Reconstruction and prediction of invasive mongoose population dynamics from history of introduction and management: a Bayesian state-space modelling approach

Authors


Correspondence author. E-mails: k.fukasawa37@gmail.com; fukasawa@nies.go.jp

Summary

  1.  An understanding of the underlying processes and comprehensive history of invasive species is necessary to assess the long-term effectiveness of invasive species management. However, continuous, long-term labour-intensive population surveys on invasive species are often not feasible. Thus, it is important to learn about their dynamics through management action and its consequences.
  2.  Amami Island, Japan, has an ongoing large-scale and long-term eradication programme of invasive small Indian mongooses. To estimate the long-term pattern of population size and the parameters determining the dynamics, including anthropogenic removal, we applied a surplus-production model within a Bayesian state-space formulation incorporating the initial population size, number of captures and capture effort. Using the estimated process model directly, we conducted stochastic simulations to evaluate the feasibility of eradication.
  3.  Estimated 32-year annual capture probability of mongooses has increased since their introduction. The population size started to decline in 2001; mean population size in 2000 was 6141 (95% CI: 5415–6817), and declined to 169 (95% CI: 42–408) by 2011. Parameter estimates of a Weibull catchability model indicated that there was large individual heterogeneity in the probability of being captured, and per-effort capture probability declined with an increase in annual capture effort.
  4.  The simulation study indicated that the eradication feasibility in 2023 would be over 90% if the same annual capture effort is upheld as in 2010 (2 075 760 corrected trap-days). However, increasing annual capture effort would have little effect on shortening the time to eradication.
  5.  Synthesis and applications. A hierarchical model that incorporates multiple types of data to reveal long-term population dynamics has the potential to be updated with the outcomes of control efforts, and will enhance adaptive management of invasive species. This approach will offer valuable information about trade-offs between time to eradication success and effort per unit time in a long-term eradication project, and the length of time needed to continue management actions to achieve eradication success.

Introduction

Invasive species pose a major threat to global biodiversity and ecological services (Millennium Ecosystem Assessment 2005). Many conservation organizations and government agencies devote considerable effort to managing invasive species, especially on islands. Fortunately, technical developments have made eradication a realistic option as a tool for invasive species management (Parkes 2006), and hundreds of successful eradications have already been achieved world-wide (Keitt et al. 2011). However, eradication on larger islands remains a difficult challenge, and many large-scale projects are currently ongoing (e.g. Campbell et al. 2004; Abe et al. 2006; Henderson & Robertson 2007; Berry & Kirkwood 2010; Genovesi 2011). Even if eradication success is achievable, it often requires continuous labour-intensive treatment over a long period.

Understanding the population dynamics and the effect of management of invasive species is essential to evaluating the feasibility of an eradication attempt (Liebhold & Bascompte 2003). In particular, long-term rate of removal and the annual intrinsic rate of increase are of eradication feasibility (Cromarty et al. 2002; Parkes & Panetta 2009). Once invasive species are introduced and successfully established, the population will expand until saturation (Cousens & Mortimer 1995). If eradication is attempted, population dynamics are determined by the intrinsic growth rate and by anthropogenic removal. To reveal the long-term effectiveness of management and the extent of the opposing force of intrinsic growth, it is valuable to examine the comprehensive history of an invasive species' population and the underlying processes. By doing so, we gain important insight and ability to predict the consequences of invasive species management that cannot be seen by short-term observations.

Decision-making regarding conservation issues often relies on multiple types of observations and knowledge (Pullin et al. 2004), and integrating them systematically and consistently is important for evidence-based decisions (Rhodes et al. 2011). When inferring the long-term dynamics of an invasive animal, a researcher might have to integrate multiple types of data, for example, history of introduction (Green 1997; Forsyth et al. 2004; Marchetti, Moyle & Levine 2004; Cassey et al. 2005), number of captures (i.e. number of individuals removed) and capture effort (Schuyler, Garcelon & Escover 2002; Forsyth et al. 2003; Abe et al. 2006; Pilotto et al. 2008). Although these data reflect the underlying process of invasion and its management, there are few studies that have explicitly modelled this relationship. We considered that a quantitative inference would be made possible by embedding these data in a model of population dynamics, which is determined by intrinsic growth and anthropogenic removal. Hierarchical Bayes is a general framework of inference that allows us to associate observations and the underlying processes, and to estimate the parameters directly (Wikle 2003; Clark & Bjørnstad 2004). Hierarchical Bayes has been frequently applied to recent ecological studies (Clark & Gelfand 2006; McCarthy 2007; Royle & Dorazio 2008). Using hierarchical Bayes, reconstruction of population dynamics of invasive species from introduction and capture history might be possible because of its potential to integrate multiple data sources into a single model considering uncertainty in both data and the underlying ecological processes (Clark 2005).

The small Indian mongoose Herpestes auropunctatus (called ‘mongoose’ hereafter) is known as one of the most noxious invasive animals in the world (Lowe et al. 2000; Hays & Conant 2007; Barun et al. 2011; Peters et al. 2011). On Amami Island (covering 712 km2), Japan, 30 mongooses were introduced in 1979 and settled. Because the predatory impact of mongooses poses a serious threat to the endemic fauna (Yamada 2002; Watari, Takatsuki & Miyashita 2008), an eradication project by the Ministry of the Environment, Japan, has been operating since 2000. Until now, world-wide eradication successes of mongooses are limited to small islands up to 1·15 km2 (Barun et al. 2011); thus, the mongoose eradication on Amami Island poses a challenge.

Although the mongoose population seems to be in decline because of the continuous eradication attempts, change in the population size, intrinsic growth rate and relationship between effort and removal rate are not known. The first aim of this study is to reconstruct the entire population size dynamics and the impact of mongoose management, using the record of introduction and capture. Considering the long-term eradication plan, the time needed to achieve eradication success is also a crucial issue. The second aim is to evaluate the eradication feasibility of mongooses on Amami Island. Our results clearly demonstrated temporal changes in population size of mongooses and their rate of removal. Simultaneously, we estimated both capture probability in relation to capture effort and intrinsic growth. The result of the stochastic simulation indicates that immediate eradication success would be difficult, even with a large increase in annual capture effort, but would be feasible by continuing the current annual capture effort for over a decade.

Materials and Methods

Mongooses on Amami Island and their eradication

Amami Island (712 km2, N28°19′35″, E129°22′28″), in the Ryukyu archipelago in southwestern Japan, is a biodiversity hotspot in Japan and has many endemic and threatened species (Yamada 2002; Kuramoto, Satou & Oumi 2011). Amami Island is subtropical and its climate is warm and wet. Annual mean temperature and annual precipitation are 21·6 °C and 2837·7 mm, respectively. The coldest and hottest months are January and July with mean temperature 14·8 and 28·7 °C, respectively. On this island, 30 individual mongooses were released in 1979 (Yamada & Sugimura 2004) as a biological control agent of an indigenous poisonous snake (Habu, Protobothrops flavoviridis). The mongooses have successfully established and expanded their range from the release point (Abe et al. 1991), and their top-down regulation has threatened the ecosystem, which is characterized by many endemic vertebrates (Yamada et al. 2000; Yamada & Sugimura 2004; Watari, Takatsuki & Miyashita 2008). Reproductive characteristics of the mongooses on Amami Island were described by Abe et al. (2006). The mean litter size varies from around two to three pups. The major breeding period ranges from March to September, but a small fraction of the population breeds in winter. However, these attributes vary according to the nutrient condition of mongooses. Population size estimations of mongooses were conducted in 1999 (Ishii 2003), 2001, 2002 and 2003(Ishii, Hashimoto & Suzuki 2006) by catch-effort method and spatial extrapolation of the estimate, which are independent of our study. The estimated population size in 1999 was 5000–10 000 individuals, which was in accordance with circumstantial evidence such as number of captures since that time. Estimates in 2001, 2002 and 2003 were 1000–2000 individuals, but the authors noted that these population sizes appeared to be underestimated and are inconsistent with annual number of captures (in the article, the reason why the underestimation occurred was not discussed; (Ishii, Hashimoto & Suzuki 2006). Since then, catch-effort surveys of mongooses have not been conducted on Amami Island because of difficulty in field sampling associated with population density decline.

An attempt to control mongooses on Amami Island was initiated in 1983, 4 years after their introduction. At first, local farmers started trapping to prevent crop damage. Then, from 1993 to 2005, the local government implemented a buyback system of the captured mongooses to help further reduce crop damage. With an increase in the social awareness of the threat to native fauna, the Ministry of the Environment started the mongoose eradication project in 2000 (Yamada 2002; Yamada & Sugimura 2004). A basic plan of eradication defined the aim of the project as eradication success by fiscal year (FY) 2014. Since 1983, live-traps have been used to control mongooses and since 2003, kill-traps have also been applied. The structure of kill-traps was changed in 2007 to decrease bycatch of endemic birds (i.e. attaching a bird-excluding guard at the entrance of the trap), and changed again in 2009 to improve capture efficiency (i.e. modifying the bird guard).

On Amami Island, annual number of captures was recorded almost every year (Fig. 1). Annual capture numbers between 1983 and 1987 were determined by an interview survey of farmers, who caught c. 300 individuals during the 5-year period (Abe et al. 1991). Since 1988, the annual capture number has been fully recorded because of a mandatory reporting system. The capture number notably increased from 1993, perhaps due to the buyback system. Annual number of captures peaked in 2000 (3884 individuals), when the eradication project started. In 2010, annual capture decreased to 311. Note that the 5-year total number of captures (300 individuals) is only known between 1983 and 1987, so we assumed that 60 individuals were caught every year. We tested this assumption and confirmed that it had little effect on the estimates (detailed description in Model specification and parameter estimation in Model Application).

Figure 1.

Number of captures, corrected trap-days (CTD) and catch per unit effort (CPUE,/100CTD). Note that CTD has been recorded since 2001.

Although capture effort has been recorded since 2001 on Amami Island, these data should be used with caution because of the variety of capture techniques (live-traps and a variety of kill-traps) that have been used. For example, live-traps have to be checked and reset by trappers every day for animal welfare purposes. However, because kill-traps kill the captured animal quickly and thus humanely, the traps are instead checked and reset once every month or 2 months. In the mongoose eradication project, trapping effort is defined by number of trap-days (TD), which for live-traps is equal to the number of trap checkings. For kill-traps, TD is defined as days after setting the trap. However, when the days after setting the trap exceeds 8 days, TD is fixed to eight regardless of the extra time to next trap check, which is a rule of thumb to account for the loss of trapping ability because of bait decay (Naha Nature Conservation Office 2009). This discrepancy means that 1 TD would be different between live-traps and the three types of kill-trap, and so trapping effort would also be different across the time frames of pre-2006, 2007–2008 and post-2009.

To make a standardized index of trapping effort, we applied a catch-effort standardization method proposed by Beverton & Holt (1957), which is frequently used for fishery catch-effort standardization. This method uses catch per unit effort ratio as the scaling factor (called ‘relative fishing power’) on the capture effort. In 2007, Naha Nature Conservation Office (2008) conducted a field test to compare capture efficiency of live-traps used pre-2006 and kill-traps used in 2007–2008. In 2008, before the post-2009 kill-traps were implemented on Amami Island, another field test was conducted to compare their efficiency with those of the 2007–2008 kill-trap model (Naha Nature Conservation Office 2009). Note that these tests were conducted on Ryukyu Island (180 km south-west from Amami Island), where a population of small Indian mongooses is established, because density of mongooses in Ryukyu Island is higher than Amami Island and provides more robust sampling opportunities. The different types of traps were set in the same area and their catch per unit effort (CPUE/100TD) compared. To reduce the effect of full and inactive traps on the substantive capture effort, all traps in these tests were checked daily and any traps with captured mongooses were reset. Results of these tests are shown in Table S1 (Supporting information). Considering the post-2009 kill-trap as the baseline, the ratio of CPUE was as follows:

[live-trap]: [pre-2006 kill-trap]: [2007–2008 kill-trap]: [post-2009 kill-trap] = 0·877: 0·931: 0·480: 1·00.

We calculated corrected trap-days (CTD) by multiplying TD and CPUE ratio for each trap type, and added 1 year's CTD to obtain total annual CTD. Again, because traps no longer function when full, the CTD of kill-traps can overestimate true trapping effort by counting full and inactive traps when the checking interval of a kill-trap is longer than that of a live-trap. However, it would be possible to ignore such biases if number of captures is much smaller than CTD. On Amami Island, number of captures is smaller than 3% of CTD (Fig. 1), and we consider the impact of differences in checking interval between kill-traps and live-traps to be sufficiently small.

CTD has been increasing since 2001; CTD in 2001 and 2010 were 145 004 and 2 075 760, respectively (Fig. 1). In this study, we regarded CTD/100 as the index of capture effort. Inverse to the CTD, the CPUE (/100 CTD) has decreased almost monotonically: 2·33 in 2001 and 0·0150 in 2010 (Fig. 1).

Model description

In this section, we describe the stochastic structure of population dynamics of an invasive animal and its control. Animal populations have stochastic temporal fluctuation and observations of them can be marked with uncertainty (Park 2004). Bayesian state-space modelling approaches (Millar & Meyer 2000; de Valpine & Hastings 2002; Buckland et al. 2004) are useful when uncertainty exists in both population dynamics processes (process error) and observation processes (observation error). A Bayesian state-space model can be written as a hierarchical model with a set of three probability density distributions (pdfs):

display math(eqn 1a)
display math(eqn 1b)
display math(eqn 1c)

where nt is a state variable (i.e. population size) at year t, n1 is an initial state, yt is a observed value (i.e. abundance index) and Θ is a vector of parameters.

The initial state distribution (1a) is a probability distribution that expresses uncertainty of the initial state variable. If introduced population size is given and is defined as the initial state, the initial state distribution is collapsed to a point mass with probability 1:

display math(eqn 2)

The process model was developed on the basis of a biomass dynamic model (or surplus-production model, Hilborn & Walters 1992; Polacheck, Hilborn & Punt 1993; Millar & Meyer 2000; Chaloupka & Balazs 2007), which represents dynamics of exploited populations and is commonly used in fishery stock assessment. The basic form of the biomass dynamic model is represented by a simple equation as follows (Hilborn & Walters 1992):

display math(eqn 3)

where ‘surplus production’ is the difference between reproduction and natural mortality. This dynamic model can also be naturally applied to invasive animal population dynamics determined by intrinsic growth and removal. The state process (1b) pdf represents surplus production and capture. Considering a population primarily regulated by capture pressure, rather than by density dependence, we assumed that intrinsic population growth was exponential. We also considered demographic variability as the process noise. Population size took a non-negative integer value, and process error was given by a Poisson distribution:

display math(eqn 4)

where r is (1 +  intrinsic population growth rate), st is (population size + surplus production) in year t.

In equation (4), we assumed that environmentally dependent fluctuation of the population was not large. Generally, intrinsic growth rate can fluctuate more than expected by Poisson distribution if the population is subject to environmental variability. On Amami Island, the major diet of mongooses comprises insects (Abe 1992), which are consistently abundant, and there are no effective predator species of the mongooses. In addition, climatic limitation, such as drought, does not appear to be an important factor because of the island's warm and wet environment. To date, there has been no report or anecdotal evidence of any environmentally dependent crashes of the mongoose population on Amami Island. For these reasons, we considered only the Poisson distributed process error as the stochastic component of population dynamics.

Population size in the next year was given by removing captured individuals:

display math(eqn 5)

Ct is observed number of captured individuals.

The observation equation represents the relationship between st, Ct and capture effort, Et. Capture success of an individual is treated as a stochastic process, and number of captures can be thought of as a binomial sampling from the population (Rivot et al. 2008). We then defined the likelihood of Ct conditional on st:

display math(eqn 6)

where pt is capture probability in year t. Ct/st is expected to be close to pt.

Capture probability increases with an increase in annual capture effort. To represent this relationship, Poisson catchability models (Seber 1982) have traditionally been used for catch-effort analyses. This model assumes that ‘effort required to capture each individual’ (called ‘trap avoidance’ or ε hereafter) follows an exponential distribution, λexp(-λε) (λ > 0, ε > 0). Therefore, capture probability with capture effort, E, is given by cumulative probability of the exponential distribution, 1 - exp(-λE) (Ross 2009). However, if individual-level heterogeneity in trap avoidance exists (King et al. 2009), and if each individual has different λ following an arbitrary continuous probability distribution, g(λ), the distribution of trap avoidance marginalized over the population (called ‘marginal trap avoidance distribution’ hereafter), math formula, would become a heavy-tailed distribution rather than exponential. For example, if g(λ) is a gamma distribution, marginal trap avoidance distribution becomes a Pareto distribution (Klugman, Panjer & Willmot 2008), which is known as a heavy-tailed distribution. For simplicity of implementation, we applied Weibull distribution to express the heavy-tailed characteristic of marginal trap avoidance distribution, which corresponds to the Weibull catch-effort model (Barron et al. 2011). We also considered temporal variation in catchability as follows:

display math(eqn 7)

ct is logarithm of catchability coefficient that corresponds capture probability when Et = 1, and β is a shape parameter of Weibull distribution. If 0 < β < 1, marginal trap avoidance distribution follows a more fat-tailed distribution than exponential and the hazard rate of an individual being captured decreases as the capture effort increases. β = 1 is equivalent to Poisson catchability model, and the hazard rate is uniform over the capture effort. If β > 1, the hazard rate increases as the capture effort increases and pt forms an s-shaped curve along the capture effort. We assumed that ct is a temporally varying random variable following normal distribution:

display math(eqn 8)

μc and σc2 are mean and variance of ct, respectively.

Model application

Model specification and parameter estimation

Hierarchical Bayes is a very flexible statistical modelling approach that can handle specific characteristics of data such as missing values (Clark & Bjørnstad 2004). In the case of mongooses on Amami Island, capture effort was recorded from 2001, and we defined observation models from 2001 to 2010. Thirty individuals were assigned as the initial state in 1979, n1. Although Bayesian models can include prior knowledge about the parameters, we applied vague prior distributions to the model parameters because prior knowledge on the specific parameter distributions is unavailable for mongooses on Amami Island. Prior specification of each parameter is shown in Table 1. We confirmed that the variances of prior distributions were large enough not to influence the shape of the posterior distribution. We checked the sensitivity of priors of ln(r), μc and 1/σc2 by comparing the posterior with the model whose prior variances of ln(r), μc and 1/σc2 were 10 times larger. For all the parameters, 95% interval of difference between parameter values of the two models included 0, and we considered the influence of prior specification on the posterior to be sufficiently small.

Table 1. Prior specification of the model parameters
ParameterExplanation of the parameterPrior distribution
ln(r)ln(1 +  intrinsic population growth rate)Normal (μ = 0, σ2 = 100)
μ c mean log catchability coefficientNormal (μ = 0, σ2 = 100)
β shape parameter of Weibull catchabilityUniform (α = 0, β = 100)
1/σc2precision of log catchability coefficientGamma (α = 0·01, β = 0·01)

The Gibbs sampling of the posterior distribution was performed using OpenBUGS 3.2.1 (Lunn et al. 2009, http://www.openbugs.info/w/). The OpenBUGS code is included in Appendix S1 (Supporting information). Three independent chains were run and we obtained 1 000 000 samples after 1 000 000 samples were discarded (burn-in phase) for each chain. A large number of iterations are required to obtain well-mixed posterior samples because of low-sampling efficiency of OpenBUGS. To reduce the absolute number of posterior samples for saving PC memory, we took one sample every 1000 iterations and obtained 3000 samples in total.

We evaluated identifiability of parameters, which were applied vague priors (i.e. r, β, μc, σc2) in terms of overlap between prior and posterior distribution as proposed by Garrett & Zeger (2000). If a model parameter is not identifiable, its posterior distribution will almost overlap the prior distribution. Coefficient of overlap, τθ, was defined as follows:

display math

where p(θ) is marginal prior distribution of a parameter θ and p(θ|X) is marginal posterior distribution of θ updated by data X. τθ is the area of overlapping region of the two probability distributions and it lies in the interval [0, 1] which corresponds to a gradient from no overlap to full overlap. When τθ is above some predetermined threshold, then θ is declared weakly identifiable. The ad-hoc threshold of 0·35 has been suggested by Garrett & Zeger (2000), and we also applied this threshold to our study. To obtain the probability density of p(θ|X) from Gibbs samples, we applied a kernel density estimator proposed by Gimenez et al. (2009).

We also confirmed that the assumption of number of captures between 1983 and 1987 (60 individuals every year) did not have a substantial effect on the result of estimation. We estimated a model assuming an extreme condition where all 300 individuals were caught in 1987, but the 95% credible interval of absolute error (i.e. difference) of all parameter values (i.e. r, ct, β, μc, σc) between the two models was contained 0.

Evaluating eradication feasibility with stochastic simulations

An important advantage of a hierarchical Bayes approach is that it offers a consistent inferential framework through estimation and prediction (Clark 2005; Clark et al. 2007). The stochastic population dynamics described and estimated above can be applied directly to the stochastic simulation of the eradication process. To evaluate the feasibility of mongoose eradication, we conducted a simulation study of the mongoose population under the various annual capture efforts from 31600 (≈ 104·5) to 31 600 000 (≈ 107·5) CTD year−1.

In our simulation study, we used the same process model as the Bayesian state-space model, and all the parameters and initial population size were determined by the fitted values. First, population size with surplus production, st, was sampled from the Poisson distribution in eqn. 4. The catchability coefficient, ct, was sampled from a normal distribution (eqn. 8) and then capture probability in year t, pt, was calculated (eqn. 7). Number of captures was sampled from a binomial distribution with probability pt and size st (eqn. 6) and then the population size in the next year, nt+1, was calculated (eqn. 5). All the distributions are described by the fitted values found in the estimation phase of this study. In the simulation, we defined ‘eradication success’ as an event where the population size becomes 0 and ‘eradication feasibility’ as the occurrence probability of eradication success over the multiple Monte Carlo simulation iterations.

For simplicity, we assumed annual capture effort was uniform each simulation year. Fifty-year simulations from 2011 were conducted with different annual capture efforts in a stepwise manner from 31 600 (≈ 104·5) CTD year−1 to 31 600 000 (≈ 107·5) CTD year−1. Three thousand simulations were run for each capture effort. In each iteration, model parameters and population size in 2011 were determined by drawing a posterior sample vector in number order from the 3000 samples obtained by the Gibbs sampling mentioned above. Thus, in our simulation study, we considered both process stochasticity and estimation uncertainty.

Results

Using the introduction and capture record, we could estimate the entire population size dynamics of the mongoose through introduction, expansion, control and eradication. Simultaneously, intrinsic growth rate and catchability could also be estimated from the data. All the parameters that were applied vague priors appeared to be identifiable according to the coefficient of overlap (Table 2). The mean intrinsic population growth rate was 0·49, and its 95% credible interval (CI) ranged from 0·43 to 0·57 (Table 2). Estimates of population size showed a temporally unimodal pattern (Fig. 2a). Although the capture probability during 1980s–1990s could slow mongoose population growth, it could not halt the increase. The population appeared to start decreasing after 2000 when the eradication project by Japanese government started. In the last decade, the population size of mongooses has decreased to about 3%. The posterior mean of population size in 2000 and 2011 was 6141 (95% CI: 5415–6,817) and 169 (95% CI: 42–408), respectively. Uncertainty of population size estimation appeared to increase in the last several years. From the year of mongoose introduction to now, capture probability (calculated by Ct/st, as an approximation of pt when capture effort, Et, is unknown) showed an increasing trend with temporal fluctuation (Fig. 2b).

Table 2. Posterior mean, SE, median, 95% credible interval (CI) of the estimated parameters and coefficient of overlapping between prior and posterior distribution, τθ (Garrett & Zeger 2000)
 MeanSE2·5% CIMedian97·5% CI τ θ
r 1·490·03581·431·491·570·00716
μ c −3·190·822−4·83−3·20−1·490·173
β 0·3310·09920·1250·3330·5290·00817
σ c 2 0·05460·04790·01640·04320·1570·0297
c 2001 −2·980·729−4·44−3·00−1·47 
c 2002 −3·280·718−4·71−3·29−1·80 
c 2003 −3·220·758−4·74−3·23−1·65 
c 2004 −3·240·793−4·84−3·26−1·61 
c 2005 −3·240·860−4·98−3·26−1·47 
c 2006 −2·890·908−4·71−2·90−0·998 
c 2007 −3·500·867−5·22−3·51−1·71 
c 2008 −3·100·880−4·88−3·12−1·26 
c 2009 −3·240·917−5·07−3·25−1·34 
c 2010 −3·190·814−4·78−3·20−1·55 
Figure 2.

(a) Estimated population size and (b) capture probability. Solid line and dashed lines indicate posterior mean and 95% credible interval, respectively. Note that capture probability was calculated by Ct/st, as an approximation of pt when capture effort Et is unknown.

Figure 3 shows the mean capture probability along capture effort and the probability in each year after 2001. The shape parameter of Weibull catchability model, β, was smaller than 1, which means that the extent of trap avoidance was heterogeneous among individual mongoose and the hazard rate of a mongoose being captured decreased with capture effort (Table 2). Therefore, capture probability showed a more highly skewed curve than expected by a standard Poisson catchability model (Fig. 3). The catchability coefficient varied among years but did not appear to increase or decrease monotonically along time (Table 2).

Figure 3.

Estimated capture probability in relation to corrected trap-days (CTD). Black solid line and broken lines indicate mean capture probability and its 95% credible interval (CI), respectively. Grey circles and error bars are posterior mean of capture probability and its 95% CI in each year, respectively.

As an example of the simulation result, we showed the predicted population size with annual capture effort being the same as in 2010 (Fig. 4). Median and 95% credible limits of the population size decreased over time, even if uncertainty in the parameter estimation and process variability were considered. In this example, eradication feasibility would exceed 50% by 2018 and 90% by 2024.

Figure 4.

Simulated population size of mongoose when the same capture effort as 2010 is deployed every year. Solid line, shaded region and dashed lines indicate posterior median, respectively.

The surface of the eradication feasibility along annual CTD and years indicated that eradication feasibility drastically changed when the annual CTD was between 100000 and 300000 (Fig. 5). If annual CTD was 300000, eradication feasibility exceeded 50% in 2033; however, if annual CTD was 100000, eradication feasibility was only 4·2% in 2033 and did not exceed 50% even after 100 years. In contrast, when annual CTD was as large as the recent actual value, eradication feasibility was not sensitive to the change in annual CTD. For example, when we added 1 000 000 CTD to the current value (i.e. 2 075 760 CTD in 2010), 50% eradication would be achieved by 2017, which is only a year sooner than the scenario whereby the current annual capture effort continues after 2010.

Figure 5.

Simulated eradication feasibility (i.e. probability of eradication success). Result was showed in accordance with annual corrected trap-days (CTD) and years.

Discussion

Our analysis clearly showed the extent to which anthropogenic removal has affected the mongoose population over an extended period. On Amami Island, capture probability of the mongooses increased with time (Fig. 2b) and the population started to decline in 2000. Increase in capture probability after 2001 was due to a strong increase in capture effort (Fig. 3). Although the recent decline in CPUE is primarily a result of population decline, our results also indicate that per-effort capture probability declined with an increase in capture effort; hence, the capture probability showed a near-saturated curve along capture effort before the capture probability became 1. Thus, increasing annual capture effort further than the current effort appears to have a limited effect in shortening the time to achieve eradication (Fig. 5). Quantitative inference of invasive species dynamics in the historical context is valuable not only to reconstruct the past but also to evaluate the current management action and to predict future eradication feasibility.

We considered that incorporating introduced population size into the population dynamics model had the added advantage of improving the identifiability of model parameters. Although capture data itself are important to understand the effect of management, it does not contain sufficient information to identify parameters of surplus-production model (Yamamura et al. 2008). In the case of the mongooses on Amami Island, the information on initial population size improved identifiability of model parameters. When noninformative prior was applied to the initial population size, it was difficult to obtain good convergence of the model parameters. Although Bayesian analysis can include prior knowledge on the parameter values, the prevailing recommendation about specification of priors for Bayesian stock assessment is to use noninformative priors (Walters & Ludwig 1994) or informative priors obtained by formal means (Punt & Hilborn 1997; Hilborn & Liermann 1998). In particular, the prior distribution of the intrinsic growth rate can have a substantial effect on the population size estimate (Yamamura et al. 2008). For the mongooses on Amami Island, relevant prior information on intrinsic growth rate is unavailable, and we estimated intrinsic growth rate without speculation, borrowing information from the initial population size, longitudinal data of number of captures and capture effort.

The estimated Weibull catchability model implied the existence of individual heterogeneity in the probability of being captured. Although interpretation of this result should be treated with caution because the index of capture effort was standardized over the different trap devices (see method by Beverton & Holt (1957), we considered this implication to be reliable because estimated annual capture probabilities from 2001 to 2010 gathered around the mean capture probability along the capture effort (Fig. 3). There are few studies that tested the existence of individual heterogeneity in probability being captured (but see King et al. (2009), and we think further research would be needed because it can influence the time to eradication success greatly.

In the case study of mongoose eradication on Amami Island, results of our simulation indicate that the current target of the project, eradication success by FY 2014, would not be feasible even with a vast increase in annual capture effort. However, we also showed that the eradication success might be feasible if eradication action is continued over the next decade. We consider that capture data are an important source of information that can support decision-making of mongoose eradication, but we also think that use of monitoring tools such as sniffer dogs (Cromarty et al. 2002) and tracking tunnels (Ratz 1997) can be beneficial for monitoring the persistence of invasive animals and to confirm eradication success. On Amami Island, sniffer dogs, hair traps and sensor cameras are in operation to search for the remaining mongooses (Naha Nature Conservation Office 2009). Although these monitoring data have not been in use long enough for quantitative inference, it would be possible to incorporate them into the hierarchical modelling approach in the future.

Generally, the feasibility of long-term eradication of invasive species is difficult to evaluate because it requires information on population status (i.e. population size) and dynamics such as intrinsic growth and catchability. In this article, we applied a surplus-production model implemented by Bayesian state-space model to estimate population status and dynamics using capture data and anthropogenic introduction record. A simulation study using the estimated parameters clearly showed a relationship between annual capture effort and eradication feasibility. Such information will help managers make decisions on the level of annual investment while taking into consideration trade-offs with time to achieve eradication success. As many scientists have discussed decision-making in the face of uncertainty (McLain & Lee 1996; Innes et al. 1999; Johnson 1999), adaptive procedures that correct old evaluations using newly acquired information are required for long-term projects of invasive pest management. Especially, ‘learning by removal’ is a crucial component of an adaptive management of invasive species (Park 2004). Capture data are continuously recorded through management action. By updating the model parameters using such data, re-evaluation of eradication feasibility will be possible during long-term management. Inference on long-term population dynamics of invasive species and their management, and integrating multiple sources of information, will offer additional evidence of the efficiency of pest management.

Acknowledgements

Kohji Yamamura and an anonymous reviewer provided valuable comments on the manuscript. We thank Yuya Watari, Takahiro Morosawa and Ken Ishida for valuable comments on an earlier version of this manuscript. Fumio Yamada offered us helpful information about the data. Trapping was performed by Amami Mongoose Busters. This research was supported by the Mongoose eradication projects on Amami Island by the Ministry of the Environment, and by the Global Environment Research Fund (D-1101, Leader: Koichi Goka) of the Ministry of the Environment, Japan, 2011. This article is dedicated to the memory of Go Ogura, mongoose researcher at the University of the Ryukyus.

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