The application of catch–effort models to estimate the efficacy of aerial shooting operations on sambar deer (Cervus unicolor)

Introduction

Six species of deer (family Cervidae), including sambar deer (Cervus unicolor), red deer (C. elaphus), fallow deer (Dama dama), rusa deer (C. timorensis), chital (Axis axis) and hog deer (A. porcinus) have established wild populations in Australia, with many populations now considered to be overabundant (Davis et al. 2016a). Globally, deer have been implicated in modifying forest ecosystems, including reducing understorey biomass and species diversity and reducing growth and survival of tree seedlings (Côté et al. 2004; Tanentzap et al. 2009; Barrette et al. 2014; Forsyth et al. 2015a). Deer are also a valued game resource popular with recreational hunters, which has led to tensions among stakeholders and government agencies around how deer should be managed. In the state of Victoria, sambar deer are the dominant deer species and are widely distributed across the state but are especially abundant in the forested parts of eastern Victoria (Forsyth et al. 2015b).

During 2019–20, large-scale, high severity bushfires burnt approximately 1.5 million hectares across Victoria, with the worst affected areas occurring in the North East and East Gippsland regions (Fig. 1). It was estimated that these bushfires affected habitat for around 215 rare or threatened species, with many of these thought to be vulnerable to impacts from invasive species following fire (DELWP 2020). As part of the Victorian Bushfire Biodiversity Response and Recovery program, helicopter-based aerial shooting was implemented as a key threat management activity within priority fire-affected and adjacent public land (DELWP 2021). The objective of the aerial shooting program was to reduce the densities of invasive animals, including sambar deer, fallow deer (Dama dama), feral pigs (Sus scrofa), feral goats (Capra hircus), feral cattle (Bos taurus) and foxes (Vulpes vulpes), within areas of high biodiversity value to assist the survival and recovery of threatened species and ecosystems (DELWP 2021).

Fig. 1.

Locations of sites where aerial control of invasive animals occurred between February 2020 and May 2022. Coloured lines indicate flight paths flown by the helicopter. Grey polygons surrounding flight paths for each site represent the total operational (search) area. Dark shaded area shows the extent of the 2019–20 bushfires. Inset shows the study area location (red rectangle).

Aerial shooting from a helicopter has been widely used to control deer populations and is considered to be the most effective method for reducing deer abundances over large areas (Forsyth et al. 2013; Latham et al. 2018; Bengsen et al. 2022a). The standard methodology used for measuring the efficacy of control operations is to conduct pre-control monitoring (Bengsen et al. 2022a) or pre- and post-control monitoring with the difference between the indices or population estimates used to infer control efficacy (Forsyth et al. 2013). Alternatively, radio-collars are fitted to deer and their fate monitored with regards to the control method (Latham et al. 2018). These methods of estimating the efficacy of control may incur substantial extra costs due to the necessity of conducting monitoring in addition to the cost of control, especially if ground-based monitoring methods are required.

The shooting of individual animals from a defined area can be viewed as a removal (or depletion) sample, which is a well-known sampling method used to estimate the size of a demographically closed population (DeLury 1947; Zippin 1958; Gould and Pollock 1997). By demographically closed, we mean that the sampled population is closed to additions or losses except those due to the removal method (i.e. no births, deaths, immigration or emigration). The classic removal model was originally developed assuming that removal effort was constant over time (Zippin 1958). However, many applications in fisheries and pest management needed to account for variable removal effort. Thus, modifications of the classic removal model were developed that allowed removal effort to vary over time. These models were termed ‘catch–effort’ models (Schnute 1983; Gould and Pollock 1997; Chao and Chang 1999; St. Clair et al. 2013). Removal methods have a long history in the estimation of animal abundance and have been regularly used to estimate the size of populations exploited by fishing or hunting (Gould and Pollock 1997; Dorazio et al. 2005; Rodriguez de Rivera and McCrea 2021). The advantage of removal or catch–effort models is that they allow estimates of the initial population size to be made directly from the sequence of removals over time. Assuming the population is demographically closed, an estimate of the residual (or post-control) population can be made by simply subtracting the known removals from the estimate of initial population size. This means that estimates of control efficacy can be derived directly from the data collected during control operations, without the need to conduct additional monitoring.

Recent theoretical work has also extended these types of removal models to populations where demographic closure should not be assumed (Dail and Madsen 2011; Link et al. 2018). Here, populations are assumed to be subject to additions or losses between periods of intensive control. Thus, these models include parameters for estimating population growth due to natural recruitment or recolonisation between these intensive control periods (Hostetler and Chandler 2015). Such models are useful when control operations are applied over extended periods where the population could be subject to breeding or immigration from uncontrolled areas.

Here we analyse the aerial shooting operational data collected for sambar deer from 2020 to 2022, conducted at 10 sites located across fire-affected areas of eastern Victoria. Sambar deer were shot from a helicopter and key data recorded as part of the aerial shooting operations, including helicopter flight path (search) data and location data for shot (and killed) animals. We use these data to estimate pre- and post-control densities of sambar deer to assess the effectiveness of the control program at reducing deer abundance. By using models allowing for additions and losses to the population between intensive periods of control, we should gain an understanding of the effect of recruitment and/or recolonisation of individuals into an area following control and its subsequent effect on the estimates of control efficacy. The model was also used to inform management by recommending the intensity of future control effort required to achieve target reductions in abundance.

Methods

Results

The total number of sambar deer shot through aerial shooting operations across the 10 sites over the five periods (February 2020–May 2022) was 5742 (Table 1). The majority of these were in the Snowy River NP (3313), with the next highest removals in the Alpine NP – Bogong High Plains (1018). Over 43 650 km of helicopter search effort was undertaken in these 10 sites over the same period, with the most effort expended in the Snowy River NP (Table 1). Average search effort per mission was 154 km, and 80% of missions were between 48 and 232 km.

Fitting of the generalised N-mixture model (Eqns 1, 2) to the joint removal data from the 10 sites was judged to have converged after 100 000 iterations, based on visual inspections of the traceplots and values for R^ < 1.01 (Supplementary Table S1). The model also appeared to provide an adequate fit to the data, as judged by the posterior predictive checks of the total number of deer removed compared with that predicted by the model (Fig. S1). Estimates of the detection (and removal) rate of individual sambar deer suggested that the average probability of detecting individuals from the helicopter was 0.11 (95% CI: 0.09, 0.12) per km of search effort, per km² of habitat. However, the detection probability varied among sites, being highest in the Alpine NP – Bogong High Plains at 0.15 per km of search effort per km² of habitat, and lowest at Errinundra NP at 0.02 per km of search effort per km² of habitat (Figs 2, S2). Apart from removals, the rate of natural recruitment (r) of sambar deer also varied with the elevation (m.a.s.l.) of each site as well as season (winter or summer). Populations of sambar deer in operational areas at the highest elevations (e.g. Alpine NP) exhibited decreases over the winter period and large increases over the summer period (Fig. 3). Conversely, populations in operational areas at the lowest elevations (e.g. Croajingolong NP) exhibited the highest increases during the winter period and the lowest during the summer period (Fig. 3). The recruitment rates in other operational areas were intermediate between these two extremes (Fig. 3).

Fig. 2.

The probability of detection and removal of sambar deer for each site during the final occasion for a helicopter search effort of 1 km searched per km² of habitat. Error bars are 90% credible intervals. NP, national park; RP, regional park; WP, wilderness park.

Fig. 3.

Relationship between the recruitment rate (e^r) of sambar deer due to natural additions and losses between periods and elevation (metres above sea level; m.a.s.l.) and season (summer/winter). Values greater than 1.0 indicate net population increases; values less than 1.0 indicate net decreases. Points represent the estimates for each site with colours in ascending order of elevation. Error bars are 90% credible intervals. NP, national park; RP regional park.

The estimated initial (N^) and residual (R^) abundance of sambar deer at each site resulted in the highest population reductions over the five periods (Eqn 3) in the Snowy River NP and Mt Mitta Mitta RP, at 68% and 66%, respectively (Fig. 4, Table 2). Population reductions of 62% and 53% were also obtained at the Mt Buffalo NP and Alpine NP – Bogong High Plains sites. Reductions at Burrowa-Pine Mountain NP, Wabba WP and Coopracambra NP were uncertain, and populations increased at the remaining operational areas (Fig. 4, Tables 2, S2).

Fig. 4.

Estimates of the initial (N^ – blue points) and residual (R^ – red points) densities of sambar deer for each period of aerial control at 10 sites in Eastern Victoria. Vertical lines indicate the 90% credible intervals for the estimates. NP, national park; RP, regional park.

Proportion of the operational area at a site covered during every period varied among sites, from an average of 34% at the Alpine NP – Eastern Alps to 95% at Mt Mitta Mitta RP (Table S3).

Search effort recommendations

The reductions achieved during each period of aerial control varied widely among sites and was dependent on the amount of search effort conducted (Fig. 5). The highest reduction during a single period occurred at Mt Buffalo NP during period 5 (March–May 2022), which reduced the abundance of sambar deer by 61% and required 5 km of search effort per km² of habitat (Fig. 5). Similarly high (>50%) reductions were achieved in the Snowy River NP and Mt Mitta Mitta RP during period 2 (June–October 2020), and again at Mt Mitta Mitta RP during period 4 (September–December 2021) (Fig. 5).

Fig. 5.

The proportional reduction in population density of sambar deer estimated for each of the five periods for each site, plotted against the actual amount of search effort undertaken (solid points). Solid line is the relationship between the proportional reduction and increasing search effort predicted for each site (Eqn 4). Shaded area is the 90% credible intervals. Horizontal dashed line indicates a 50% reduction. Search effort is total helicopter search effort expended during the period. NP, national park; RP, regional park.

More generally, the amount of search effort predicted to be required to achieve various levels of proportional reductions in sambar deer densities (Eqn 4) over a single period suggested that a 50% reduction in density could be achieved with 7 km of search effort per km² of habitat (Fig. 6). This equates to 1.4 km/km² of effort in each of five removal occasions. Simulated reductions in sambar deer densities and associated 90% credible intervals encompassed the majority of the actual reductions achieved at each site over the five periods, suggesting that the simulated relationship was a good match for the estimated reductions (Fig. 6).

Fig. 6.

Relationship between the proportional reduction in sambar deer density and increasing search effort predicted from the combined data from each site (Eqn 4). Shaded area is the 90% credible interval. Points are the estimated reductions achieved in each site for each period against the actual amount of search effort undertaken in each period. Horizontal dashed line indicates a 50% reduction.

Discussion

The analyses presented here used standard operational data collected during an extensive and intensive aerial shooting program to reduce introduced animal abundance in eastern Victoria. During this program, the collection of location data for all shot (and killed) deer, as well as the recording of concurrent search effort data (helicopter search paths), allowed initial abundance, detectability (removal rate) and proportion of the population removed to be estimated using models based on ‘removal’ (or ‘catch–effort’) sampling (Gould and Pollock 1997; Dorazio et al. 2005; Haines 2020). Estimates of these parameters were obtained for sambar deer removal from 10 sites. Initial densities of sambar deer estimated by the removal model ranged from 0.1 to 2.8 deer/km² (mean 1 deer/km²). These were similar to those estimated recently for sambar deer from similar forest types in nearby Kosciuszko NP using spatial capture–recapture methods (mean 1.6 deer/km²) (Bengsen et al. 2022b). An important aspect of the catch–effort model used here was the ability to relax the assumption of demographic closure, allowing an estimation of additions and losses between periods of intensive control. Population growth between periods of control was shown to be strongly related to elevation and season, which had implications for the recovery of sambar deer populations from aerial shooting among the different sites.

Analysis of the aerial shooting data suggested that sambar deer abundance was reduced by around 50–70% at sites where aerial search effort was high (i.e. >3 km/km²) for most periods. However, results at the remaining sites suggest that sambar deer densities have either remained static or increased over the five periods of aerial control. There were two main reasons for the variation in efficacy of the aerial shooting program among the different sites. The first reason was that the level of population reduction achieved was strongly related to the amount of aerial search effort per unit area, a result also found by Bengsen et al. (2022a). Deer populations in sites that exhibited no change or increases in deer densities inevitably were subject to relatively low helicopter search effort per km² of habitat (e.g. Coopracambra NP, Errinundra NP) compared with sites that exhibited decreases in sambar deer densities (e.g. Snowy River NP, Mt Mitta Mitta RP). The second reason was that there was variation in the recruitment rates of sambar deer among different sites, which was dependent on both season and elevation, with areas at the highest elevations (Alpine NP – Bogong High Plains and Eastern Alps) exhibiting a net decrease in abundance during winter followed by net increases during summer. This pattern was reversed for areas at low elevation (e.g. Croajingolong NP), where recruitment was highest during winter and lowest during summer. Other studies have shown that sambar deer move to lower elevations when snow cover increases at high elevations (Comte et al. 2022). The seasonal variation in recruitment among sites estimated here would appear to support this phenomenon, and suggests that recruitment during our study was driven largely by seasonal movement of sambar deer.

Sambar deer recruitment at some sites (e.g. Errinundra NP, Croajingolong NP, Alpine NP – Eastern Alps) was sufficient to offset reductions due to aerial shooting, resulting in increases in sambar deer densities over the duration of the study. Increased recruitment of deer may be related to the recovery of vegetation in these areas post-fire, especially in areas heavily burnt during 2019–20 (e.g. Errinundra NP, Croajingolong NP). Deer have been shown to re-occupy areas recovering from bushfires within 18–24 months post fire (Forsyth et al. 2012); the abundances of sambar deer in areas heavily burnt during the 2019–20 bushfires may have been depleted initially when aerial control commenced, with populations now increasing as the understorey vegetation recovers in these areas. These areas were also ones that received relatively lower aerial control effort, which was more concentrated at those sites with higher initial densities of deer. As the deer population recovers in those areas heavily burnt by the 2019–20 bushfires, their priority for future aerial control effort should also increase to limit the potential recovery of deer populations in these areas.

Aerial control efficiencies differed among locations, being relatively high in some areas such as the Alpine NP – Bogong High Plains, Mt Buffalo NP, Burrowa-Pine Mt NP and the Snowy River NP, and relatively low in other areas such as the Alpine NP – Eastern Alps, Errinundra NP and Coopracambra NP. In general, reductions in Sambar deer densities of 50% could be achieved over a single period of intensive control with 7 km of search effort per km² of habitat. For areas with relatively high control efficiencies, this could be reduced to 5 km/km² of search effort. In practice, the recommended search effort for a single period would need to be undertaken over several occasions, defined as the number of helicopter missions required to undertake at least one complete search of the operational area. Thus, five occasions would be equivalent to at least five complete searches of the operational area, with each occasion consisting of 1.4 km/km² of search effort (i.e. 7 km/km² total).

Despite a long history of animal abundance estimation, especially in fisheries management (DeLury 1947; Schnute 1983; Mäntyniemi et al. 2005), there are few examples of the use of catch–effort models on data collected during aerial shooting operations (Ramsey et al. 2009; Davis et al. 2016b, 2018). Studies applying catch–effort models to feral pig removal in the USA found that aerial shooting removed between 47% and 67% of feral pigs following three removal occasions (Davis et al. 2016b, 2018). Similarly, an analysis of the removal of feral pigs from Santa Cruz Island, California showed that around 77% of the total population of pigs were removed by aerial shooting (Parkes et al. 2010). A recent study of the efficacy of aerial shooting for removing deer from agricultural areas in NSW and Qld found that shooting from a helicopter achieved reductions in deer densities ranging from 5% to 75% for fallow deer and 48–88% for chital deer (Bengsen et al. 2022a).

In Australia, aerial shooting has been used to reduce the abundance of introduced animals such as deer (Bengsen et al. 2022a), feral pigs (Choquenot et al. 1999), dromedary camels (Camelus dromedarius) (Hampton et al. 2016), donkeys (Equus asinus) (Wheeler 1984) and feral goats (Capra hircus) (Pople et al. 1998). However, none of these studies attempted to use the operational data to estimate population abundance. Rather, the efficacy of aerial shooting was evaluated by conducting additional monitoring either before or both before and after the aerial shooting operation (Pople et al. 1998; Choquenot et al. 1999). This could add a considerable additional expense to the control program, especially if ground-monitoring methods are required. In contrast, the analyses presented here offer an alternative method for measuring the efficacy of aerial animal control operations that does not rely on the collection of additional monitoring data. However, one advantage of conducting additional monitoring is that the estimates of animal abundance are obtained in advance of applying control, and can then be used to aid the operational planning of resources (Bengsen et al. 2022a). This is not possible with the present approach, which requires collection of the control data first to estimate population abundance.

A disadvantage of catch–effort models is that not all aerial shooting operational data may be suitable for estimating population abundance. For valid and precise estimates to be obtained from catch–effort data, the removal method must be able to remove individuals at a rate faster than they can be replaced, either by reproduction or immigration. However, by jointly analysing data from 10 sites in the current analyses, reasonable estimates were still able to be obtained for sites with sparse removal data. Another assumption of the catch–effort model used here is that successive removals should be representative of the total population. This could be violated if search effort occurs sequentially across the area of interest rather than as repeated searches of the same area. Analysis of the coverage of the total search area achieved during each of the control periods ranged from 34% to 95%, indicating the proportion of the total search area that was subject to repeat searching, across the five periods. The implications of some sequential coverage of the area of interest on estimates from catch–effort models remains unknown, but would be a worthy topic for future investigation.

The analysis of aerial search effort required has suggested the amount of search effort needed to effect various proportional reductions of sambar deer. These estimates can be used by management agencies to plan future deer control operations and estimate likely costs to achieve target densities. This was undertaken in the recent study by Bengsen et al. (2022a) using hours of operation as the metric of search effort. Most studies of aerial shooting operations have quantified effort in terms of the number of hours of aerial operation rather than the distance travelled, as was used here. It is likely that both distance and time spent searching would be highly correlated and whether one is better than the other for quantifying search effort should be the subject of future investigation.

Finally, how much reduction in deer densities is required to protect biodiversity assets remains a point of conjecture. Studies using exclosures to measure deer impacts have provided evidence that deer reduce vegetation cover and inhibit tree regeneration and sapling growth (Forsyth et al. 2015a; Davis et al. 2016a). In Victoria, the relationships between deer densities and deer impacts have only recently been investigated (Bennett et al. 2022), and additional studies are likely to be required to set appropriate management targets for deer control.

Supplementary material

Supplementary material is available online.

Data availability

The data and code used to undertake the analyses in this study will be made available at Zenodo (https://doi.org/10.5281/zenodo.7302401).

Conflicts of interest

The authors declare no conflicts of interest.

Declaration of funding

The aerial shooting program was established and supported through the Victorian Government’s funding package to support the Bushfire Biodiversity Response and Recovery program. Additional funding was also provided through the Australian Government’s Regional Fund for Wildlife and Habitat Bushfire Recovery.