested in the global population size dynamics N = n1 + n2 we rewrite the system (D.1) as follows:

r1(1 N(t)/K1+n2(t)/K1) N(t + 1) = (N(t) n (t)) e − + (1 + r )n (t) − 2 2 2  (D.2)   n (t + 1) = (1 α)(1 + r )n (t). 2 − 2 2   The equation satisﬁed by N does not depends explicitly on α. It only depends on α through the coupling with n2. The equilibrium (K1, 0) is still a stable equilibrium for the new system and corresponds to N ∗ = n1∗ + n2∗ = K1. The convergence of the solution of (D.2) to the equilibrium

(K1, 0) is driven by the eigenvalues of system (D.2) linearised around the equilibrium (K1, 0): λ = (1 r ) and λ (α) = (1 α)(1 + r ). The eigenvalue λ does not depend on the dispersion 1 − 1 2 − 2 1 rate α while the eigenvalue λ2(α) is a decreasing function of α. The (normalized) eigenvectors associated with λ and λ (α) are respectively u1 = (1, 0) and u2 = (1, y(α)) where y(α) = 1 1 2 − α(1 + r )/(r + r2) = (λ (α) λ )/(λ (0) λ ). 2 1 2 − 1 2 − 1 For any α (0, 1) and (N(0), n (0)) close to (K , 0), the dynamics of the global population size ∈ 2 1

16 N α satisﬁes λ (α)t λt N α(t) = K + λt N(0) + 2 − 1 n (0), for t > 0. 1 y(α) 2

Thus, for any α (0, 1) the diﬀerence between the global population size with dispersion N α and ∈ without dispersion N 0 satisﬁes

λ (α)t λt N α(t) N 0(t) = 2 − 1 (λ (0)t λt ) n (0). (D.3) − y(α) − 2 − 1 2

The eﬀect of the dispersion will thus crucially depend on the sign of (λ λ (0)). We distinguish 1 − 2 two cases: a globally favorable landscape (r1 + r2 > 0 that is λ1 < λ2(0)) and a globally poor landscape (r + r 0 that is λ λ (0)). 1 2 ≤ 1 ≥ 2

Case 1: Globally favorable landscape (r > r ). First we consider patches that form a 1 | 2| globally favorable landscape in the sense that r1 + r2 > 0. In this landscape we have λ1 < λ2(0) and λ (α) < λ (0) for any α (0, 1]. In this parameter range, the impact of the dispersion is always 2 2 ∈ negative when (N, n2) is close to the equilibrium (K1, 0). Indeed we have for any t > 1 and α (0, 1) ∈

t t t 1 λ2(α) λ1 − k t 1 k λ2(0) λ1 − = λ2(α) λ1 λ2(α) λ1− − − y(α) − λ2(α) λ1 k=1 − tX1 k − λ2(α) k t 1 k (D.4) = (λ2(0) λ1) λ2(0) λ1− − − λ2(0) Xk=1 λ (0)t λt . ≤ 2 − 1

From equation (D.3), we have N α(t) < N 0(t), for any t > 1. Thus when the population (1) is close to the carrying capacity K1, the presence of dispersion α > 0 will accelerate the extinction of population (2) and the saturation of population (1) to the carrying capacity K1.

Case 2: Globally poor landscape (r r 1). Let us now assume that the patches 1 ≤ | 2| ≤ form a globally poor landscape in the sense that r + r 0. In this landscape we always have 1 2 ≤ λ (α) λ (0) λ for any α (0, 1]. In this parameter range, the impact of dispersion is always 2 ≤ 2 ≤ 1 ∈

17 positive. Indeed, from equation (D.4) we obtain for any t > 1 and α (0, 1) ∈

t 1 t t k λ2(α) λ1 − λ2(α) k t 1 k − = (λ2(0) λ1) λ2(0) λ1− − y(α) − λ2(0) Xk=1 λ (0)t λt . ≥ 2 − 1

Thus, the presence of dispersion α > 0 will accelerate the extinction of population (2) but will slow down the saturation of population (1) to the carrying capacity. Consequently, the dispersion ﬂow will enhance the population without threatening its long term viability.

D.1.3 Far away from the equilibrium: numerical results.

When the populations (n1, n2) are not close to the equilibrium (K1, 0), the linearization approach fails and the dynamics are much more complicated. We perform numerical simulations to under- stand the eﬀect of dispersion, α, on the dynamics of the population. We focus on the case where n1 is between (K1/2,K1) and n2 is between (0, 3K1). This parameter range covers most of the cases which occur in the model for the emperor penguin.

Case 1: Globally favorable landscape (r > r ). When the landscape is globally favorable 1 | 2| (r1 + r2 > 0), a large dispersion rate leads to larger percentage decrease in the population size relative to a scenario without dispersion ( N = N α(t) N 0(t) < 0) than low dispersion (Fig. S3 4 − a and b). Furthermore, the eﬀect of dispersion is positive ( N > 0) only when the total initial 4 population is not too large compared to the carrying capacity of the good quality patch K1.

Case 2: Globally poor landscape (r r ). When the landscape is globally poor (r + r < 1 ≤ | 2| 1 2 0), the dispersion eﬀect is always positive N > 0 (Fig. S3 c and d). 4

18 ieol nagoal orlnsaeo ngoal aoal adcp a wyfo saturation. from away far landscape favorable globally in or landscape poor globally a in only size Diﬀerence D.1: Figure iecrepnst h case the to corresponds line ( iprinrate dispersion landscape α Initial size of population (2) N2(0) dispersion low and landscape Favorable (a) Initial size of population (2) N2(0) 1000 1500 2000 2500 3000 3500 4000 4500 1000 1500 2000 2500 3000 3500 4000 4500 )adwt iprin( dispersion with and 0) = 500 500 c orlnsaeadlwdispersion low and landscape Poor (c) 0 0 800 800 nta ieo ouain(1) population of size Initial (1) population of size Initial 900 900 r 1 1000 1000 0 = α 1100 1100 sete o ( low either is . 02, 1200 1200 r 2 1300 1300 N 0 = α ( 1400 1400 t N ) > α . 1 n lblypo landscape poor globally and 019 α − N N α 1500 1500 ( 1 1 0 = N (0) (0) t = ) )acrigt nta ouainsz nec ac.Teblack The patch. each in size population initial to according 0) 0 1600 1600 . ( )o ih( high or 1) t ttime at ) N b aoal adcp n ihdispersion high and landscape Favorable (b) 0 Initial size of population (2) N2(0) Initial size of population (2) N2(0) ( 1000 1500 2000 2500 3000 3500 4000 4500 1000 1500 2000 2500 3000 3500 4000 4500 d orlnsaeadhg dispersion high and landscape Poor (d) 500 500 t ) 0 0 800 800 . hr r w ieethbtt:goal favorable globally habitats: diﬀerent two are There nta ieo ouain(1) population of size Initial nta ieo ouain(1) population of size Initial 900 900 19 α t 0 = 0btenteseai ihu dispersion without scenario the between 30 = 1000 1000 . ) iprinicesstettlpopulation total the increases dispersion 9). 1100 1100 1200 1200 1300 1300 r 1 1400 1400 0 = N N 1500 1500 1 1 . (0) (0) 1and 01 1600 1600 r 2 0 = . 3 The 03. D.2 Case 3: Random dispersion between poor quality habitats

Case 3 corresponds to 1 r 0 and 1 r < 0. Our second model is, for any t > 0, − ≤ 1 ≤ − ≤ 2

n (t + 1) = (1 α )R n (t) + α R n (t) 1 − 1 1 1 2 2 2    n (t + 1) = α R n (t) + (1 α )R n (t), 2 1 1 1 − 2 2 2   where the reproduction rate R := 1 + r = 1 r and R := 1 + r = 1 r . Thus, starting 1 1 − | 1| 2 2 − | 2| 0 0 from population size n1 > 0 and n2, the population size at time t > 0 is given by

0 n1(t) n1 (1 α1)R1 α2R2 = At with A = − .    0    n2(t) n2 α1R1 (1 α2)R2      −        The eigenvalues of A are given by

2 (1 α1)R1 + (1 α2)R2 (1 α1)R1 (1 α2)R2 + 4α1α2R1R2 λ1(α1, α2) = − − + − − − 2 q 2 2 (1 α1)R1 + (1 α2)R2 (1 α1)R1 (1 α2)R2 + 4α1α2R1R2 λ2(α1, α2) = − − − − − 2 − q 2

λ and λ satisfy λ > λ and 0 < λ < 1. Thus the population 1 and 2 go extinct at rate λt . 1 2 | 1| | 2| 1 1 In addition, we can compute the partial derivative of λ1 with respect to α1 and α2 as follows

R R R ∂ λ (α , α ) = 1 1 1 1 − 2 α1 1 1 2 2 2 − − s − (1 α1)R1 (1 α2)R2 + 4α1α2R1R2 ! − − − R R R ∂ λ (α , α ) = 2 1 + 1 − 2 1 . α2 1 1 2 2 2 s (1 α1)R1 (1 α2)R2 + 4α1α2R1R2 − ! − − − The principal eigenvalue λ is a decreasing function in α , since ∂ λ 0 (because R > R ). 1 1 α1 1 ≤ 1 2 Moreover it is an increasing function in α (∂ λ 0) because R > R . Dispersion from the more 2 α2 1 ≥ 1 2 favorable patch will accelerate the extinction of the population—that is α1 > 0—while a massive dispersion from the poorest quality patch will slow down the extinction—that is α2 close to 1.

20 aia ult fteoeallandscape: overall the of quality habitat rate growth local the the of colonies example, the EP all the over sum In by deﬁned rate. is growth rate global growth time each the for by given and by are patch characterized rates is each growth it of precisely, rate More growth model landscape. baby intrinsic overall the the the of of outcome suitability the the that seen on have case depends We study crucially 2). our in (Fig. obtained colonies patterns penguins complex emperor the 45 on featuring light penguin shed above emperor presented the scenarios three for The results theoretical of Implications landscape. D.3 quality patch habitat poorest poor the a from in Emigration population total quality. the of poor extinction of patches two rate between Growth D.2: Figure • • rmFg4 ecndcmoeteftr etr notretm eid codn othe to according periods time three into century future the decompose can we Fig.4, From rm23 o28:goal orlnsaewt odhbttclne ( colonies habitat good with 0) landscape poor globally 2088: to 2036 from ( landscape favorable globally 2036: to 2010 from

λ Migration rate α2 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 1 0

ftettlpplto safnto fdseso rates dispersion of function a as population total the of 0.1 0.2 t R by ( 0.3 t irto rate Migration = ) r i ( 0.4 t X i eemndb eovire l 21) h global The (2014). al. et Jenouvrier by determined ) 45 =1 0.5 21 r i ( 0.6 t ) > t , α 0.7 > R 1 0.8 0 . 0); 0.9 1

0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 r α i < R ( 2 t ) lassosdown slows always , htis that n max( and 0 α 1 and (D.5) r i ) α > 2 and from 2088 to 2100: globally poor landscape with only poor habitat colonies (R < 0 and • max(ri) < 0), except during two years for one colony in the Ross Sea with ri > 0.

These three periods correspond respectively to our three cases explained below. We have seen that in the case 1, the dispersion increases the global population size compared to a case without dispersion at least during a short period of time far from equilibrium. This is consistent with our observations from Fig. 2 from 2010 to 2036; the global population size increases faster with dispersion from poor quality colonies to favorable colonies than without dispersion.

For case 2, dispersion is expected to slow the extinction of the global population, which is observed in Fig. 2 from 2036 to 2088. Indeed, for all dispersion scenarios, the size of the global population remains signiﬁcantly higher than without dispersion.

Conversely, in case 3, we have seen that dispersion between colonies tends to accelerate the extinction of the global population when dispersion from the most favorable patch occurs. We observe from Fig. 2 that from 2088 to 2100, the curves corresponding to the long dispersal distance and high dispersion scenario tend to approach the curve without dispersion, indicating an acceleration of the extinction.

22 E Local and regional population dynamics

Although, we focused on the global population that sets species persistence in the face of climate change, our model operates at the local scale, and thus projects the regional meta-population dynamics that could also be relevant for speciﬁc management actions. This appendix E shows the population size at each colony, and the regional meta-population size for ﬁve major regions in

Antarctica (Fig. A.1).

E.1 Population size of each colony

Figures E.1 and E.2 describe the population dynamics of each colony without dispersion (gray line) and for the informed dispersal as an example. We observe that the dynamics at the local scale is much more complex than at the global scale. For example, we predict that immigration to

Umbeashi and Admundsen Bay colonies can locally rescue these colonies from extinction during the mid-century, especially with a long dispersal distance. Conversely, we observe a faster extinction of colonies in which the habitat begins to deteriorate early in the century, such as Ragnhild. In addition, some colonies will increase in size and reach carrying capacity during the mid-century (see

Ross Sea colonies, Queen Mary Land colonies, Enderby Land colonies and Snowhill and Dolleman colonies). In these cases, the size of several colonies can increase abruptly from year to year. This large increase in the number of individuals results from the second dispersal event when individuals that ﬁrst reach a saturated colony then settle randomly around it. Thus, penguins may reach an unsaturated colony or overcrowd the surrounding colonies as they settle randomly around the over-crowded target colony, resulting in high amplitude population variations.

23 4 Astrid Lazarev Ragnhild Gunnerus Snowhill Dolleman Smith x 10Gould 6000 5000 10000 2 4000 2000 10000 5000

4000 5000 1 2000 1000 5000

2000 0 0 0 0 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 4 4 Umbeashi Amundsen Bay Kloa Point Fold Island xLuitpold 10 Dawson x 10Halley Stancomb 2 10000 4 10000 200 500 4000 1000

1 5000 2 5000 100 2000 500

0 0 0 0 0 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 Drescher Riiser Atka Sanae Taylor Glacier Auster Cape Darnley Amanda Bay 10000 5000 10000 4000 2000 10000 10000 10000

5000 5000 2000 1000 5000 5000 5000

0 0 0 0 0 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 (a) (b)

Haswell Island Shackleton Ice Shelf Bowman Island Peterson Bank 4000 10000 2000 2000 4 Beaufort Island Cape CrozierCape Colbeckx Edward10 VII PeninsulaRupert Coast 5000 2000 3 4000 2000 5000 1000 1000 1000 2 2000 0 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 0 0 1 0 2050 2100 2050 2100 2050 2100 2050 2100 4 Dibblex 10 Glacier Point Geologie Mertz Glacier Davis Bay 2 4000 10000 4000 Thuston Glacier, Mt SipleBear Peninsula Brownson Islands Noville Peninsula 4000 10000 10000 4000

1 2000 5000 2000 2000 5000 5000 2000

0 0 0 0 0 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 4 4 4 4 Capex 10 Roget Coulmanx 10 Island Capex 10Washington Franklinx 10 Island Smyley Dion Islands 2 6 3 2 10000 1000

1 4 2 1 5000 500

0 2 1 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 (c) (d)

Figure E.1: Global number of breeding pairs of emperor penguins from 2010 to 2100 projected by the metapopulation model without dispersion (light gray thick line), or for the informed dispersal with high dispersion rates and a short dispersal distance (green line) at each colony.

24 Snowhill Dolleman Smith Gould Astrid Lazarev Ragnhild Gunnerus 6000 5000 5000 10000 2000 1000 10000 5000

4000 5000 1000 500 5000

2000 0 0 0 0 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 4 Umbeashi Amundsen Bay Kloa Point Fold Island Luitpold Dawson x 10Halley Stancomb 10000 5000 4 10000 400 400 4000 1000

5000 2 5000 200 200 2000 500

0 0 0 0 0 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 4 Drescher Riiser Atka Sanae Taylor Glacier x Auster10 Cape Darnley Amanda Bay 5000 5000 10000 4000 1000 2 10000 10000

5000 2000 500 1 5000 5000

0 0 0 0 0 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 (a) (b)

1 2000 5000 2000 2000 5000 5000 2000

1 5 2 1 5000 500

0 0 1 0 0 0 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 2050 2100 (c) (d)

Figure E.2: Global number of breeding pairs of emperor penguins from 2010 to 2100 projected by the metapopulation model without dispersion (light gray thick line), or for the informed dispersal with high dispersion rates and a long dispersal distance (green line) at each colony.

25 E.2 Regional population size

Figures from E.3 to E.6 describe the meta-population dynamics of each region deﬁned on ﬁgure

A.1 for various distance of dispersal.

Regional meta-population dynamics with or without dispersal processes strongly diﬀer for dispersal distance larger than 500 km. For a scenario with informed search, high emigration and short distance dispersal (1000 km), the meta-populations of the Indian Ocean, West Paciﬁc and

Bellingshausen and Amundsen Seas are almost extinct by the end of the century while the metapopulation in the Ross Sea reaches a plateau at high density. Obvioulsy, EPs leave poor habitat quality colonies of the Indian Ocean, West Paciﬁc and Bellingshausen and Amundsen Seas and settle in the Ross Sea colonies of better habitat quality. However, for a scenario with random search, high emigration and long distance dispersal, the meta-population of the Ross Sea crashes by the end of the century well below the size projected without dispersion, while the meta-population sizes of the other regions are similar or higher than the sizes projected without dispersion (Appendix

E). This crash occurs because the quality of the habitat decreases at end of the century in the

Ross Sea. As a result EPs leave the Ross Sea in mass (high emigration) but do not settle in higher quality colonies, given that EPs are more likely to settle in a poorest habitat than their resident colony when the dispersal distance is large (Fig. 4).

26 ×104 ×104 ×104 10 5

8 3 4

6 2 3 4 2 1 2 1 0 0 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100

(a) Wedell Sea (b) Indian Ocean (c) West Paciﬁc Ocean

×105 ×104 ×105 3 1.4 3 2.5 1.2 2 1 2 1 0.8 1.5

0.6 1 0 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100

(d) Ross Sea (e) Bellingshausen and Amundsen (f) Global Seas

Figure E.3: Regional and global number of breeding pairs of emperor penguins from 2010 to 2100 projected by the metapopulation model with a dispersal distance of 200 km. Thick light gray line is the population trajectory without dispersion. Colored solid lines are population trajectories under 1 1 high emigration rates (m (rc) = 0.9), while dashed lines show low emigration rates (m (rc) = 0.1). Green lines are trajectories under informed search, while red lines show the random search.

27 ×104 ×104 ×104 10 5

8 3 4

6 2 3 4 2 1 2 1 0 0 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100

(a) Wedell Sea (b) Indian Ocean (c) West Paciﬁc Ocean

×105 ×104 ×105 3 1.4 3 2.5 1.2 2 1 2 1 0.8 1.5

0.6 1 0 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100

(d) Ross Sea (e) Bellingshausen and Amundsen (f) Global Seas

Figure E.4: Regional and global number of breeding pairs of emperor penguins from 2010 to 2100 projected by the metapopulation model with a dispersal distance of 500 km. Thick light gray line is the population trajectory without dispersion. Colored solid lines are population trajectories under 1 1 high emigration rates (m (rc) = 0.9), while dashed lines show low emigration rates (m (rc) = 0.1). Green lines are trajectories under informed search, while red lines show the random search.

28 ×104 ×104 ×104 10 5

8 3 4

6 2 3 4 2 1 2 1 0 0 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100

(a) Wedell Sea (b) Indian Ocean (c) West Paciﬁc Ocean

×105 ×104 ×105 3 1.4 3 2.5 1.2 2 1 2 1 0.8 1.5

0.6 1 0 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100

(d) Ross Sea (e) Bellingshausen and Amundsen (f) Global Seas

Figure E.5: Regional and global number of breeding pairs of emperor penguins from 2010 to 2100 projected by the metapopulation model with a dispersal distance of 1000 km. Thick light gray line is the population trajectory without dispersion. Colored solid lines are population trajectories under 1 1 high emigration rates (m (rc) = 0.9), while dashed lines show low emigration rates (m (rc) = 0.1). Green lines are trajectories under informed search, while red lines show the random search.

29 ×104 ×104 ×104 10 5

8 3 4

6 2 3 4 2 1 2 1 0 0 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100

(a) Wedell Sea (b) Indian Ocean (c) West Paciﬁc Ocean

×105 ×104 ×105 3 1.4 3 2.5 1.2 2 1 2 1 0.8 1.5

0.6 1 0 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100

(d) Ross Sea (e) Bellingshausen and Amundsen (f) Global Seas

Figure E.6: Regional and global number of breeding pairs of emperor penguins from 2010 to 2100 projected by the metapopulation model with a dispersal distance of 6000 km. Thick light gray line is the population trajectory without dispersion. Colored solid lines are population trajectories under 1 1 high emigration rates (m (rc) = 0.9), while dashed lines show low emigration rates (m (rc) = 0.1). Green lines are trajectories under informed search, while red lines show the random search.

30 F Isolating the colonies on the Ross Sea

Recently, Younger et al. (2015) have shown that the EP population around Antarctica is genetically structured. In particular, the colonies on the Ross Sea (Cape Roget, Coulman Island, Cape Washington, Franklin Island, Beaufort Island, Cape Crozier, Cape Colbeck Edward VII Peninsula,

Rupert Coast) are genetically isolated from the others. This might be explained by a lack of dispersion between these colonies and the other colonies around Antarctica. In our initial approach, we did not take into account this genetic structure in the connectivity of the environment. How- ever, the isolation of the Ross Sea colonies may have critical consequences on the global population projection. These colonies are among the biggest in Antarctica, and they are projected to be the best colonies in term of habitat quality at the end of the century. So, if they are isolated from the others, local rescue eﬀects due to dispersion from poor quality habitat to high quality habitat might be reduced or vanish, and the global population size may be lower than if such isolation does not occur.

In order to address such an hypothesis, we have modiﬁed our metapopulation model such that immigration to colonies on Ross Sea and emigration from these colonies do not occur. We have thus demographically isolated the Ross Sea colonies by setting the settling probabilities, Se, to zero between these colonies and the other colonies. More precisely, the colonies are numbered from 1 to

45, and the Ross Sea colonies’ label range from iR = 33 to iR = 40 (see Table 1 of Supplementary Appendix 6). The searching matrices Se, e 1, 2 , is thus ∈ { }

Se = Se = 0 for all j = i , i 33, , 40 and j 1, , 46 . (F.1) iR,j j,iR 6 R R ∈ { ··· } ∈ { ··· }

Note that we only assume that the Ross Sea colonies are isolated from the rest of the colonies; dispersal among the Ross Sea colonies occurs with either random or informed dispersal.

Figures 1(a) and 1(b) show that isolating the Ross Sea colonies does not reduce the ecological rescue eﬀect observed during the period from 2036 to 2050 when all colonies are connected. How- ever, it does accelerate the decline of the global population during the second half of the century, decreasing the global population by up to 15% at the end of the century for a random search and

31 long dispersal distance compared to a scenario without dispersion.

32 x 105 x 105 2.8 2.8 2.6 2.6 2.4 2.4 2.2 2.2 2 2 1.8 1.8 1.6 1.6 1.4 1.4 total population size total population size 1.2 1.2 1 1 0.8 0.8 2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 time (t) time (t) (a) Short-distance dispersion (d = 1000 km) (b) Long-distance dispersion (d = 6000 km)

Figure F.1: Global number of breeding pairs of emperor penguins from 2010 to 2100 projected by the metapopulation model without dispersion (light gray thick line), for a random search dispersal (red lines) and an informed search dispersal (green lines). Colored solid lines are population trajectories 1 1 under high dispersion rates (m (rc) = 0.9), while dashed lines show low dispersion rates (m (rc) = 0.1).

33 G Random departure and random search dispersal

In our study we have investigated two diﬀerent dispersal searching behaviors: random search and informed search. We assume that the decision to leave the resident patch is always informed (i.e. informed departure) because the emigration rate M1 depends on the patch quality measured by the realized population growth r∗. In order to compare our results with a random departure and search, we use an emigration rate that does not depend on the realized growth rate r∗. Thus the emigration rate during the ﬁrst dispersal event is

M1 := m1 Id, (G.1) where the probability of leaving a colony m1 is a constant in the range (0, 1) and Id is the identity matrix. Under this scenario, even individuals from good quality habitat may leave their colony during the ﬁrst dispersal event.

Figures 1(b) and 1(a) show that the global population size projected with a random dispersal always has a lower size compared to population trajectories projected without dispersion or other dispersal behaviors. In the context of an Evolutionary Stable Strategy, Holt (1985) and Hastings

(1983) have already shown that random dispersal is always worse than a philopatry strategy (i.e. no dispersion) in temporally constant but spatially varying environment. In our empirical example, the environment varies spatially and temporally, but their results hold.

34 x 105 x 105

2.5 2.5

2 2

1.5 1.5

1 1

0.5 0.5

2020 2040 2060 2080 2100 2020 2040 2060 2080 2100 (a) Short-distance dispersion (d = 1000 km) (b) Long-distance dispersion (d = 6000 km)

Figure G.1: Global number of emperor penguins breeding pairs from 2010 to 2100 projected by the metapopulation model without dispersion (light gray thick line); informed departure and search (green lines); informed departure but random search (red lines); random departure and search 1 dispersal (blue lines). Solid lines show a high dispersion rate (m (rc) = 0.9), while dotted lines are 1 a low dispersion rate (m (rc) = 0.1).

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