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Consequences of violating assumptions of integrated population models on parameter estimates

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parameter estimates

Floriane Plard, Daniel Turek and Michael Schaub

Supplementary material

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−0.20

−0.10 0.00 0.10

recapture probability

−0.20

−0.10 0.00 0.10 0.20

adult survival

−0.20

−0.10 0.00 0.10 0.20

juvenile survival

−1.00

−0.50 0.00 0.50 1.00

reproductive success

Model

IPM0 all IPM0 S−

IPM0 R−

IPMi all IPMi S−

IPMi R−

Fig. 1: Comparison of bias for estimates of recapture probabilities, juvenile and adult survival, and reproductive success in a short-lived species when dierent amount of data have been used.

6 scenarios are shown: null scenario, 1: Heterogeneity in recapture when only breeders are recap- tured 2: Heterogeneity in timing of the collection of datasets. 3: Immigration inuences population dynamics. 4: Non-breeders inuence population dynamics: breeding probability<1. 5: Density- dependent eect on reproductive success. Parameters were estimated underIP M0(beige/yellow) andIP Mi(reddish). Violin plots show the distributions of mean bias over 1000 simulations. The median of each distribution is shown with a black point. Survival and reproductive parameters

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−0.20

−0.10 0.00

recapture probability

−0.20

−0.10 0.00 0.10 0.20

adult survival

−0.20 0.00 0.20 0.40

juvenile survival

−0.20

−0.10 0.00 0.10 0.20

reproductive success

−0.40

−0.30

−0.20

−0.10 0.00

Model

IPM0 all IPM0 S−

IPM0 R−

IPMi all IPMi S−

IPMi R−

Fig. 2: Comparison of bias for estimates of recapture probabilities, juvenile and adult survival, and reproductive success in a long-lived species when dierent amount of data have been used. 6 scenarios are shown: null scenario, 1: Heterogeneity in recapture when only breeders are recap- tured 2: Heterogeneity in timing of the collection of datasets. 3: Immigration inuences population dynamics. 4: Non-breeders inuence population dynamics: breeding probability<1. 5: Density- dependent eect on reproductive success. Parameters were estimated underIP M0(beige/yellow) andIP Mi (reddish). Violin plots show the distributions of mean bias over 1000 simulations. The median of each distribution is shown with a black point. Survival and reproductive parameters were estimated with 100% of all the collected data (all: violin plots with a black border), using 20% of the survival data (and 100% of the reproductive and count dataset: S-), and using 20%

of the reproductive dataset (and 100% of the survival and count dataset: R-).

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0.000 0.050 0.100 0.150

recapture probability

0.000 0.050 0.100 0.150 0.200

adult survival

0.000 0.050 0.100 0.150 0.200

juvenile survival

0.000 0.250 0.500 0.750 1.000 1.250

reproductive success

Model

IPM0 all IPM0 S−

IPM0 R−

IPMi all IPMi S−

IPMi R−

Fig. 3: Comparison of mean square errors (MSE) for estimates of recapture probabilities, juvenile and adult survival, and reproductive success in a short-lived species when dierent amount of data have been used. 6 scenarios are shown: null scenario, 1: Heterogeneity in recapture when only breeders are recaptured 2: Heterogeneity in timing of the collection of datasets. 3:

Immigration inuences population dynamics. 4: Non-breeders inuence population dynamics:

breeding probability<1. 5: Density-dependent eect on reproductive success. Parameters were estimated underIP M0 (beige/yellow) and IP Mi (reddish). Violin plots show the distributions of mean MSE over 1000 simulations. The median of each distribution is shown with a black point.

Survival and reproductive parameters were estimated with 100% of all the collected data (all:

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0.000 0.005 0.010

recapture probability

0.000 0.010 0.020 0.030 0.040 0.050

adult survival

0.000 0.100 0.200 0.300

juvenile survival

0.000 0.010 0.020 0.030 0.040

reproductive success

0.00 0.05 0.10

Model

IPM0 all IPM0 S−

IPM0 R−

IPMi all IPMi S−

IPMi R−

Fig. 4: Comparison of mean square errors (MSE) for estimates of recapture probabilities, juve- nile and adult survival, and reproductive success in a long-lived species when dierent amount of data have been used. 6 scenarios are shown: null scenario, 1: Heterogeneity in recapture when only breeders are recaptured 2: Heterogeneity in timing of the collection of datasets. 3: Immigra- tion inuences population dynamics. 4: Non-breeders inuence population dynamics: breeding probability<1. 5: Density-dependent eect on reproductive success. Parameters were estimated under IP M0 (beige/yellow) and IP Mi (reddish). Violin plots show the distributions of mean MSE over 1000 simulations. The median of each distribution is shown with a black point. The median of each distribution is shown with black point. Survival and reproductive parameters were estimated with 100% of all the collected data (all: violin plots with a black border), using 20% of the survival data (and 100% of the reproductive and count dataset: S-), and using 20%

of the reproductive dataset (and 100% of the survival and count dataset: R-).

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−0.20

−0.10 0.00 0.10

recapture probability

−0.20

−0.10 0.00 0.10 0.20

adult survival

−0.20

−0.10 0.00 0.10 0.20

juvenile survival

−0.50 0.00 0.50

reproductive success

Model

SD IPM0 IPMi

Fig. 5: Comparison of bias for estimates of recapture probabilities, juvenile and adult survival, and reproductive success in a short-lived species using a Poisson distribution for the likelihood of the count data. 6 scenarios are shown: null scenario, 1:Heterogeneity in recapture when only breeders are recaptured 2: Heterogeneity in timing of the collection of the three datasets. 3:

Immigration inuences population dynamics. 4: Non-breeders inuence population dynamics:

breeding probability<1. 5: Density-dependent eect on reproductive success. Parameters were estimated under single data CMR and reproduction models (SD, white), simpleIP M0 (beige) and IP Mi (red). Violin plots show the distributions of mean bias over 1000 simulations. The

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−0.20

−0.10 0.00

recapture probability

−0.20

−0.10 0.00 0.10 0.20

adult survival

−0.20

−0.10 0.00 0.10 0.20

juvenile survival

−0.20

−0.10 0.00 0.10 0.20

reproductive success

−0.40

−0.30

−0.20

−0.10 0.00

Model

SD IPM0 IPMi

Fig. 6: Comparison of bias for estimates of recapture probabilities, juvenile and adult survival, and reproductive success in a long-lived species using a Poisson distribution for the likelihood of the count data. 6 scenarios are shown: null scenario, 1:Heterogeneity in recapture when only breeders are recaptured 2: Heterogeneity in timing of the collection of the three datasets. 3:

Immigration inuences population dynamics. 4: Non-breeders inuence population dynamics:

breeding probability<1. 5: Density-dependent eect on reproductive success. Parameters were estimated under single data CMR and reproduction models (SD, white), simple IP M0 (beige) and IP Mi (red). Violin plots show the distributions of mean bias over 1000 simulations. The median of each distribution is shown with a black point.

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0.000 0.025 0.050 0.075

recapture probability

0.000 0.025 0.050 0.075 0.100

adult survival

0.000 0.025 0.050 0.075 0.100

juvenile survival

0.000 0.100 0.200 0.300 0.400

reproductive success

Model

SD IPM0 IPMi

Fig. 7: Comparison of mean square errors (MSE) for estimates of recapture probabilities, juvenile and adult survival, and reproductive success in a short-lived species using a Poisson distribution for the likelihood of the count data. 6 scenarios are shown: null scenario, 1:Heterogeneity in recapture when only breeders are recaptured 2: Heterogeneity in timing of the collection of the three datasets. 3: Immigration inuences population dynamics. 4: Non-breeders inuence population dynamics: breeding probability < 1. 5: Density-dependent eect on reproductive success. Parameters were estimated under single data CMR and reproduction models (SD, white), simpleIP M0 (beige) and IP Mi (red). Violin plots show the distributions of mean MSE over

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0.000 0.005 0.010

recapture probability

0.000 0.005 0.010 0.015 0.020

adult survival

0.000 0.025 0.050 0.075 0.100

juvenile survival

0.000 0.005 0.010 0.015 0.020

reproductive success

0.00 0.05 0.10

Model

SD IPM0 IPMi

Fig. 8: Comparison of mean square errors (MSE) for estimates of recapture probabilities, juvenile and adult survival, and reproductive success in a long-lived species using a Poisson distribution for the likelihood of the count data. 6 scenarios are shown: null scenario, 1:Heterogeneity in recapture when only breeders are recaptured 2: Heterogeneity in timing of the collection of the three datasets. 3: Immigration inuences population dynamics. 4: Non-breeders inuence population dynamics: breeding probability < 1. 5: Density-dependent eect on reproductive success. Parameters were estimated under single data CMR and reproduction models (SD, white), simple IP M0 (beige) and IP Mi (red). Violin plots show the distributions of mean MSE over 1000 simulations. The median of each distribution is shown with a black point.

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Fig. 9: Graphical representation of the scenario 2 where the count occurred 6 months after the recapture of females and the monitoring of reproductive success, compared to other scenarios.

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