Online appendix 1: Detailed statistical tests referred to in Wild goose dilemmas by Black, Prop & Larsson

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1 Online appendix 1: Detailed statistical tests referred to in Wild goose dilemmas by Black, Prop & Larsson Table 1. Variation in length of goslings association (days) with parents in relation to birth year and gosling sex. Length of association was a function of birth year. General Linear Models Procedure (SAS 1996). Class variables included: Birth year (1977, , , 1995), and gosling sex (Female, Male, Unknown). The Dependent Variable was number of days spent with parents starting from 27 Sept., the first arrival back to Scotland (n = 542 birds, range days, R 2 = 0.060, CV = , root MSE = days, mean number days with parents days). See Fig Source df Type III SS Mean square F P Model Error Corrected Total Birth year Gosling sex

2 Table 2. Variation in offspring parent length of association for (A) female and (B) male goslings. Length of association was a function of natal brood size, controlled for birth year. General Linear Models Procedure (SAS 1996). Class variables included: Birth year (1986, , 1995), and brood size (1 6, 8). The Dependent Variable was number of days spent with parents starting from 27 Sept., the first arrival back to Scotland (female and male range days)(female n = 192, R 2 = 0.180, CV = 79.05, root MSE = days, mean number days with parents days)(male n = 213, R 2 = 0.127, CV = 88.79, root MSE = days, mean number days with parents days). See Fig (A) Female goslings Source df Type III SS Mean square F P Model Error Corrected Total Birth year Natal brood size (B) Male goslings Source df Type III SS Mean square F P Model Error Corrected Total Birth year Natal brood size

3 Table 3. Variation in goslings parent length of association in relation to brood size and sex ratio within the brood. General Linear Models Procedure (SAS 1996). A more conservative data set was used in this analysis, including only birds that arrived together with parents, thus excluding the earliest orphaned goslings. Class variables included birth year (1986, , 1995), natal brood size (1 4, 6) and sex ratio of brood (male alone, female alone, male only with other males, female only with other females, male with more than one female, female with more than one male, equal sex ratio). The Dependent Variable was number of days spent with parents starting from 27 Sept., the first arrival back to Scotland (range days)(n = 340 birds, R 2 = 0.137, CV = 70.87, root MSE days, Mean number of days with parents days). Referred to in Chapter 5, stats note 9. (1) Overall model Source df Type III SS Mean square F P Model Error Corrected Total Birth year Natal brood size Brood sex ratio Testing length of gosling parent association in relation to brood sex ratio for each sex separately indicated that the link between association with parents was stronger in males than in females (females n = 165, df = 4, Type III SS = , Mean Square , F = 1.15, P = )(males n = 175, df = 4, Type III SS = , Mean Square , F = 2.54, P = ).

4 Table 4. Variation in age of first breeding was a function of length of association with parents for (A) males, but not (B) females. General Linear Models Procedure (SAS 1996) for the 1986 cohort. Class variable: natal brood size (0 4). The Dependent Variable was age of first breeding for the 1986 cohort (range 2 9 yrs)(males n = 59, R 2 = 0.254, CV = , root MSE 2.51 yrs, Mean age of first breeding = 1.81 yrs)(females n = 61, R 2 = 0.046, CV = , root MSE 2.61 yrs, mean age of first breeding = 1.62 yrs). Referred to in Chapter 5, stats note 13. (A) Male goslings Source df Type III SS Mean square F P Model Error Corrected Total Natal brood size Length of association (B) Female goslings Source df Type III SS Mean square F P Model Error Corrected Total Natal brood size Length of association A similar set of results indicating male age of first breeding was a function of length of association with parents (df = 1, Type III SS = 25.11, Mean Square 25.11, F Value 4.91, P = ) was found with an increased sample (234 birds) from multiple birth-years ( , 79, 86 87, 89 93), while controlling for gosling birth year (df = 10, Type III SS = , Mean Square = 30.45, F Value = 5.96, P < ). Dependent variable, age of first breeding, was not influenced by the independent variables, (i) lifespan, or (ii) original family size. None of the models for either sex (n = 61 females, n = 59 males) approached the 0.05 level of significance in a step-wise General Linear Model procedure (SAS 2001). Average lifespan was 7.5 years for nonfamily goslings (brood size = 0) and 7.6 for family goslings (those still together on arrival in Scotland).

5 Table 5. Program MARK results modelling survival (Phi Φ) of 1972 barnacle goose cohort from Dunøyane colony. The smallest Delta QAICc indicates the best model; in this case the values for a linear and quadratic trend (with bird-age) are almost equal (0 and 0.01, respectively). QAICc weights denote strength of evidence for a given model as the most parsimonious model in the set and summing QAICc weights of all models containing the variable of interest gives a score of the importance of the variable. For example, the sum of all scores including linear and quadratic trends is 0.56 and 0.41, respectively, whereas models not including an age effect only amounts Models including sex were also quite strong indicating variation between the sexes; sum of QAICc weights with sex (0.58) compared to without sex (0.41). Model selection based on c-hat = Sample size: 46 males and 44 females captured as yearlings. Detection probabilities were held constant. Resightings of individually marked geese were recorded on a daily basis throughout the 7-month wintering period and periodically at other times of year. See Fig Delta QAICc Model Survival (Φ) QAICc Weight #Par QDeviance 1 Φ linear trend with age Φ quadratic trend with age Φ sex+linear trend with age Φ sex*linear trend with age Φ sex+quadratic trend with age Φ sex*quadratic trend with age Φ annual variation Φ sex+annual variation

6 Table 6a. Multi-strata model selection results for female barnacle goose (n = 3,429) cost of reproduction and social feedback loop analysis. Models include parameters for survival (Phi Φ), detection (p) and transition (Psi ψ) probabilities for non-breeder (N) and breeder (B) strata. Covariates include (t) time ( ), (a) bird age (3 23 years), annual reproductive success (ars), cumulative reproductive success (crs), and skull length (skull) as an index for body size. Model number 1 is the most parsimonious model for the data, indicating that female survival varied between breeders and non-breeders (see Fig. 14.3) and that larger females with a larger cumulative reproductive success were more likely to move from a non-breeder to breeder state, and that females with a larger cumulative reproductive success were less likely to move from a breeding to non-breeding status (see Fig ). Likelihood ratio tests (LRT) were performed on competing nested models. P-values < 0.05 indicate that the additional parameter provides significantly more information than the reduced model. P-values > 0.05 indicate no additional information in the additional parameter, so parsimony requires considering the reduced model superior to the model with additional parameter(s). Non-nested models cannot be tested by LRT, and rely on AIC to select the model containing the most information. We first examined the possibility that age structure (model # 12) should be used in lieu of time (year) as the main source of temporal variation. Delta AIC value between time and age structured models was 665, meaning time structure explained much more variation in the data than age structure. We continued model selection with time structure in all parameters. See Fig. 10.2, Model Survival (Φ) Resight (p) Movement (ψ) non breed breed non Φ (t+state) p N(t) = p B(t) ψ N to B(t+crs+skull) ψ B to N (t+crs) Φ (t+state) p N(t) = p B(t) ψ N to B(t+crs+skull) ψ B to N(t+crs+skull) Φ (t+state+skull) p N(t) = p B(t) ψ N to B(t+crs+skull) ψ B to N(t+crs) Φ (t+state) p N(t) = p B(t) ψ N to B(t+crs) ψ B to N(t+crs) Φ (t+state) p N(t) = p B(t) ψ N to B(t+crs) ψ B to N(t+crs+ars) Φ (t+state) p N(t) = p B(t) ψ N to B(t) ψ B to N(t) Φ (t+state+crs) p N(t) = p B(t) ψ N to B(t) ψ B to N(t) Φ (t+state,b+ars) p N(t) = p B(t) ψ N to B(t) ψ B to N(t) Φ N(t) = Φ B(t) p N(t) = p B(t) ψ N to B(t) ψ B to N(t) Φ N(t) Φ B(t) p N(t) = p B(t) ψ N to B(t) ψ B to N(t) Φ N(t) Φ B(t) p N(t) p B(t) ψ N to B(t) ψ B to N(t) TIME Φ N(a) Φ B(a) p N(a) p B(a) ψ N to B(a) ψ B to N(a) AGE Φ N(t) Φ B(t) p N(t) = p B(t) ψ N to B(t) = ψ B to N(t) Delta AICc AICc Weight #Par Deviance test χ 2 df P-value vs vs vs < vs vs vs vs vs vs vs <.0001

7 Table 6b. Multi-strata model selection results for male barnacle goose (n = 3,428) cost of reproduction and social feedback loop analysis. Models include parameters for survival (Phi Φ), detection (p) and transition (Psi ψ) probabilities for non-breeder (N) and breeder (B) strata. Covariates include (t) time ( ), (a) bird age (3 23 years), annual reproductive success (ars), cumulative reproductive success (crs), and skull length (skull) as an index for body size. Model number 1 is the most parsimonious model, indicating that male survival is the same for breeders and non-breeders (see Chapter 14) and that larger males with a larger cumulative reproductive success were more likely to move from a non-breeder to breeder state, and that males with a larger cumulative reproductive success were less likely to move from a breeding to non-breeding status (see Fig ). Likelihood ratio tests (LRT) were performed on competing nested models. P-values < 0.05 indicate that the additional parameter provides significantly more information than the reduced model. P-values > 0.05 indicate no additional information in the additional parameter, so parsimony requires considering the reduced model superior to the model with additional parameter(s). Non-nested models cannot be tested by LRT, and rely on AIC to select the model containing the most information. We first examined the possibility that age structure (model # 12) should be used in lieu of time (year) as the main source of temporal variation. Delta AIC value between time and age structured models was 638, meaning time structure explained much more variation in the data than age structure. We therefore continued model selection with time structure in all parameters. See Fig. 10.2, Model Survival (Φ) Resight (p) Movement (ψ) Non breed non breed non breed breed non Φ N(t) = Φ B(t) p N(t) p B(t) ψ N to B(t+crs+skull) ψ B to N(t+crs) Φ N(t) = Φ B(t) p N(t) p B(t) ψ N to B(t+crs+skull) ψ B to N(t+crs+skull) Φ N(t) = Φ B(t+ars) p N(t) p B(t) ψ N to B(t+crs+skull) ψ B to N(t+crs) Φ N(t+crs) = Φ B(t+ars+crs) p N(t) p B(t) ψ N to B(t+crs+skull) ψ B to N(t+crs) Φ N(t) = Φ B(t) p N(t) p B(t) ψ N to B(t+crs) ψ B to N(t+crs+ars) Φ N(t) = Φ B(t) p N(t) p B(t) ψ N to B(t+crs) ψ B to N(t+crs) Φ N(t) = Φ B(t) p N(t) p B(t) ψ N to B(t) ψ B to N(t) Φ (t+state) p N(t) p B (t) ψ N to B(t) Φ N(t+skull) = Φ B(t+skull) p N(t) p B(t) ψ N to B(t) ψ B to N(t) ψ B to N(t) Φ N(t) Φ B(t) p N(t) p B(t) ψ N to B(t) ψ B to N(t) Φ N(t) Φ B(t) p N(t) = p B(t) ψ N to B(t) ψ B to N(t) Φ N(a) Φ B(a) p N(a) p B(a) ψ N to B(a) ψ B to N(a) Φ N(t) Φ B(t) p N(t) p B(t) ψ N to B(t) = ψ B to N(t) Delta AICc 0.9 AICc Weight #Par Deviance test χ 2 df P-value vs vs vs vs vs < vs vs vs vs < vs <.0001

8 Table 7. Program MARK table of model selection results for apparent survival (Phi Φ) of the 1985 female barnacle geese from two different colonies (colony 1, Dunøyane (n = 49); Colony 2, Nordenskiöldkysten (n = 81). Delta QAICc of zero indicates the best model. Detection probability (p). QAICc weights denote strength of evidence for a given model as the best model in the set. The top model has 0.85 QAICc weight indicating overwhelming evidence that apparent survival of the two colonies were different. Model selection based on c-hat = Detection probabilities were held constant. Resightings of individually marked geese were recorded on a daily basis throughout the 7-month wintering period and periodically at all other times of year. See Fig Model Survival (Φ) QAICc Delta QAICc QAICc Weights Model Likelihood Number of parameters Qdeviance 1 Φ (colony) Φ (.) Φ (colony+year) Φ (year) Φ (colony*year)

9 Table 8. Model selection results for barnacle goose annual movement and fidelity to spring staging sites in Helgeland, Norway ( ). Age differences were included in top model as determined by AIC. The data set was grouped by age class where spring-time location (month of May) was for 1) yearlings (22 mo of age) in relation to their previous location as 10 mo old goslings, 2) youngadults (34 mo of age) in relation to their previous location as yearlings, and 3) adults (46+ mo of age) in relation to their previous location as younger adults. The data set included 2,212 tarsal-banded birds resighted over 5 years at three locations among traditional, outer island and recently discovered agricultural sites. Trends indicated move movement toward the agricultural site, especially by younger birds. Older birds were more site faithful at all locations. See Fig Model Survival (Φ) Detectability (p) Movement (ψ) AICc Delta AICc AICc Weight #Par Deviance 1 Φ (age+t+site) p (age+t+site) ψ (age+site) Φ (age+t+site) p (age+t+site) ψ (age+t+site) Φ (age+t+site) p (t+site) ψ (age+t+site) Φ (t+site) p (age+t+site) ψ (age+t+site) Φ (age+t+site) p (age+t+site) ψ (site)