TAIGA BEAN GOOSE POPULATION MODELLING PROGRESS … · doc. aewa/egmiwg/inf.5.16 date: 22 may 2020...

Doc. AEWA/EGMIWG/Inf.5.16

Date: 22 May 2020

AEWA EUROPEAN GOOSE MANAGEMENT PLATFORM

5th MEETING OF THE

AEWA EUROPEAN GOOSE MANAGEMENT

INTERNATIONAL WORKING GROUP

15-18 June 2020, Online conference format

The 5th Meeting of the AEWA European Goose Management International Working Group is taking place remotely in

an online conference format.

TAIGA BEAN GOOSE POPULATION MODELLING PROGRESS REPORT

AEWA EUROPEAN GOOSE MANAGEMENT PLATFORM

TAIGA BEAN GOOSE POPULATION MODELING PROGRESS REPORT

March 31, 2020

1

An Integrated Population Model for the

Central Management Unit of Taiga Bean Geese

Prepared by the EGMP Data Centre: Fred A. Johnson, Aarhus University, Denmark

Samu Mäntyniemi, Natural Resources Institute, Finland Henning Heldbjerg, Aarhus University, Denmark

Summary

In 2019, Finland (Finnish Wildlife Agency and Natural Resources Institute) funded the development of an integrated population model (IPM) for the purpose of improving harvest management for the Central Management Unit of Taiga Bean Goose (Anser fabalis fabalis). This document describes progress on development of that IPM. Due to a paucity of data for this population, we relied heavily on previous work to specify model structure and for parameterizing prior distributions of model parameters. Observational data included population counts from Sweden at three times during the year (January, March, and October) and estimates of harvest from Finland, Sweden, and Denmark. Both counts and harvest estimates contain some relatively small, but largely unknown, portion of the tundra subspecies (Anser fabalis rossicus). Among key demographic parameters, only the posterior distribution for reproductive rate, differed markedly from its prior distribution. This was not unexpected due extrinsic identifiability problems arising from the limited nature of the available data. The posterior estimate of the slope of the relationship between the January count and January temperature in southern Sweden was positive, suggesting that January counts are biased low in cold winters. On average, the January count was 44% less than the true abundance. Results suggest strong population growth coincident with a sharp decrease in harvest pressure that accompanied the Finnish harvest moratorium in 2014. For the last five years, the January and March populations appear to have been within the management target of 60-80k at the end of winter, with the most recent estimates of abundance approaching the upper bound. If the desire is to keep the population near the median target of 70k, some harvest liberalization may be permissible. A total harvest of 7800, in which 4600 is allocated to Finland, 2300 to Sweden, and 900 to Denmark, could be expected to maintain the population near the median goal over the long term. For comparison, the mean total harvest in the last five years was 3347, with an average of 45, 2199, and 1103 Bean Geese harvested in Finland, Sweden, and Denmark, respectively. A final report from this project will be available in October 2020.

Integrated Population Model for Taiga Bean Geese

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Introduction

The International Single Species Action Plan for the Conservation of Taiga Bean Goose (Marjakangas et al. 2015) recognized a dramatic and range-wide decline in population size and thus mandated a variety of corrective measures. Chief among these was the development and implementation of an international Adaptive Harvest Management (AHM) framework to adjust harvest levels to reflect the status of the population, based on agreed upon objectives, management alternatives, predictive models, effective monitoring programs, and iterative learning. This report focuses on the Central Management Unit of Taiga Bean Goose, encompassing breeding areas in northernmost Sweden, Northern and Central Finland, Northeast Norway, and in Russian Karelia, the Kola Peninsula and Arkhangelsk district. Abundance of Taiga Bean Geese in the Eastern and Western Management units is considered too low to support recreational harvest. An initial assessment of harvest potential for the Central Management Unit was completed in 2016. In 2017, the European Goose Management Platform adopted a strategy consisting of a constant harvest rate of 3% to assist recovery of the population while providing limited hunting opportunities. In 2018, significant advances were made in harvest-assessment methods for species with sparse data, using taiga bean geese as a case study (Johnson et al. 2018). In 2019, Finland (Finnish Wildlife Agency and Natural Resources Institute) funded the development of an integrated population model (IPM) for the purpose of further improving harvest management. This document describes progress on development of that IPM. Integrated population models represent an advanced approach to modeling, in which all available demographic data are incorporated into a single analysis. IPMs have many advantages over traditional approaches to modeling, including the proper propagation of demographic uncertainty, better precision of demographic rates and population size, the ability to handle missing data and estimate latent (i.e., unobserved) variables, and the capacity to guide development of monitoring programs. Moreover, use of a Bayesian estimation framework for IPMs provides a natural framework for adaptation, in which model parameters can be updated over time based on observations from operational monitoring. The following sections describe the model of population dynamics, the sources of data used to fit the model, some preliminary results, and recommendations for further work.

Methods Population Dynamics Due to a paucity of data for this population, we relied heavily on previous work to specify model structure and for parameterizing prior distributions of model parameters (Johnson et al. 2018). In particular, we relied on the discrete theta-logistic model rather than on an age-specific matrix model. The theta-logistic model appears to be capable of providing reasonable management performance even if the population is age structured (Johnson et al. 2018). A key consideration in constructing the IPM is how to account for abundance that is observed at multiple times during the annual cycle. Counts of Taiga Bean Geese are available in January, March, and October (albeit with some level of contamination from Tundra Bean Geese, Anser fabalis rossicus). We consider March abundance as the start of the breeding season and the annual cycle. The challenge is to reframe the theta-logistic model, which only predicts annual changes in abundance, to one that will predict population size at other times during the year. In the following, we show how this can be done, initially assuming no density dependence in survival or production, and then accounting


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for density dependence. In this approach we make a limited number of assumptions: (1) all production occurs between March and October; (2) natural mortality is evenly distributed throughout the year; (3) density-dependence acts on both production and annual survival, and is based on abundance in March; and (4) the Finnish harvest represents the number of birds taken prior to the October count (Mikko Alhainen, personal communication). To accommodate multiple counts during the year, we begin with the theta-logistic model with density dependence:

(1)

1 1

1 1

tt t t t

tt t

NN N N r H

K

NN r H

K

where N is population size, r is the intrinsic (or maximum) rate of growth, K is carrying capacity, θ is a parameter describing the type of density dependence (i.e., concave, linear, or convex), H is total harvest, and t is year. Now we omit harvest and density dependence:

(2)

1

1t t t

t

N N N r

N r

The expression 1 r is the finite rate of population growth, which can also be expressed in terms of

survival from natural causes, ψ, and production, :

(3)

1t t t

t

N N N

N

Therefore:

(4) 1

1

r

r

In the theta-logistic model, the realized rate of growth results from a reduction in the intrinsic rate of growth based on the size of the population relative to carrying capacity:

(5) 1 tNr r

K

Thus, to incorporate density dependence into a model with explicit survival and production rates, we

simply multiply both sides of Equation 4 by 1 tN

K

:

(6) 1 1 1t tN Nr

K K

And now by substitution in our original theta-logistic model:


4

(7) 1 1 1 1 1 tt t t

NN N H

K

Having survival and production as explicit parameters allows us to implement our assumptions concerning timing of annual events. Thus, we predict abundance in October as a function of March

abundance, MN :

(8) 7 112 1 1 1M

O M M Ftt t t t

NN N N H

K

in which we assume 7 months of natural mortality, all the reproduction, and a portion of the harvest prior to October, where F

tH represents the harvest in Finland.

Abundance in January is conditional on October abundance:

(9) 312J O D S

t t t tN N H H

where DtH and S

tH represent harvests in Denmark and Sweden, respectively, and where represents

the portion of the Swedish harvest occurring prior to January (i.e., the regular hunting season). Abundance in the following March is thus:

(10) 212

1 1M J St t tN N H

where 1 represents the portion of the Swedish harvest that is taken after the regular season to help

prevent crop damage (i.e., conditional hunting).

Sources of Data

Abundance and harvest statistics are compiled annually by the EGMP Data Centre and provided in an annual population status report (https://egmp.aewa.info/sites/default/files/meeting_files/documents/AEWA_EGM_IWG_4_9_TBG%20population%20status.pdf).

March counts of Taiga Bean Geese in southern Sweden (Skyllberg 2015) were compiled for the years 2007-2019, with the exception of 2010 and 2013 when no counts were conducted. March counts in Norway and Denmark are also available since 2011 and 2014, respectively, but these counts were not used because of the shorter time series (generally there are <1000 birds in these countries in March). It is believed that about 4000 of the birds in the March count in Sweden are of the tundra subspecies.

Bean Geese have also been counted in Sweden in October since 1977. Only since 2016 has an attempt been made to differentiate the subspecies, with an average of 12% (about 9000 birds) likely being of the tundra subspecies. However, October is considered among the best months to count Taiga Bean Geese of the Central Management Unit (Leif Nilsson, personal communication). At this time of the year the breeding birds from northern Fennoscandia and neighboring parts of Russia have reached southern Sweden and according to neck-banding studies have only rarely left the country.


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Finally, bean geese have been counted in January in Sweden since 1978 and in Denmark since 2014. Attempts to differentiate the subspecies in both countries have been made since 2014. Since then, about 13% (about 6000 birds) of the bean geese in Sweden have been identified as being of the tundra subspecies. In Denmark, about 6000 Taiga Bean Geese have been counted since 2014. Therefore, to take advantage of the longest time series, we used only January counts from Sweden, reasoning that the number of Tundra Bean Geese included in those counts was about equal to the excluded count of Taiga Bean Geese in Denmark.

From a biological perspective, we would expect October abundance to be the highest, followed by January and then by March (i.e., reproduction and a limited harvest occurs between March and October; only mortality occurs between October and March). Generally, October counts are highest, but January counts in Sweden (which has the most complete data and harbors most of the geese in January) are lower than the counts in Sweden in March, which is not biologically plausible (i.e., the January counts may be biased low) (Fig. 1). It is well known that Taiga Bean Geese winter in Germany and Poland, where they are not counted. Managers suspect that harsh winters drive more birds into Germany and Poland, a conclusion apparently supported by the positive relationship between the January count and January temperature in southern Sweden (https://www.tutiempo.net/clima/ws-26360.html; accessed February 19, 2020) (Fig. 2).

Fig. 1. The empirical cumulative distributions of available Swedish counts of Bean Geese (in thousands), 1977-2019, during three months of the year. Distributions further to the right reflect higher counts.

0 20 40 60 80

0.0

0.2

0.4

0.6

0.8

1.0

Bean Goose Count

Cum

ula

tive

Dis

trib

utio

n F

un

ctio

n

OctoberMarchJanuary


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Fig. 2. January counts of Bean Geese in Sweden as a function of the average January temperature (Celsius) at the Malmo airport in southern Sweden. The dashed line represents the best-fitting linear model.

Estimates of total Bean Goose harvest are available from 1996 onward for Finland, Sweden, and Denmark. In recent years, efforts have been made to distinguish the two subspecies in the harvest. In Sweden in 2017, 10-24% of the Bean Goose harvest was judged to be of the tundra subspecies. In Finland in 2017 and 2018, 15-69% of the harvest was judged to be of the tundra subspecies, but sample sizes and total harvests were extremely low.

For purposes of fitting the IPM, we assembled a complete set of population and harvest data for Finland, Sweden, and Denmark for the calendar years 1996-2019. At the time of this progress report, we only used the March count from 2019. Although the October 2019 count was available, we did not use it due to a lack of an estimate of the Finnish harvest in 2019. The following table provides the complete set of data used to fit the IPM. Note that January counts are aligned with the annual cycle of the model (i.e., the January count in calendar year t+1 is aligned with the March and October counts in calendar year t).

-6 -4 -2 0 2 4

0

10

20

30

40

50

60

January temperature

Jan

uary

cou

nt (

tho

usa

nds)

1978

1979 1980 1981

1982

1983

1984

1985 1986

1987

1988

1989

1990

1991

1992

1993

19941995

19961997

1998

1999

2000

2001

20022003

2004

2005

2006

20072008

2009

2010

2011

2012

2013 2014 20152016

2017

20182019


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Table 1. Data used to fit an IPM for Taiga Bean Geese in the Central Management Unit.

Year March count

October count

Harvest: Finland

Harvest: Sweden

Harvest: Denmark

January count

January temperature

1996 NA 60090 5500 1700 600 8925 -2.7 1997 NA 48651 4000 934 400 22648 1.5 1998 NA 48467 10900 1620 2703 15186 1.2 1999 NA 53900 8600 2409 2357 28923 1.5 2000 NA 41657 3200 3088 992 24109 1.3 2001 NA 68248 4700 4124 1203 14022 1.6 2002 NA 42667 4000 3323 1074 15036 -1 2003 NA 49446 8900 3457 1437 19326 -2 2004 NA 52123 4800 2540 1428 34560 2.1 2005 NA 44544 6400 6402 1329 19283 -1.7 2006 NA 42998 11200 3950 352 40291 4 2007 56960 62602 6300 3140 364 40133 3.1 2008 55405 65969 5600 2910 405 32532 -0.1 2009 49280 53871 7900 1597 602 29085 -3.8 2010 NA 47859 5100 4151 782 8734 -0.6 2011 46930 56497 3600 3093 563 34603 1.1 2012 47395 61201 3900 1619 3619 42103 -1 2013 NA 50988 3300 2735 1927 41962 0.9 2014 53855 59444 0 1675 1296 41367 2.4 2015 60033 70975 0 1582 1440 42337 -0.9 2016 58386 75579 0 2212 1301 55434 0.2 2017 65418 76928 176 1977 822 36945 2.2 2018 65060 68297 49 3547 654 39170 1.1 2019 63518 NA NA NA NA NA NA

Prior Distributions of Model Parameters

We used the methods described by Johnson et al. (2018) to develop informed priors for key demographic parameters. Using a combination of allometric relationships, fragmentary monitoring and research information, and expert judgment, we generated 100k replicate samples of survival in the

absence of harvest and density dependence , reproductive rate in the absence of density

dependence , spring carrying capacity K , and the form of density dependence . We then fit

statistical distributions using quantiles from these samples:

~ beta 58.17,7.89

~ log-normal 1.21,0.26

~ log-normal 0.85,0.79

~ log-normal 11.38,0.04K


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We also required prior distributions for the observation errors in the March, October, and January counts. These observation errors are actually residual errors, reflecting both random errors in the counts as well as unspecified demographic stochasticity (Kéry and Schaub 2012). In a true state-space model, observation errors and so-called process errors, for example arising from environmental variation, are both estimated. However, we encountered identifiability problems in trying to estimate both sources of error, likely because there is no information about the magnitude of the errors in the counts nor in our prior distributions. Nonetheless. we were able to fit a model with fixed-year and random-year effects in the intrinsic (i.e., density-independent) reproductive rate using highly informative priors. We specified the prior distributions for the observation error of the counts as

~ uniform 0,1 on the log scale.

The difficulty in estimating density dependence from a time series of population counts, when those counts are subject to observation error, is well established (Knape 2008). We encountered identifiability problems in both and when using the previously described prior distribution for .

A more informative prior for the form of density dependence alleviated these problems:

~ log-normal log 0.85, log 0.30 . This places 95% of the probability mass between 1.3 and

4.2, which seems biologically plausible given the intrinsic rate of growth estimated for this species of 0.15r (using the methods of Johnson et al. 2012).

We attempted to account for the apparent bias in the January count by modeling the count as a function of true (unobserved) abundance and the January temperature in southern Sweden using a linear model and a logit link. The priors for the intercept and slope of the regression model were specified as

0 ~ normal 0, 10 and 0 ~ normal 0, 1000 , respectively. The more informative

prior for the intercept was needed to help with parameter convergence.

Relatively uninformative prior distributions for annual, country-specific harvests were specified as

uniform 0,15000 for Finland and uniform 0,10000 for Sweden and Denmark. We used expert

opinion to define a prior distribution for the portion of Swedish harvest occurring prior to the January

count (i.e., regular hunting season) as ~ beta 30,10 , which has a mean of 0.75 and places 95% of

the probability mass between 0.61 and 0.87. We are initially assuming that is fixed over time. Finally, the population model was initialized using a log-normal prior for March 1996 abundance, assuming a mean abundance of 50k (and a standard deviation of 10k), which is slightly less than the October count in that year.

We used the fitted IPM to project population size (Kéry and Schaub 2012) for five future years under three harvest scenarios: (a) mean harvests in Finland, Sweden, and Denmark from the last five years (2014-2018) (total = 3346); (b) mean harvests of the five years prior to the moratorium in Finland (2009-2013) (total = 8898); and at a total harvest (7800) expected to keep the population near the median goal of 70k, using the agreed upon allocation among Range States (https://egmp.aewa.info/sites/default/files/meeting_files/documents/aewa_egm_iwg_1_9_ahm_tbg_set_up_phase_0.pdf). We note that the Russian harvest is unknown, and in the IPM it is implicitly


9

included as natural mortality. We thus re-normalized the remaining Range States’ desired harvest allocation as 58%, 30%, and 12% for Finland, Sweden, and Denmark, respectively. All priors for hypothetical future harvests for each Range State and for each year were specified as Poisson distributions with means based on the three harvest scenarios.

In addition to the deterministic model described above, we also fit models with fixed-year and random-year effects for the density-independent reproductive rate, , reasoning that in geese it is likely that

temporal variation in reproduction exceeds that of natural mortality (Pfister 1998, Schmutz 2009). A fixed-year effect model estimates reproductive rate independently for each year, while a random-effects model draws annual reproductive rates from a common distribution. This variation in both of these models is of a density-independent nature; for example, as related to weather on the breeding grounds (Jensen et al. 2014). In the fixed-year effect model, we simply replicated the previously described prior for for all years of the analysis. For the random-effects model, we specified a prior distribution for

the logarithm of the mean annual reproductive rate as ~ normal 1.21,0.27 , and a temporal

variance ~ uniform 0,0.25 , such that:

~ normal 0,

log

t

t t

e

e

Observation Models for the Data Sets

There were only two sources of data for which observation models were required: abundance and harvest. March and October counts were specified as log-normal, with mean abundance dictated by the expectation from the process model (Mäntyniemi et al. 2013) and observation errors as described

above. The model for January counts JC had to account for a potential bias related to the January

temperature in southern Sweden:

0 1

2 2

log temperature1

~ log-normal log 0.5 ,

tt

t

J Jt t t

p

p

C p N

We used Poisson distributions for the conditional probability distribution of harvest data, with expectation provided by the process model. The observation error in estimates of harvest is unknown, but is likely to exceed that described by a Poisson distribution. Therefore, we tried using a negative binomial (Bolker 2008), which would allow for overdispersion in harvest estimates relative to the Poisson. The estimate of the overdispersion parameter was near 1.0 (i.e., extreme overdispersion), but we experienced convergence problems and poor fit of the count data. Thus, we retained use of the Poisson likelihoods for harvests.

We assumed independence of the individual data sets, such that the joint likelihood of all the parameters was simply the product of the likelihoods implied by individual data sets (Kéry and Schaub 2012).


10

Computation

To fit the IPMs we used JAGS 4.3.0 (Plummer 2003), run in the R computing environment (R Core Team 2018) using runjags (Denwood 2016). For each model we used three chains of ≥550k iterations each and retained the last 50k samples from each chain for analysis. We assessed parameter convergence using the potential scale reduction factor, psrf (Gelman and Rubin 1992), and assumed values of psrf < 1.1 indicated parameter convergence (Gelman and Hill 2006). Unless otherwise noted, we report the medians and 95% credible intervals of posterior estimates. R code and other necessary files for running the model is provided here: TBG IPM Codes.

Results

Among the four key demographic parameters in the deterministic model , , ,K , only the posterior

distribution for reproductive rate, , differed markedly from its prior (Fig. 3). This was not

unexpected due extrinsic identifiability problems (Kéry and Schaub 2012) arising from the limited nature of the available data. Likewise, the posterior distribution for the proportion of Swedish harvest occurring prior to the January count, , was essentially identical to its prior. However, the posterior estimate of the slope of the relationship between the January count and temperature was positive (with 96% probability), suggesting that January counts are biased low in cold winters. The mean annual bias was 56% (39-70%), suggesting the count was 44% less on average than the true abundance.

Posterior population estimates aligned reasonably well with the counts in March and October, with the exception of March counts at the beginning and end of the time series. As expected, posterior estimates of population size exhibited less variability than the counts due to the random observation errors of the latter and the autoregressive nature of the population model (Fig. 4). Posterior estimates of abundance were reasonably precise, but it is important to remember that these estimates are from a deterministic model that omits any environmental variation. As we will see, the precision of the population estimates is considerably less when considering fixed-year or random-year effects in reproduction. Posterior estimates of population size increased over time for all three months, especially after the Finnish harvest moratorium in 2014. Estimated population size was 81.4k (76.5-86.6k) in October 2018, 76.2k (71.4-81.4k) in January 2019, and 74.1k (69.1-79.2k) in March 2019.

Not surprisingly, the posterior estimates of harvest corresponded extremely well with the data due to the low observation error of the Poisson model (Fig. 5).

We also derived estimates of harvest rate of the population in autumn and the finite rate of population growth in spring for each year in the time series (Fig. 6). Harvest rates appeared to decline dramatically following the Finnish harvest moratorium in 2014, and this decrease in harvest pressure coincides with strong growth in the population. However, it is notable that estimated population growth rates remained largely positive for the seven years preceding this moratorium, when harvest rate averaged about 16% compared to the average of about 5% since 2014. This population growth appears to be related to the fact that abundance at that time was far below the estimated carrying capacity. Recent harvest rates have been relatively constant, and the recent decline in the rate of


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population growth is largely being driven by density dependence as the population approaches carrying capacity.

In Fig. 7, we depict predicted harvest rates and March abundance for five years into the future based on the three harvest scenarios described in the Methods. Some decline in population size is expected with an increase in harvests, although mean population size would be expected to stabilize sometime after the 5-year period. Based on an equilibrium analysis (Conroy and Carroll 2009), and using the posterior estimates of demographic parameters from the theta-logistic population model, a constant harvest rate of 0.10 would be expected to produce a long-term mean population size of 70.1k (66.2-74.5k) in spring (i.e., approximately the median population goal) and an average annual harvest of about 7800 (7400-8300).

Fig. 3. Prior (red) and posterior distributions (grey) of natural survival rate, , reproductive rate, ,

carrying capacity, K, and form of density dependence, , in a theta-logistic population model of Taiga

Bean Geese in the Central Management Unit. 1 is the slope of a logistic regression between the

January count and average January temperature in southern Sweden. is the portion of Swedish harvest occurring prior to the January count. Dashed, vertical lines represent medians.

Den

sity

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0

5

10

15

Den

sity

0.0 0.2 0.4 0.6 0.8 1.0

0123456

K

Den

sity

60000 70000 80000 90000 100000 110000

0e+00

1e-04

Den

sity

0 2 4 6 8

0.0

0.2

0.4

0.6

1

Den

sity

-1.0 -0.5 0.0 0.5 1.0

0.00.51.01.52.02.53.0

Den

sity

0.0 0.2 0.4 0.6 0.8 1.0

0123456


12

Fig. 4. Raw counts (red) and posterior estimates of population size (black, with 95% credible intervals) in thousands at three times during the year for Taiga Bean Geese in the Central Management Unit as based on a deterministic integrated population model.

1995 2005 2015

20

40

60

80

March

Year

Abu

ndan

ce

1995 2005 2015

20

40

60

80

October

Year

Abu

ndan

ce

1995 2005 2015

20

40

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80

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Year

Abu

ndan

ce


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Fig. 5. Reported harvests (red) and posterior estimates (black, with 95% credible intervals) in thousands for Taiga Bean Geese in the Central Management Unit as based on a deterministic integrated population model.

1995 2005 2015

0

2

4

6

8

10

12

Finland

Year

Har

vest

1995 2005 2015

0

2

4

6

8

10

12

Sweden

Year

Har

vest

2005 2010 2015 2020

0

2

4

6

8

10

12

Denmark

YearH

arve

st


14

Fig. 6. Posterior estimates of harvest rate of the autumn population and finite rates of growth in the spring population (with 95% credible intervals) for Taiga Bean Geese in the Central Management Unit as based on a deterministic integrated population model.

2000 2010

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Year

Ha

rve

st r

ate

2000 2010

0.85

0.90

0.95

1.00

1.05

1.10

1.15

Year

Po

pu

latio

n g

row

th r

ate


15

Fig. 7. Three future harvest scenarios for Taiga Bean Geese in the Central Management Unit as based on a deterministic IPM. In each pair of plots, the following harvest levels are projected five years into the future. Top: mean harvest levels from 2014-2018 for Finland, Sweden, and Denmark. Middle: mean harvest levels for the preceding five years (2009-2013). Bottom: a hypothetical harvest at the desired Range-State allocation intended to keep the population near its median target of 70k. Harvest rate is for the autumn population and abundance (in thousands) is in spring. Dashed vertical lines represent the last year of observational data.

1995 2005 2015

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Year

Ha

rve

st r

ate

1995 2005 2015 2025

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Year

Ab

un

danc

e

1995 2005 2015

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rve

st r

ate

1995 2005 2015 2025

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40

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80

Year

Ab

un

danc

e

1995 2005 2015

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Har

vest

rate

1995 2005 2015 2025

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40

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80

Year

Ab

und

ance


16

The model with fixed-year effects in reproduction generally produced higher posterior estimates of natural survival, , and the form of density dependence, , than the deterministic model (Fig. 8). In

contrast, the year-specific estimates of the density-independent reproductive rate were generally lower than the fixed rate of the deterministic model. Allowing for environmental variation in reproductive rate generally improved the fit of abundance estimates to the count data (Fig. 9).

Fig. 8. Prior (red) and posterior distributions (grey) of natural survival rate, , carrying capacity, K,

and form of density dependence, , in a theta-logistic population model of Taiga Bean Geese in the Central Management Unit. Dashed, vertical lines represent medians. Year-specific posterior estimates of reproductive rate, , are from a model allowing fixed-year effects in density-independent

reproductive rate.

Den

sity

0.70 0.75 0.80 0.85 0.90 0.95 1.00

0

5

10

15

20

2000 2005 2010 2015

0.0

0.2

0.4

0.6

0.8

1.0

Year

K

Den

sity

60000 70000 80000 90000 100000 110000

0e+00

1e-04

Den

sity

0 2 4 6 8

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


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Fig. 9. Raw counts (red) and posterior estimates of population size (black, with 95% credible intervals) at three times during the year for Taiga Bean Geese in the Central Management Unit as based on an integrated population model with fixed-year effects for the density-independent reproductive rate.

The model with random-year effects for the density-independent reproductive rate had posterior estimates of key demographic parameters mode similar to those from the deterministic model than the fixed-year effects model (Fig. 10). The pattern of annual variability in the reproductive rate was similar in both the fixed-effects and random-effects models, and the magnitude of variation in both models was relatively small. The fit of population counts in the random-effects model was similar to that of the fixed-effects model (Fig. 11).

1995 2000 2005 2010 2015 2020

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40

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80

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Year

Abu

ndan

ce

1995 2000 2005 2010 2015 2020

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60

80

October

Year

Abu

ndan

ce

1995 2000 2005 2010 2015 2020

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80

January

Year

Abu

ndan

ce


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Fig. 10. Prior (red) and posterior distributions (grey) of natural survival rate, , carrying capacity, K,

and form of density dependence, , in a theta-logistic population model of Taiga Bean Geese in the Central Management Unit. Dashed, vertical lines represent medians. Year-specific posterior estimates of reproductive rate, , are from a model allowing random-year effects in density-independent

reproductive rate.

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Fig. 11. Raw counts (red) and posterior estimates of population size (black, with 95% credible intervals) at three times during the year for Taiga Bean Geese in the Central Management Unit as based on an integrated population model with random-year effects for the density-independent reproductive rate.

Discussion

Results suggest strong population growth coincident with a sharp decrease in harvest pressure in 2014. For the last five years, the January and March populations appear to have been within the management target of 60-80k at the end of winter, with the most recent estimates of abundance approaching the upper bound. If the desire is to keep the population near the median target of 70k, some harvest liberalization may be permissible. A total harvest of 7800, in which 4600 is allocated to Finland, 2300 to Sweden, and 900 to Denmark, could be expected to maintain the population near the median goal over the long term. For comparison, the mean total harvest in the last five years was 3347, with an average of 45, 2199, and 1103 Bean Geese harvested in Finland, Sweden, and Denmark, respectively.

Not unexpectedly, we found it difficult to estimate key demographic parameters using a time series of only counts and harvests, especially when those estimates include the tundra subspecies to varying degrees. Additional data on survival and/or reproduction from a capture-mark-recapture program and observations of the ratio of young to adults in the autumn would be immensely helpful in deriving more

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robust estimates of key demographic parameters. With respect to population counts, we agree with the recommendation of the Taiga Bean Goose Task Force to maintain all three seasonal counts at least through 2021 when a more informed decision about monitoring efforts can be made. We also recommend that recent efforts to identify subspecies in both the counts and harvests be continued. Finally, we have treated the portion of harvest occurring before and after the January count in Sweden as a constant, based on expert opinion. If an estimate of January population size remains an objective of an IPM, then we will need observational data to apportion the Swedish harvest, preferably on an annual basis.

This report represents progress midway through a 1-year project, and there are a number of tasks remaining. First, it may be possible to use data that exist for autumn age ratios for a small number of years, as well as the recent data available to distinguish subspecies in the counts and in harvests. Some retooling of the model would be necessary, however, and it’s unclear whether the fragmentary data are sufficient to materially affect estimates of abundance and demographic parameters. Second, it would be useful to project future population sizes using the model with random-year effects for reproduction, in spite of the fact that inter-annual variation appears to be small at this time.

After development of a satisfactory IPM, the final component of this project is the development of an optimization framework to guide the annual setting of harvest quotas. Using the IPM and agreed upon management objectives, we can derive state-dependent harvest strategies using stochastic dynamic programming (SDP). A key advantage of SDP is its ability to produce a feedback policy specifying optimal management decisions for possible future system states rather than expected future states. In practice this makes SDP appropriate for systems that behave stochastically, absent any assumptions about the system remaining in a desired equilibrium or about the production of a constant stream of resource benefits. Moreover, use of a Bayesian estimation framework for IPMs provides a natural framework for adaptation, in which model parameters can be updated over time based on observations from operational monitoring programs or external studies.

A final report from this project will be available in October 2020. Suggestions for model improvement are welcome, and should be addressed to Dr. Fred Johnson at [email protected].

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Jensen, G. H., J. Madsen, F. A. Johnson, and M. Tamstorf. 2014. Snow conditions as an estimator of the breeding output in high-Arctic pink-footed geese Anser brachyrhynchus. Polar Biology 37:1–14.

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Skyllberg, U. 2015. Numbers of Taiga Bean Geese Anser f. fabalis utilizing the western and central flyways through Sweden during springtime 2007--2015. Ornis Svecica 25:153–165.

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