Informed conservation and management of wildlife require sufficient monitoring to understand population dynamics and to direct conservation actions. Because resources available for monitoring are limited, conservation practitioners must strive to make monitoring as cost-effective as possible.
Our focus was on assessing the value of monitoring to the adaptive harvest management (AHM) programme for pink-footed geese Anser brachyrhynchus. We conducted a retrospective analysis to assess the costs and benefits of a capture–mark–resight (CMR) programme, a productivity survey and biannual population censuses. Using all available data, we fit an integrated population model (IPM) and assumed that inference derived from it represented the benchmark against which reduced monitoring was to be judged. We then fit IPMs to reduced sets of monitoring data and compared their estimates of demographic parameters and expected management performance against the benchmark IPM.
Costs and the precision and accuracy of key demographic parameters decreased with the elimination of monitoring data. Eliminating the CMR programme, while maintaining other monitoring instruments, resulted in the greatest cost savings, usually with small effects on inferential reliability. Productivity surveys were also expensive and some reduction in survey effort may be warranted. The biannual censuses were inexpensive and generally increased inferential reliability.
The expected performance of AHM strategies was surprisingly robust to a loss of monitoring data. We attribute this result to explicit consideration of parametric uncertainty in harvest-strategy optimization and the fact that a broad range of population sizes is acceptable to stakeholders.
Synthesis and applications. Our study suggests that existing or potential monitoring instruments for wildlife populations should be scrutinized as to their cost-effectiveness for improving biological inference and management performance. Using Svalbard pink-footed geese as a case study, we show that the loss of some existing monitoring instruments may not be as adverse as commonly assumed if data are jointly analysed in an IPM. Finally, regardless of the monitoring data available, we suggest that conservation strategies that explicitly account for uncertainty in demography are more likely to be successful than those that do not.

1 INTRODUCTION

Monitoring the demography and relevant environmental conditions of a wildlife population costs time and money. Because resources available for monitoring are always limited, wildlife managers must strive to make monitoring as cost effective as possible. The challenge thus facing managers is to assess the trade-off between the cost of monitoring and the benefits derived from it in terms of understanding population dynamics and effectively directing conservation and management activities.

Generally, we can think of three basic types of monitoring (Nichols & Williams, 2006). The first is surveillance monitoring, in which resources are broadly (but perhaps not intensively) monitored in the hope that the information will eventually be useful to science or to decision-making. Because this type of monitoring lacks unambiguous objectives, it is impossible to assess its cost-effectiveness. The second type is science-focused monitoring, in which the primary goal is to discriminate among competing hypotheses of population dynamics (e.g. whether survival rates vary over time as a function of harvest). In this case, the researcher must balance the cost of monitoring data against the statistical power to discriminate among alternative hypotheses. Finally, there is decision-focused monitoring, in which the goal is to inform management actions and track their performance. Here the manager must balance monitoring costs with the efficacy of meeting conservation objectives. We can also describe an integration of the latter two types of monitoring within the context of adaptive management, in which the goals are both informing management actions and reducing uncertainty about population dynamics so that future decisions can be improved.

Our focus here is on the management of the Svalbard population of pink-footed geese and, in particular, on the adaptive harvest management process that has been in place since 2013 (Madsen et al., 2017). Pink-footed geese breed in Svalbard, migrate through Norway, Sweden and Finland, and winter in Denmark, the Netherlands and Belgium. The Svalbard population is demographically closed from the Icelandic/East Greenland population wintering in the British Isles (Madsen et al., 2014). The Svalbard population has more than doubled in size in the last 30 years, causing degradation of vulnerable tundra vegetation during the breeding season and conflict with agricultural interests in the migration and wintering areas.

Unlike most goose populations in Europe, an extensive science-focused monitoring programme has been in place for Svalbard pink-footed geese for three decades with the aim of understanding population dynamics, migratory behaviour and anthropogenic impacts. The wealth of available information about population size, survival, productivity and harvests has facilitated the construction of an integrated population model (IPM), which is used to guide harvest-management decisions in Norway and Denmark (Johnson et al., 2020). The monitoring programme has been maintained by a network of researchers, volunteers and contract employees. After 30 years, however, the programme is financially challenged, and one could ask whether there is a need to continue monitoring in its current form or whether some monitoring efforts and associated costs could be reduced without a significant sacrifice in biological inference and management performance.

We can address this question using a conceptual framework known as the value of information (VoI) (Williams & Johnson, 2015). In simple terms, VoI is the expected management performance with complete information minus the expected performance with incomplete information. We stress that VoI analyses can only be conducted within the context of a formalized decision problem, in which there are unambiguous objectives, alternative choices of actions, and the predicted consequences of those choices in terms that are relevant to the objectives. In this sense, VoI analyses can be used to evaluate both science-focused and decision-focused monitoring and, therefore, for monitoring conducted within the context of adaptive management.

In the research described here, we conducted a retrospective analyses of various monitoring instruments for pink-footed geese. We focused on those monitoring efforts that are not associated with some broader monitoring effort (e.g. monitoring wildlife harvests in Norway and Denmark), which would be conducted regardless of its utility for managing pink-footed geese. Rather, we focused on monitoring efforts that involve additional expense, in terms of money, time or both. We refer to our analyses as retrospective in the sense that we look back in time and ask: what loss of inference and management performance could be expected if we had not had access to some monitoring data in the past? Retrospective analysis is a common diagnostic in fisheries management, in which model performance is assessed when fewer years of data are included (e.g. Deroba, 2014; Miller & Legault, 2017). By examining various monitoring instruments, and by varying the time in the past they were theoretically discontinued, we can understand the relative importance of various monitoring instruments and whether the improvement in management performance they produce can be justified by their costs.

Herein we focus on how elimination of monitoring programmes for population size and demography could affect the performance of harvest management strategies for pink-footed geese, where performance is measured with respect to managers' ability to maintain a spring population of about 60,000 birds. This agreed-upon population target is a surrogate for a host of management objectives, including sustaining the population and its range, minimizing agricultural conflicts and damage to fragile habitats in the Arctic and providing sustainable hunting opportunities (Madsen & Williams, 2012). We also recognize that monitoring data are used for a variety of purposes other than harvest management. In deference to those needs, we also report changes in the reliability of inference about population demography that might attend reductions in monitoring.

2 MATERIALS AND METHODS

2.1 Monitoring instruments

We here explain the extant monitoring programme for pink-footed geese as described by Johnson et al. (2020), as well as annual costs of the various monitoring instruments. The average annual cost for all focused monitoring of pink-footed geese is €124,143, which has been shared by Aarhus University (95%) and the Norwegian Environment Agency (5%) (Appendix S1). The costs given for each monitoring activity do not include time spent by volunteers in the field (although they do include reimbursed travel costs). The Aarhus University funding, which was a one-time investment in developing tools to support adaptive management, expired at the end of 2021 and thus was a motivating factor in this research.

2.1.1 Population counts conducted in spring and autumn

Internationally coordinated population counts of pink-footed geese have been performed annually since 1990 in Denmark, Belgium and the Netherlands in late October or early November (hereafter referred to as the November count) (Madsen et al., 1999). Over time, the population has expanded its distribution and the spatial coverage of the count has repeatedly been extended to capture new sites occupied by geese (Madsen et al., 2015). Since 2005, the population has also been counted in Norway, and since 2016 in Sweden. Because of increasing challenges in monitoring the autumn population, an additional count was introduced in May in 2010, which includes Norway, Denmark, Sweden and, since 2016, Finland. The known sites are covered by a network of trained observers who coordinate the coverage. The May census costs €5327 per year for academic staff salary and travel costs of volunteers. The cost of the November census is similar, costing €3350 per year.

2.1.2 Harvest estimates

Pink-footed geese are subject to an open hunting season in Norway, including Svalbard, and in Denmark. The species is protected in the Netherlands, Belgium, Sweden and Finland. In both Norway and Denmark, reporting the harvest is mandatory and hunters report their harvests online. Harvest monitoring imposes no additional costs on the pink-footed goose management community.

2.1.3 Temporal distribution of harvest in Denmark

The November count occurs after the start of hunting seasons in Norway and Denmark and therefore it is important to be able to partition harvest into that occurring before and after the count. We assumed all the harvest in Norway occurs prior to the November count. In most years, the harvest in Norway occurs prior to the November count (Gundersen et al., 2017; Jensen et al., 2016). Moreover, the average number of pink-footed geese in Norway during the November count is very low, consisting of less than 5% of the total. The temporal distribution of the pink-footed goose harvest in Denmark is derived from wings submitted to the Danish wing survey. Danish hunters voluntarily submit wings from harvested individuals, providing information on date, location and age of harvested geese. Monitoring the temporal distribution of the harvest in Denmark imposes no additional costs on the pink-footed goose management community.

2.1.4 Proportion of young in the autumn

Based on age-specific plumage characteristics, random counts of the number of young of the year and of older geese in flocks have been conducted by trained observers in the Netherlands and Denmark since 1980 (Madsen, 1982; Madsen et al., 1999), and in more recent years in Belgium, Norway and Sweden as migratory behaviour has changed. To minimize the effect of seasonal changes in age ratios, we used only counts occurring between 12 October and 4 November, inclusive. Fall counts of young and adults are relatively expensive, and at the current level of effort cost €21,897 per year for academic staff salary, contract observers and travel costs.

2.1.5 Capture–mark–recapture (CMR) programme

Estimates of annual survival rate (i.e. reflecting all sources of mortality) are available from a CMR programme (Madsen et al., 2002). During the period 1991–2020, 4984 pink-footed geese were captured and fitted with neck collars and tarsus metal rings during spring staging in Denmark and Norway and, in 4 years (2007, 2008, 2012 and 2018), on the Svalbard breeding grounds. At marking, all birds had survived at least one fall migration and one hunting season. Re-sightings were made by a network of professional and volunteer observers outside the breeding grounds (September–May). Dead recoveries are reported by members of the public to the ringing centres involved (Denmark and Norway). They include both geese reported shot by hunters and those found dead by other members of the public. Using programme MARK, we fit a number of Burnham's joint recovery–recapture models (Burnham, 1993) by including all possible combinations of fixed and fully time-dependent survival (S), resighting probability (p), recovery probability (r) and fidelity (F). The fidelity parameter expresses the proportion of geese surviving from year to year that are available for resighting and might, therefore, (among other things) reflect marker retention and emigration to poorly covered sites or other populations. Models were evaluated using AICc (Burnham & Anderson, 2003) and we chose for our use model S(t) p(t) r(t) F(.), indicating a fixed F-parameter and full temporal variability in survival, detection and recovery probability. Estimates of annual survival and their standard errors (inflated using a variance inflation factor of $\hat{c} = 1.371$ ) from this best-performing model were used to specify prior beta distributions for the IPM using the method of moments (Bolker, 2008). We omitted the last survival estimate in the time series due to identifiability issues.

It should be noted that using survival estimates to generate informative prior distributions is not necessarily equivalent to using the encounter data directly in the IPM joint likelihood. Although we investigated the possibility of including the encounter histories as data in the joint likelihood, we eventually abandoned this approach for several reasons. First and foremost, the CMR data are needed to estimate both annual survival and May population size. To do this simultaneously from the raw data within the IPM requires the use of the Jolly–Seber model (Jolly, 1965; Seber, 1965). A major obstacle with use of this model, however, is a key assumption that the ‘capture’ rate of marked and unmarked birds is the same. This assumption is certainly violated when the initial capture is a physical capture and subsequent ‘captures’ are sightings from a distance. Failure of this assumption biases the estimates of population size (although not of survival) (Nichols et al., 1984). We also considered embedding the Cormack–Jolly–Seber model (Cormack, 1964; Jolly, 1965; Seber, 1965) to estimate survival from live encounters, but mortality and permanent migration are confounded and, thus, survival estimates can be biased low (especially if re-sightings occur primarily in only a portion of the animal's range). Finally, we considered the use of Burnham's joint model (Burnham, 1993) for live and dead encounters. There were practical problems with this model related to excessive computing time (especially when many data-reduction scenarios had to be run) and to the necessity of specifying a single set of constraints for the structure of the encounter data in the IPM. The latter contrasts with the independent analysis in MARK, in which many constraints could be tested to provide the most parsimonious model. Using informative priors based on previous studies is a widely accepted approach in Bayesian analysis (Hobbs & Hooten, 2015; King et al., 2009). McCaffery and Lukacs (2016) provide an example involving the use of informative priors for survival in birds. Nonetheless, the ideal approach would be to use the encounter histories as data in the IPM joint likelihood when possible and practical (Kéry & Schaub, 2012).

The CMR data are also used to derive an estimate of pink-footed goose population size (N) by dividing the number of marked geese in the population (M) by the ratio of the number of marked geese to the number of geese observed (R) (Sheaffer & Jarvis, 1995): $N = \frac{M}{R}$ . This approach has been used in the monitoring programme since 1991 (Ganter & Madsen, 2001) and resighting effort has increased significantly since 2011. As described by Clausen et al. (2019), the CMR data are used to derive estimates of pink-footed goose population size in spring, which are independent of the May counts. M is estimated from the number of marked birds seen alive in any given year corrected for annual variation in detection probability, and R is estimated as the average of the ratios from observations of marked individuals throughout the flyway. The time series of population estimates were used as input data for the IPM using a log-normal likelihood.

The CMR programme is the most expensive of all monitoring instruments, costing €93,569 per year for materials, salary and travel.

2.1.6 Spring temperature in Svalbard

Warm May temperatures on the breeding grounds, used as a proxy for snow melt in relation to the timing of egg-laying by geese, tend to improve reproductive success of pink-footed geese (Jensen et al., 2014). Therefore, daily average temperatures during May at two locations in Svalbard (Ny Ålesund and Svalbard Airport) are retrieved each year from the Norwegian Center for Climate Services (https://seklima.met.no/observations/). The number of days in which the average temperature is above freezing are tabulated and the number of ‘thaw days’ are calculated by averaging values from the two stations. There is no additional cost incurred in acquiring these data.

2.2 Analyses

We used a slightly modified version of the IPM described by Johnson et al. (2020). When using CMR survival estimates as prior information, annual changes in population size in May are described by a difference equation:

N_{t + 1}^{M} = N_{t}^{M} [s_{t} + r_{t} θ_{t} (1 - {υh}_{t}^{n} - {υh}_{t}^{d})],

where

N_{t}^{M}

is May population size in year t,

s_{t}

is the annual survival rate (reflecting both harvest and natural mortality),

r_{t}

is the ratio of young of the year to older birds at the start of the hunting season as a measure of reproductive rate,

θ_{t}

is survival from natural causes,

h_{t}^{n}

and

h_{t}^{d}

are per capita harvest rates of birds aged >1 year in Norway and Denmark, respectively, and

υ

is the differential vulnerability of young relative to older birds in the harvest (Clausen et al., 2017; Johnson et al., 2020). In the absence of CMR survival estimates as priors, changes in population size are described as:

N_{t + 1}^{M} = N_{t}^{M} θ_{t} [(1 - h_{t}^{n} - h_{t}^{d}) + r_{t} (1 - {υh}_{t}^{n} - {υh}_{t}^{d})] .

Population size in November is a function of population size in May, 6 months of natural mortality, all of the Norwegian harvest, and the portion of harvest in Denmark occurring prior to November:

N_{t}^{N} = N_{t}^{M} θ_{t}^{\frac{6}{12}} [(1 - h_{t}^{n} - h_{t}^{\overset{´}{d}}) + r_{t} (1 - {υh}_{t}^{n} - {υh}_{t}^{\overset{´}{d}})],

where

N_{t}^{N}

is November population size and

h_{t}^{\overset{´}{d}}

is the harvest rate of older birds in Denmark prior to November.

Within the IPM, we specified a generalized linear model for reproductive rate (r) using the number of thaw days (D) as a covariate: $r_{t} = \frac{γ_{t}}{(1 - γ_{t})}$ , where $γ_{t}$ is the binomial probability of young, and: $\log (\frac{γ_{t}}{(1 - γ_{t})}) = β_{0} + β_{1} D_{t}$ . Thaw days and their logistic relationship to reproductive rate were always included in the IPM, even when productivity data were absent.

The population model for pink-footed geese relies on the following assumptions: natural mortality and reproduction are year dependent; natural mortality is distributed evenly throughout the year and is age independent after the first autumn migration; young are more vulnerable to harvest than older birds (Clausen et al., 2017) and this rate of differential vulnerability is temporally constant; hunting seasons in September and October in Norway and Denmark expose a common group of birds to harvest (i.e. harvest does not occur sequentially, but simultaneously); harvest mortality is additive to natural mortality; and hunters report only retrieved harvests and any mortality due to crippling is subsumed in annual survival rates.

The IPM was first fit using the entire record of three decades of monitoring data, following the methods described by Johnson et al. (2020). We note that although some dependency existed among datasets (e.g. survival and population estimates from the CMR programme), recent work suggests this is less problematic than traditionally assumed (Weegman et al., 2021). We used jags 4.3.0 (Plummer, 2003), run in the R computing environment (R Core Team, 2018) using jagsUI (Kellner, 2021). Typically, long chains of Markov chain Monte Carlo samples were required to achieve convergence. We used three chains of ≥1,000,000 iterations each and retained the last 50,000 samples, which were thinned to produce 10,000 samples from each chain for analysis. We assessed parameter convergence using the potential scale reduction factor (Rhat) (Gelman & Rubin, 1992), and assumed values of Rhat <1.1 indicated parameter convergence (Gelman & Hill, 2006). Posterior-predictive checks (Korner-Nievergelt et al., 2015) based on chi-squared and Freeman–Tukey discrepancy statistics (Kéry & Royle, 2016) were used to assess goodness of fit of the IPM to available data. The goal of post-predictive checks is to assess whether the model can predict data that are ‘similar’ to the data in hand. Goodness of fit is judged by Bayesian p values (i.e. the frequency with which discrepancy statistics for the predicted data exceed those of the observed data), where extreme values (e.g. those <0.1 or >0.9) are considered indicative of poor model fit (Hooten & Hobbs, 2015).

Posterior estimates of natural mortality, differential vulnerability of young to harvest, and the regression coefficients expressing the relationship between thaw days and reproductive success were used to derive an optimal harvest policy. We used a computation algorithm known as stochastic dynamic programming (SDP), which can explicitly account for various sources of uncertainty in modelled systems (Marescot et al., 2013). SDP was implemented using the publicly available software MDPSolve (© 2010–2011 Paul L. Fackler, https://github.com/PaulFackler/MDPSolve), which is a set of SDP tools written in the proprietary MATLAB® programming language.

For computational purposes, the optimal value (V*) of a management strategy (A) for system state (x) at time t is the maximum (max) of the expectation (E) of the temporal sum of discounted population utilities:

V^{*} (A_{t}| x_{t}) = \max_{(A_{t}| x_{t})} E [\sum_{τ = t}^{\infty} λ^{τ} u (a_{τ}| x_{τ})| x_{t}],

where

λ = 0.99999

is the discount factor for an infinite time horizon. This particular discount factor means that population utility 100 years hence will still retain 99.9% of its current value, in keeping with the desire to protect exploited resources for use by future generations (Sumaila & Walters, 2005). Population utility

u (a_{τ}| x_{τ})

is action

(a_{τ})

and state dependent

(x_{τ})

and is defined as:

u (a_{τ}| x_{τ}) = \frac{1}{1 + \exp (|N_{t + 1} - 60| - 10)} .

where

N_{t + 1}

is the population size (in thousands) expected due to the realized harvest quota and the population target is 60 (thousand) (Figure 1). The 10 (thousand) in the equation for population utility represents the difference from the population target when utility is reduced by one half. Thus, the objective function devalues harvest quotas that are expected to result in a subsequent population size different than the population target, with the degree of devaluation increasing as the difference between population size and the target increases.

Details are in the caption following the image — **FIGURE 1**
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Utility (i.e. stakeholder satisfaction) expressed as a function of population size of Svalbard pink-footed geese. The population target is 60,000 individuals (red dashed line), but population sizes between about 55,000 and 65,000 (dark grey band) are acceptable (and thus have utility ≅1), while those outside that range are less desirable (and thus have lower utility). The light grey bands represent population sizes that have utility ≥0.5.

In optimizing the harvest policy, we explicitly accounted for the uncertainty in all demographic parameters as characterized by their marginal posterior distributions from the IPM. We used Gaussian quadrature to specify five nodes and associated weights for differential vulnerability (gamma distribution) and natural survival (beta distribution). For the two parameters of the logistic relationship between productivity and thaw days, we used five nodes each for $β_{0}$ and $β_{1}$ while maintaining their variance–covariance structure (bivariate-normal distribution). We refer to the resulting harvest policy as the full-data policy. The expected performance of this policy was assessed using the resulting stationary Markov transition matrix to calculate the expectations of long-term population size and harvest (Williams et al., 2002, p. 208).

We next assumed that posterior estimates of population size and demographic parameters from the IPM using the full set of available monitoring data represented the benchmark against which reduced monitoring was to be judged. Thus, the process for evaluating performance with reduced data involved the following steps (Figure 2):

We eliminated some of the data used to fit the IPM. For example, we might have eliminated data from the productivity surveys and then re-fit the IPM. In practice, we simply eliminated the likelihood for one or more datasets in the IPM. The reliability of biological inference of the reduced-data IPM was measured using the root mean squared error ( $RMSE$ ) of key demographic parameters (Bolker, 2008). The $RMSE$ accounts for both the precision and accuracy of an estimate: $RMSE = \sqrt{(variance + {bias}^{2})}$ , where bias is measured relative to the parameter estimate derived from the full set of monitoring data. Small values of $RMSE$ are best.
We then derived a new optimal harvest strategy using the posterior estimates from this reduced-data IPM. The expected performance of this harvest policy was evaluated, assuming that the harvest policy from the full-data IPM was the benchmark against which it was judged. We then plotted the long-term expectation of population size of each reduced-data scenario against its annual cost. We sought the Pareto-efficient frontier (Kennedy et al., 2007), in which no data-modification scenario could improve management performance without a concomitant increase in monitoring costs. A Pareto frontier describes the trade-offs inherent in both maximizing performance and minimizing costs and identifies those data-reduction scenarios not worthy of further consideration.

Based on preliminary investigations, we ultimately restricted our attention to 13 data-reduction scenarios, in which the entire record of CMR survival and population estimates, May counts, November counts and/or productivity surveys were eliminated (Table 1). The most basic IPM includes one set of population sizes and one source of demographic information. Thus, at least one set of the CMR population estimates, May counts, or November counts had to be present in all scenarios. If no CMR population estimates were included, we also eliminated the informative priors for annual survival estimates based on CMR data. All data-reduction scenarios included harvest estimates (because they were obtained at no cost) and therefore productivity data could be excluded from any or all scenarios. The data scenarios ranged from €3350 to €124,143 in annual cost (Table 1).

TABLE 1. Data scenarios for assessing the value of monitoring to biological inference and management performance for Svalbard pink-footed geese. CMR, capture–mark–recapture programme; May, May count; Nov, November count; and Prod, productivity survey. Inclusion or omission of a monitoring instrument is indicated by 1 and 0, respectively

Scenario	CMR	May	Nov	Prod	Annual cost (€)
1	1	1	1	1	124,143
2	1	0	0	0	93,569
3	1	0	1	0	96,919
4	1	1	0	0	98,896
5	1	1	1	0	102,246
6	1	0	0	1	115,467
7	1	1	0	1	120,794
8	1	0	1	1	118,816
9	0	0	1	0	3350
10	0	1	0	0	5327
11	0	1	1	0	8677
12	0	0	1	1	25,247
13	0	1	0	1	27,224
14	0	1	1	1	30,574

Finally, we note that this study did not include field work, nor did it require ethical approvals.

3 RESULTS

The full-data IPM adequately described the seven individual datasets (CMR population estimates, May counts, November counts, proportion of wings prior to the November count in Denmark, proportion of young observed in autumn, and harvests in Norway and Denmark) as indicated by Bayesian p values all close to 0.5 (minimum = 0.449; maximum = 0.578, Figure S1). All posterior parameter estimates had values of Rhat = 1.00. Posterior estimates of abundance increased rapidly until about 2010 and have been somewhat stable since (Figure 3). Estimates of parameters used in the optimization of harvest policy (natural mortality, differential vulnerability of young to harvest, and the regression coefficients expressing the relationship between thaw days and reproductive success) are provided in Table 2.

TABLE 2. Posterior estimates of demographic parameters and 95% credible intervals from the full-data integrated population model (IPM) that are used in the optimization of harvest policy for Svalbard pink-footed geese. Posterior estimates of natural survival are year-specific. Here we provide the mean and 2.5% and 97.5% quantiles of those annual estimates

Parameter	Mean	95% CI
Natural survival ( $θ$ )	0.882	0.872 to 0.897
Differential vulnerability ( $υ$ )	1.732	1.461 to 2.032
Coefficients for production ( $β_{i}$ )
Intercept ( $β_{0}$ )	−1.860	−2.009 to −1.712
Slope ( $β_{1}$ )	0.482	0.358 to 0.606

Among data-reduction scenarios, the reliability of estimates of natural mortality ( $θ$ ) was not critically dependent on the inclusion of informative priors for annual survival (Figure 4, top; scenarios beginning with ‘0’). Rather, reliability depended more on the inclusion of November counts, with the inclusion of May counts further improving the quality of estimates (scenarios 0010 and 0110, respectively). The most reliable estimates resulted from the inclusion of CMR-related data (priors for annual survival, May abundance estimates) and November counts. Inclusion of the CMR programme resulted in high monitoring costs, however, and a more acceptable trade-off between cost and parameter reliability may be to exclude CMR monitoring and maintain other monitoring instruments (Figure 4, bottom).

With respect to the relationship between thaw days and productivity, estimates of the intercept and slope ( $β_{0}, β_{1}$ , respectively) were often unreliable when productivity data were omitted from the IPM (Figure 5, top and middle; scenarios ending in ‘0’). Estimates improved when CMR-related data and multiple population counts were included. Because the intercept and slope were strongly correlated, we only examined the trade-off between cost and parameter reliability for the slope (Figure 5; bottom). Because the inclusion of productivity data was relatively important in estimating the relationship with thaw days, the most cost-effective solution may be to eliminate the CMR programme despite the resulting increase in the $RMSE$ of $β_{1}$ .

The $RMSEs$ of differential vulnerability varied less among data-reduction scenarios than other parameters, reflecting the informative prior for this parameter and lack of identifiability given available monitoring data (Figure 6, top). Generally, the reliability of the parameter estimate was poorest when CMR-related data were excluded. Nonetheless, elimination of the CMR programme may provide the best trade-off between monitoring cost and reliability of this parameter estimate (Figure 6, bottom).

Finally, in terms of parameter reliability, we examined the times series of posterior estimates of annual survival with and without the inclusion of CMR-related data, and the time series of preseason age ratio with and without productivity data (Figure 7). Recall that the CMR and productivity monitoring instruments were the costliest of all programmes. Although credible intervals of survival and productivity estimates were wider when their key source of data were excluded, they nonetheless largely overlapped those from the full-data IPM. It must also be borne in mind that an IPM will ensure ‘self-consistency’ in estimates (King et al., 2009), in that estimates in an IPM arise from a joint likelihood of all the data and, thus, those estimates are likely to differ when different datasets are included. This is particularly so if there are spatiotemporal mismatches in the datasets, which is likely in migratory populations (Saunders et al., 2019).

Regarding management performance, long-term expectation of population size was surprisingly robust under all but two data-reduction scenarios (mean = 59.3, SD = 1.8, in thousands) (Figure 8). Expectation of long-term, annual harvests was similarly robust (mean = 8.1, SD = 0.2, in thousands). Expected population utility was even more robust, reflecting the near-total satisfaction among stakeholders for population sizes between 55,000 and 65,000. In fact, all but one data-reduction scenarios were very close to the Pareto frontier, representing the best trade-offs between cost and management performance that could be attained. The exception was scenario ‘1000’, representing the elimination of all but the CMR data. Scenario ‘1000’ is referred to as a dominated alternative, in that there are other data-reduction scenarios available that could improve both cost and management performance. Perhaps the best trade-off between monitoring cost and management performance lies with elimination of the CMR programme and maintenance of at least two other monitoring instruments.

4 DISCUSSION

In terms of future monitoring efforts for Svalbard pink-footed geese, it appears that cut-backs or elimination of some abundance and productivity monitoring could be considered without a large sacrifice in biological inference or expected management performance, but with substantial savings in cost. In particular, it appears that the omission of the CMR programme would cause no immediate loss in management performance, but would result in a cost saving of €93,569 annually. The productivity survey is also relatively expensive, and its elimination might be considered because the relationship between thaw days and productivity is already firmly established. An alternative to total elimination of the productivity survey would be to scale back the effort. In a typical recent year, over 20,000 birds were examined in the field for age. We suspect that many fewer samples would provide a reasonable estimate of productivity. Finally, our analyses suggest that the November count is relatively important, and it is also inexpensive. Similarly, the May count is inexpensive and provides an estimate of spring abundance, which is used to guide harvest decisions. Therefore, there seems to be no compelling reason to discontinue these counts.

Any decisions to reduce monitoring efforts for pink-footed geese should consider the limitations of these analyses, however. First and foremost, we must assume that the dynamics of this population will not change in any substantive way in the future. A reduced monitoring effort could lead to a failure to recognize any such changes. This may be particularly important in light of rapid warming occurring in the Arctic (Jansen et al., 2020), potentially changing agricultural policies and practices on the wintering grounds (Odgaard et al., 2011), changes in migratory behaviour (Madsen et al., 2015) and/or disease outbreaks (e.g. avian influenza). We also emphasize that reliable biological inference and harvest decisions in the future are conditioned on the range of abundance and demography experienced in the past. If monitoring is reduced, there is the danger that extrapolation will be unreliable should abundance and/or demography exceed historical ranges.

While it appears that some monitoring instruments could be curtailed or scaled back without significant impacts to an understanding of the demography of Svalbard pink-footed geese, there are ancillary uses of monitoring data not considered in our study. For example, when geese are caught and tagged for the CMR programme, they are also screened by X-ray for the presence of shotgun pellets to help evaluate crippling rates (Noer et al., 2007). Some geese are also fitted with GPS tags, resulting in new information on movements, which is highly dynamic within the existing range of the Svalbard population of pink-footed geese (Clausen et al., 2018). Moreover, November population counts are used as reference values by international organizations such as Wetlands International and the Ramsar Convention. The November count is also the most important contribution to the International Single Species Management Plan (ISSMP) (Madsen & Williams, 2012) from the Netherlands and Belgium. If the November counts were discontinued, these range states would ‘lose’ some of their connection to the ISSMP and the contrast in management approaches between Norway/Denmark (where hunting is allowed) and the Netherlands/Belgium (no hunting) would be more obvious. In the Netherlands, the November count would be carried out for national reasons regardless of whether it was conducted range wide, as fieldwork is mainly carried out by volunteers. The same is true for Belgium, and being a partner in the ISSMP is an important incentive to organize the count. Finally, the November count serves as a source of ecosystem services in terms of bird-watching and goose damage assessments.

A primary focus of the monitoring programme for Svalbard pink-footed geese is to ensure robust decisions regarding the harvest required to maintain the population near its spring target of 60,000 birds. In the past, annual harvest decisions were based strictly on the May population count. In 2015, there was a problem with the count and population size was biased low, which led to inappropriate restrictions on the harvest in Denmark (Madsen et al., 2017). To avoid similar ‘mistakes’, the CMR population estimates were included in assessing population status to avoid being dependent on a single count. In 2018, the IPM was developed and used in the annual assessment. The IPM includes the November and May counts as well as the CMR population estimates as input, and has ‘smoothed’ the population trajectory and ensured more predictable and reliable hunting regulations. If monitoring is reduced, the management community may again be at risk that the remaining programme will be more prone to uncertainty and bias, which could ultimately result in less effective harvest decisions.

We were surprised, however, that optimal harvest policies for data-reduction scenarios generally performed well relative to the full-data scenario. The optimization process relies on estimates of natural survival, the coefficients for the relationship between thaw days and productivity, and differential vulnerability of young. We note that there was often broad overlap in the posterior distributions of these parameters between the full-data and data-reduction scenarios. Thus, when parametric uncertainty is considered explicitly in the optimization process, the resulting harvesting policy can do reasonably well in prescribing harvests even if the underlying population model is ‘wrong’. The fact that there is a broad range of acceptable population sizes no doubt also played a role in the robustness of harvest policies.

5 CONCLUSIONS

While decision-makers and funders of long-term monitoring programmes may find our results gratifying, we emphasize that the wealth of monitoring data available for pink-footed geese is not typical of waterbirds in Europe, where monitoring data are often sparse and sometimes biased (Johnson et al., 2018; Johnson & Koffijberg, 2021). In addition, we had ancillary data to develop informative priors for some demographic parameters (e.g. differential vulnerability and natural survival). Nonetheless, our results highlight the ability of IPMs to leverage available data to estimate latent (unobserved) parameters.

Our approach was retrospective in that we examined complete elimination of monitoring instruments from the historical record. In more data-poor cases, one might also examine partial elimination of a time series of data. Yet, another approach would be a prospective analysis, in which a population model is postulated, ‘observational’ data are generated with the IPM (as in posterior predictive checks), and then some data are eliminated and an IPM fit to the remaining data. The ‘observational’ data would need to be replicated many times to account for sampling error. This approach could be useful in deciding what additional investments in monitoring might be needed to meet minimum standards of biological inference and management performance. Prospective approaches of this nature fall within the conceptual framework of the ‘value of sample information’, which has recently been emphasized as a means to assess the importance of collecting additional data to support conservation decision-making (Canessa et al., 2015; Williams & Brown, 2020; Williams & Johnson, 2018).

AUTHOR CONTRIBUTIONS

Fred A. Johnson and Jesper Madsen conceived the ideas and designed the methodology; Jesper Madsen, Kevin C. Clausen, Morten Frederiksen and Gitte H. Jensen supplied the data; Fred A. Johnson conducted the analyses; Fred A. Johnson and Jesper Madsen led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication.

ACKNOWLEDGEMENTS

We thank the network of collaborators and observers in the range of the pink-footed goose for providing data, particularly national coordinators Ingunn Tombre (Norway), Kees Koffijberg and Fred Cottaar (the Netherlands), Eckhart Kuijken and Christine Verscheure (Belgium), Leif Nilsson (Sweden) and Jorma Pessa (Finland). The work was primarily funded by Aarhus University, with additional funding from the national governments of the European Goose Management Platform under the Agreement on the Conservation of African-Eurasian Migratory Waterbirds.

CONFLICT OF INTEREST

The authors declare no conflicts of interest.

Open Research

DATA AVAILABILITY STATEMENT

Data and code available via the Dryad Digital Repository http://doi.org/10.5061/dryad.j3tx95xjg (Johnson et al., 2022).

Supporting Information

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Volume60, Issue1

January 2023

Pages 132-145

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Assessing the value of monitoring to biological inference and expected management performance for a European goose population

Abstract

1 INTRODUCTION