Monthly Analysis of Teal Ring-Recovery Data

Diana Cole, Takis Besbeas, and Byron Morgan

Introduction

• Interested in modelling survival of Teal (Anas Crecca)

• Ring-Recovery Data available• Standard analysis would be biased because

– Teal are born in April– Ringing Year starts in August– Ringed in November, December or January

Standard Model (Annual / Annual)

1 – first year survival probability (annual survival)

a – adult survival probability (annual survival)

– reporting probability

j

i No. ringed 1 2 3 4

1 132 10 2 0 0

2 23   2 1 0

3 426   29 18

4 447       38

ij

jip

aij

a

ij

)1(

)1(1

1

1

Simulation• Simulated data with 40 years of ringing and

recovery, 200 animals ringed each year 1 = 0.3

a = 0.5

= 0.2

• mb month animal born (in previous year)

• mr month animal ringed

• Parameters estimated using the standard yearly model. Simulation repeated 100 times.

Simulation Standard Model (Annual / Annual Model)

1 a

True Value 0.3 0.5 0.2

mb mr mean bias std mean bias std mean bias std

13 (Aug) 1 (Aug) 0.30 0.00 0.011 0.50 0.00 0.017 0.20 0.00 0.004

12 (Jul) 1 (Aug) 0.31 0.01 0.012 0.50 0.00 0.018 0.20 0.00 0.005

9 (Apr) 5 (Dec) 0.53 0.23 0.012 0.50 0.00 0.014 0.20 0.00 0.004

Annual / Monthly Model

1,m – 1st y. monthly survival probability 1,m12 = 1

a,m – adult monthly survival probability a,m12 = a

– reporting probability

model assumes ringed in December

j

i No. ringed 1 2 3 4

1 132 10 2 0 0

2 23   2 1 0

3 426   29 18

4 447       38

ij

jip

ma

ij

mam

mam

ij

)1(

)1(12

,

4)1(12

,

4

,1

4,

4,1

Simulation mb = 9 (Apr), mr = 5 (Dec)

1 a

Model

0.3 0.5 0.2

mean bias std mean bias std mean bias std

annual / annual 0.53 0.23 0.012 0.50 0.00 0.014 0.20 0.00 0.004

annual / monthly 0.30 0.00 0.017 0.50 0.00 0.015 0.20 0.00 0.004

Simulation mb = 9 , mr = 4 (52%), 5 (31%), 6 (17%)

1 a

Model

0.3 0.5 0.2

mean bias std mean bias std mean bias std

annual / annual 0.52 0.22 0.029 0.50 0.00 0.027 0.20 0.00 0.009

annual / monthly 0.28 0.02 0.055 0.50 0.00 0.028 0.20 0.00 0.009

Monthly / Monthly Model

Bird i, ringed in year yr, recovered in year yc, born in month

mb = 9, ringed in month mr, recovered in month mc has probability

bcrcmammyy

mamm

m

bcrcmamm

mamm

m

bcrcmmm

m

i

mm yy

mm yy

mm yy

P

bcrcrb

bcrb

rc

and if)1(

and if)1(

and if)1(

,)(12

,,1

,,,1

,1,1

Index (i) Ringyr (yr) Ringmo (mr) Recyr (yc) Recmo (mc)

1 1959 4 1960 6

2 1959 4 1959 4

3 1959 4 1964 5

4 1959 4 1959 4

Simulation mb = 9 , mr = 4 (50%), 5 (23%), 6 (17%)

1 a

Model

0.3 0.5 0.2

mean bias std mean bias std mean bias std

annual / annual 0.52 0.22 0.029 0.50 0.00 0.027 0.20 0.00 0.009

annual / monthly 0.28 0.02 0.055 0.50 0.00 0.028 0.20 0.00 0.009

monthly / monthly 0.30 0.00 0.035 0.50 0.00 0.025 0.20 0.00 0.009

Results

model 1 a

annual/annual 0.46 (0.037) 0.55 (0.045) 0.10 (0.004)

annual/monthly 0.18 (0.029) 0.55 (0.045) 0.10 (0.004)

monthly/monthly 0.11 (0.015) 0.59 (0.046) 0.10 (0.004)

Conclusion and Further Work

• If birds are not ringed soon after birth and / or the ringing year does not start when the birds are ringed, there will be bias in estimating first year survival.

• A monthly structure will remove this bias• Survival does not have to be the same each month –

e.g. lower survival in winter• Teal data also include birds ringed as adults. The sex of

the bird is known. Most of the returns were hunted (2% not hunted).

• Also census data on Teal. Plan to include this as part of an integrated statistical analysis.