Immigration drives ship rat population irruptions in marginal high-elevation habitat in response to pulsed resources

Abstract

Pest animal populations, such as rodents, often irrupt in response to pulsed resources. However, few studies have considered how understanding the propagation of irruptions across landscapes could lead to more efficient pest suppression. Resource pulses might create temporary source–sink dynamics in heterogeneous environments, whereby reservoirs of animals living in high-quality habitat increase and spill over into more marginal habitat. Low-density populations in marginal habitat could also increase through in situ breeding by residents in response to increased food availability. Understanding the relative importance of these two nonmutually exclusive processes is important as pest outbreaks could potentially be more efficiently controlled by targeting source populations early in an outbreak. We used a Bayesian hierarchical model to estimate the importance of density-dependent emigration from lower elevation habitats versus in situ breeding by resident animals to the population growth of invasive ship rats (Rattus rattus) in marginal, high elevation habitats during a pulsed resource event (beech seed mast). We found that emigration from lower elevations was important for facilitating rapid population growth at high elevations, enabling rats to reach peak densities of 10.6 rats ha⁻¹. Without immigration, rats were predicted to reach peak densities of only 1.8 rats ha⁻¹ at high elevation, given their densities in that habitat when we started monitoring (0.6 rats ha⁻¹). This result suggests that rat control that targets low and mid-elevations only may be sufficient to suppress irruptions in high-elevation habitat if control effectively prevents immigration. Our study suggests spillover from higher quality habitats may enable outbreaks to rapidly propagate over landscapes. However, for r-selected taxa such as rodents, even very low densities of animals living in marginal habitats can increase significantly when resource pulses occur, albeit at lower densities than for populations in higher quality habitat.

INTRODUCTION

Most landscapes are heterogeneous, encompassing gradients and patchworks of habitat that vary in quality for the species present. Resource pulses can disrupt these dynamics by temporarily flooding landscapes with food, elevating habitat quality for food-limited species (Ostfeld & Keesing, 2000). Examples of resource pulses include mast seeding events (Bogdziewicz et al., 2016), insect outbreaks (Drever et al., 2009), synchronous salmon spawning (Bentley et al., 2012), and rainfall in arid systems (Chesson et al., 2004). For species that are primarily regulated by bottom-up processes, these infrequent, large-magnitude, short-duration events of increased resource availability can drive increased reproduction that results in population irruptions (Yang et al., 2010). We define an irruption here as a sudden, large increase in abundance that exceeds usual seasonal fluctuations. For example, outbreaks of several species of rodent follow episodic bamboo blooming in neotropical forests (Bovendorp et al., 2020). While the spatial dynamics of resource pulses and their effect on the movement of consumers have been well studied (e.g., Polis et al., 1997; Wilmers et al., 2003), the influence of baseline heterogeneity in habitat quality on consumer responses to resource pulses is less understood. However, heterogeneity in habitat quality across landscapes could have important impacts on how and when irruptions propagate.

Resource pulses could create temporary source–sink dynamics in heterogeneous environments, whereby persistent reservoirs of animals living in high-quality habitat suddenly increase and spill over into more marginal habitat. Populations can persist and increase in source habitats because their average rate of increase is neutral or positive, respectively. Sink habitats obtain individuals by migration, so populations in sink habitats will become extinct if migration ceases (Pulliam, 1988; Singleton et al., 2007). For example, Sachser et al. (2021) found that bank voles (Myodes glareolus) spilled over from forest into open habitat patches when mast seeding occurred in the forest. Low-density populations in marginal habitat may also increase through opportunistic breeding by residents in response to sudden increases in food availability. For example, two Australian desert rodents (Pseudomys hermannburgensis and Notomys alexis) persist for months or years at very low densities and then increase their rates of capture (and presumably density) by one to two orders of magnitude in the wake of drought-breaking rains (Dickman et al., 2010). While the outcome of increased abundance may be similar, the processes that underpin these two, nonmutually exclusive hypotheses differ: density-dependent emigration from high- to low-quality habitat versus in situ breeding at low-quality habitat sites. Both immigration and in situ breeding may operate together to drive irruptions if the pulsed resource is available in the marginal habitat when immigrants arrive, allowing them to breed and further augment the outbreak.

Understanding the relative contributions of these two processes to population growth in marginal habitat is important because resource pulses often drive irruptions of invasive animals that necessitate landscape-scale control operations (Griffiths & Barron, 2016; Köhnke et al., 2020). Rodent outbreaks, in particular, can have “dramatic economic, ecological, societal, and even political ramifications” (Andreassen et al., 2020), and understanding the ecology of these outbreaks is important for controlling them efficiently. If migration from high- to low-quality habitat is the key process propagating an irruption across the wider landscape, then rodents in source populations could be controlled before they spill over into sink habitats. Singleton et al. (2007) found that spillover from refuge habitats was the key process driving outbreaks of house mice (Mus musculus) in nonirrigated cereal production areas of southeastern Australia. In high rainfall years, house mice moved from refugia in seepage areas and farm buildings into crops, where they then spilled over into woodland habitats. Singleton et al. (2007) suggested that population control in refuge habitats in the spring would reduce population outbreaks in the autumn.

Here we examine how population irruptions propagate across high- and low-quality habitats by testing the importance of density-dependent immigration versus in situ breeding for a ship rat (black or roof rat; Rattus rattus) irruption in response to a pulsed resource. In New Zealand, intermittent mast seeding by beech trees (Nothofagaceae) historically provided a bonanza of food for endemic parrots and invertebrates before the introduction of mammalian pests such as ship rats. Now these beech mast events drive population irruptions of ship rats, house mice (M. musculus), and stoats (Mustela erminea), resulting in high levels of nest predation for vulnerable native bird species (Elliott & Kemp, 2016). Landscape-scale poisoning operations in beech mast years are required to suppress rodent populations and prevent further declines in native bird species (Elliott & Kemp, 2016). In the 2019 beech mast year, the New Zealand Department of Conservation aerially applied poison to 691,000 ha of conservation lands to suppress pest mammal outbreaks (Environmental Protection Authority, 2020).

Forests where ship rat irruptions occur are heterogeneous, and ship rat densities show spatiotemporal variation across these landscapes in ways suggestive of source–sink dynamics (Carpenter et al., 2022). In nonmast years, ship rats are common in warm, low-elevation, floristically complex forests, but are typically at low densities or absent in cold, high-elevation beech forests (Walker et al., 2019). However, they can become temporarily abundant in high-elevation forest in beech mast years (Carpenter et al., 2022; Christie et al., 2017). It is unclear whether these irruptions in high-elevation forests are primarily triggered by resident, very-low-density populations breeding in response to the sudden resource flush, or are augmented by density-dependent immigration from lower, more favorable habitats. If immigration from lower elevations is the key mechanism contributing to rodent irruptions in these systems, control operations could target these source populations before immigration begins, thereby reducing the area of landscape that needs to be treated with poison.

Carpenter et al. (2022) measured ship rat density, survival, and recruitment following a beech mast across an elevational gradient in southern New Zealand and found increases of ship rats at high elevation lagged increases at low and mid-elevations. However, the process that led to increases at high elevation was unclear. Here, we use Bayesian hierarchical models to assess the importance of density-dependent immigration versus in situ breeding to increases of ship rats at high elevation. We aimed to (1) compare population models with and without an immigration process to assess the importance of immigration to population growth at high elevations, and (2) use parameter estimates from the best fitting model to predict ship rat population growth at high elevations with no immigration (i.e., a scenario where rat control was applied across low and mid-elevations so that no immigration could happen, but in situ growth of rats at high elevation could occur).

METHODS

Study site and data

The study was undertaken on the eastern side of Lake Alabaster/Wāwāhi Waka, in northwest Fiordland, New Zealand (44.5167° S, 168.1572° E). The lake is approximately 20 m above sea level (asl), and the treeline is at approximately 1100 m. The bottom of the valley comprises mixed beech–podocarp–kāmahi forest, which grades to species-poor upland silver beech forest around 500 m asl (Mark & Sanderson, 1962). The area has a wet, temperate climate with an average rainfall of 4250 mm per year (Ruscoe et al., 2001). The site is bounded by high mountains to the east and a lake to the west, which probably act as immigration barriers for ship rats.

We stratified the study site into three elevation bands: low (20–80 m asl), mid (400–500 m asl), and high (800–900 m asl), with the mid-elevation grids located just below the zone where the comparatively species-rich forest grades into species-poor upland forest. Each elevational band contained two capture–mark–recapture grids to estimate ship rat density (Figure 1), two rodent snap-trap lines (to examine breeding parameters), two rodent-tracking tunnel lines, and seed traps and invertebrate pitfall traps (to assess resource availability). In this paper, we use data only from the capture–mark–recapture grids; the other data have been published separately (Carpenter et al., 2022).

FIGURE 1

Map showing study site (Lake Alabaster, New Zealand) and capture–mark–recapture grids (to estimate ship rat density), stratified into three elevation bands: low (20–80 m above sea level [asl], colored light blue), mid (400–500 m asl, colored yellow), and high (800–900 m asl, colored red). Green shading represents forest, and white shading represents grasslands and rock.

Beech trees in the valley masted heavily in autumn (March–May) 2019. From July 2019, we carried out capture–mark–recapture sessions approximately every 3 months until January 2021 (although the time between sampling sessions varied due to logistics and Covid-19 lockdowns) (for more details on live trapping methods, see Carpenter et al., 2022). All animal manipulations were approved by the Manaaki Whenua—Landcare Research Animal Ethics Committee (AEC approval number 19/04/03). We used spatially explicit capture–recapture (SECR) models (Efford & Fewster, 2013) implemented using the “secr” package in program R (Efford, 2019) to estimate ship rat density (rats per hectare) for each grid in each session. Models used conditional likelihood and contained a baseline detection rate at a ship rat's center of activity (g₀) and a scale parameter (σ) specifying the half-normal detection probability function. This function describes the probability of detecting the animal using a detection device (e.g., a trap) placed at a known distance from the animal's center of activity. We specified models in which g₀ and σ were allowed to vary with session and elevation band, as this specification fitted the data best according to Akaike information criterion values.

Model of rat population dynamics

We used a Bayesian hierarchical framework and a Ricker-type density-dependent population model (Turchin, 2003) to explore how the SECR density estimates varied across the six grids following the beech mast. An initial assessment of the SECR estimates showed three patterns that influenced the structure of our statistical model. First, density started high in July 2019 at mid- and low elevations (Figure 2). Second, at high elevations, the density started very low and grew rapidly. Lastly, the population density declined very quickly (crashed) following the density measurement in January 2020. We allowed the modeled carrying capacity parameter (K) to vary over time, because we expected the carrying capacity of grids to drop over time as beech seed rotted or germinated (Wardle, 1984) and therefore became unavailable to rats. It started at a maximal level (maxK) and remained constant up to an estimated date (kChangeDate), at which time K decreased with an exponential decay. This model assumption aimed to capture the high initial densities and growth rates, and the consistent density decline.

FIGURE 2

Mean ship rat density estimates (with 95% confidence intervals) for the six grids and seven mark–recapture sessions, following a mast seeding event in early 2019 at Lake Alabaster, New Zealand. The five open circles were sessions in which zero rats were captured on that grid; the densities for these missing points were estimated using data imputation as outlined in the methods.

Another feature of the data that influenced our model structure was the unequal time interval between successive measurements of density, which had a minimum and maximum of 9 and 17 weeks, respectively. To account for this in our autoregressive model, we estimated a latent initial density for 15 March 2019 and simulated density weekly up to the next observed density measurement (July 2019). Between subsequent measured densities, we simulated density at weekly time steps, with the measured density at the beginning of each interval used as the initial density for the interval. Parameter likelihoods were then calculated using the measured densities and the corresponding weekly predicted densities.

Density across all six grids (i = 1, 2, …, 6) at time t (D_it) was modeled as a multivariate normal as follows:

$$$$ \ln \left({D}_{it}\right)\sim \mathrm{MVN}\left(\ln \left({\mathrm{M}}_{it}\right),{C}_{i{i}^{\prime }}\right), $$$$ (1)

$$$$ {\mathrm{M}}_{it}={\mathrm{M}}_{it-1}{e}^{r_0\left(1-\frac{{\mathrm{M}}_{it-1}}{K_{it-1}}\right)}, $$$$ (2)

where $$$ {\mathrm{M}}_{it} $$$ is a direct prediction of D_it at grid i, r₀ is the maximum weekly population growth rate, K_it−1 is the time- and site-varying carrying capacity, and C_ii′ is a covariance matrix to account for a potential lack of spatial independence in model residuals across grids. C_ii′ is calculated as follows:

$$$$ {C}_{ii^{\prime }}={\upsigma}^2{e}^{\left(-\upphi {d}_{ii^{\prime }}\right)}, $$$$ (3)

where σ² is the variance, ϕ is a distance correlation parameter, and $$$ {d}_{ii^{\prime }} $$$ is a distance matrix among all SECR sites.

The weekly autoregressive predictions of $$$ {\mathrm{M}}_{it} $$$ (Equation 2) were reset to the SECR density estimates following each density estimate. The result of this was a simulated population trajectory with a weekly time step between each density estimate. The prediction of $$$ {\mathrm{M}}_{it} $$$ 1 week after a population density estimate was done by modifying Equation (2) as follows:

$$$$ {\mathrm{M}}_{it}={D}_{it-1}{e}^{r_0\left(1-\frac{D_{it-1}}{K_{it-1}}\right)}. $$$$ (4)

K_it−1 are calculated as follows:

$$$$ {K}_{it-1}=\left\{\begin{array}{cc}\max {K}_i,& \mathrm{if}\ t-1<\mathrm{kChangeDate}\\ {}\max {K}_i{e}^{\left(-{\upgamma}_i\left(\left(t-1\right)-\mathrm{kChangeDate}\right)\right)},& \mathrm{if}\ t-1\ge \mathrm{kChangeDate}\end{array}\right. $$$$ (5)

where maxK_i is the maximum carrying capacity for grid i, kChangeDate is the date (i.e., week) after which the exponential decline in K began, and γ_i is the exponential decay parameter for grid i. The timing of the decline in the measured density appeared to be similar across grids in the raw data (Figure 2), and so we fitted a single kChangeDate parameter for all grids. Preliminary analysis showed that the maximum level of K_it−1 and its decay rate were similar for low- and mid-elevation grids, but that the high-elevation grids differed. Consequently, maxK_i and γ_i were the same for the low- and mid-elevation grids, but the high-elevation grids were allowed to have a different value for each parameter.

To test the relative contribution of immigration to the observed rapid increase in density at the high-elevation grids, we added an immigration effect to the Ricker model (Equations 2 and 3). The immigration effect was limited so that it could only occur from the mid-grids to the high grids directly uphill (i.e., mid-A to high-A, and mid-B to high-B), as Carpenter et al. (2022) detected no movements downslope of rats radio-collared on high-elevation grids. There was no explicit emigration effect on the mid-elevation grids that reduced their density by the corresponding amount of immigration into high grids. The model already accounted for nonmechanistic density-dependent constraints on population growth in mid- and low-elevation grids, which could have been less births, more deaths, or more rats emigrating. The immigration model is as follows:

$$$$ {\mathrm{M}}_{{\mathrm{high}}_{it}}={\mathrm{M}}_{{\mathrm{high}}_{it-1}}{e}^{r_0\left(1-\frac{{\mathrm{M}}_{{\mathrm{high}}_{it-1}}}{K_{it-1}}\right)}+{\mathrm{imm}}_{it}{\mathrm{M}}_{{\mathrm{mid}}_{it-1}}, $$$$ (6)

where imm_it is a density-dependent diffusion coefficient that determines the proportion of immigrants per hectare moving into high grid i from the mid-grid directly below, and $$$ {\mathrm{M}}_{{\mathrm{mid}}_{it-1}} $$$ is the predicted density at the mid-grid directly below high grid i. As in Equation (4), $$$ {\mathrm{M}}_{{\mathrm{high}}_{it-1}} $$$ and $$$ {\mathrm{M}}_{{\mathrm{mid}}_{it-1}} $$$ in Equation (6) were replaced with $$$ {D}_{{\mathrm{high}}_{it-1}} $$$ and $$$ {D}_{{\mathrm{mid}}_{it-1}} $$$, respectively, when t was 1 week following an SECR density estimate.

The imm_it coefficient is a function of densities at the corresponding high- and mid-elevation grids and their respective carrying capacities, reflecting both density-dependent pressures to emigrate, and constraints on immigration in the receiving grid. We assumed there was high potential for immigration when density at a mid-elevation grid was near or above its carrying capacity, and the density at the corresponding uphill high grid was well below its carrying capacity, and low when the reverse was true. This specification was based on the assumption that territories must be available at high elevation in order for ship rats to successfully immigrate there, and that immigrating ship rats will be more likely to find available territory when densities at high elevation are lower. For example, Pichlmueller and Russell (2018) found that reduction of the resident rat population on an island facilitated establishment by immigrant rats that were arriving from the mainland. In the interests of model parsimony, we did not model immigration between low and mid-grids. Both elevational bands had similar densities of rats, and hence similar immigration constraints and emigration pressures and therefore adding in movement from low to mid-grids and vice versa would be unlikely to affect results.

The imm_it is calculated as follows:

$$$$ {\mathrm{imm}}_{it}={r}_{\mathrm{imm}}\frac{{\mathrm{M}}_{{\mathrm{mid}}_{it-1}}/{K}_{{\mathrm{mid}}_{it-1}}}{{\mathrm{M}}_{{\mathrm{high}}_{it-1}}/{K}_{{\mathrm{high}}_{it-1}}}, $$$$ (7)

where r_imm is an immigration rate parameter, $$$ {\mathrm{M}}_{it-1} $$$ and $$$ {\mathrm{M}}_{{\mathrm{mid}}_{it-1}} $$$ are the predicted densities at high-elevation grid i and the mid-grid directly below at time t − 1, respectively; and $$$ {K}_{it-1} $$$ and $$$ {K}_{{\mathrm{mid}}_{it-1}} $$$ are the corresponding carrying capacities. As in Equations (4 and 6), $$$ {\mathrm{M}}_{it-1} $$$ and $$$ {\mathrm{M}}_{{\mathrm{mid}}_{it-1}} $$$ in Equation (7) were replaced with density measurements when t was 1 week following an SECR density estimate.

Two additional parameters were included in the immigration process that could potentially limit the period in which immigration could occur. These were the immStart and immEnd, the start and end weeks of immigration, respectively. imm_it was set to 0 when t was before immStart or after immEnd (Equation 6).

No SECR estimates were obtained for five grid-by-session combinations due to ship rats being at such low densities that no individuals were captured (Figure 2). We estimated these missing points with data imputation so that we would have a complete time series. The missing density data were modeled using the likelihood in Equation (1).

We used a Bayesian hierarchical model and Markov chain Monte Carlo methods to estimate parameters. All parameters that had priors with normal and uniform distributions (Table 1) were updated using Metropolis and Metropolis–Hastings algorithms, respectively (Clark, 2007). All prior distributions spanned ecologically plausible ranges for the parameters. Convergence on the posterior target distribution was assessed visually and confirmed with a scale reduction factor <1.04 calculated on four parallel chains (Gelman et al., 2004; Gelman & Rubin, 1992). Convergence for all models was achieved following a burn-in of 10,000 iterations. Posterior summaries were taken from four chains containing 300,000 samples with a thinning rate of 30 (i.e., 3000 samples in each chain and a total of 12,000).

TABLE 1. Grid-specific prior distributions for model parameters.

Parameters	Grid	Distribution
ln(r0)	All	Normal(ln(0.1), 2.0)
ln(rimm)	High	Normal(ln(0.05), 2.0)
ln(σ^2)	All	Normal(ln(1.0), 2.0)
ln(ϕ)	All	Normal(ln(1.0), 2.0)
maxK	All	Uniform(4, 24)
kChangeDate	All	Uniform(20, 70)
ln(γ)	All	Normal(ln(0.1), 2.0)
immStart	High	Uniform(1, 33)
immEnd	High	Uniform(34, 80)
missingDensity	All	Uniform(0.1, 1.75)
Initial density	All	Uniform(0.05, 18.0)

The nonimmigration and immigration models were compared using the deviance information criterion (DIC; Spiegelhalter et al., 2002). We then used the best fitting model to estimate population growth at high elevation without immigration by fixing immigration at zero but retaining the values for all other parameters. This represents the scenario where ship rats were controlled at low and mid-elevations to the extent that no rats emigrated to high elevation, and population growth was therefore entirely reliant on in situ breeding.

RESULTS

SECR density estimates

Ship rat densities varied through time and across elevation, although most of the grids exhibited a general pattern of ship rat density peaking in January 2020, then declining over the following year (Figure 2). When we began monitoring in July 2019, densities were already high at low- and mid-elevation grids. On mid-B grid, we recorded the highest density estimate of the study in this session, with an estimated density of 21.4 rats ha⁻¹ (95% CI 13–35). However, we only captured two rats at high elevation in this session, giving a density estimate of 0.6 rats ha⁻¹ (95% CI 0.1–2.9). There were five instances where we could not estimate density for a grid because we captured no rats in that session, mainly at high elevation in the last 6 months of the study.

Modeled rat population dynamics

The ΔDIC of the nonimmigration model relative to the immigration model was 25.8, indicating that the immigration model explained the data better than the nonimmigration model. Most of the improved performance came from the explanatory power of the high-elevation grids, as both models showed similar predictions of the low and mid-elevation grids.

In the immigration model, the γ parameter for the exponential decay of K was indistinguishable between the two elevation levels (high vs. low and mid; Table 2). The mean of the maximum weekly population growth rate (r₀) was 0.05. Assuming the population grows unhindered by density dependence for 35 weeks (8 months) of the year, this weekly rate converts to an annual intrinsic rate of growth of r_m = 1.75 (or a finite growth rate of 5.75). This estimate from density data is at the low end of the theoretical range in Hone et al. (2010).

TABLE 2. Posterior mean and 90% credible intervals for parameters of the immigration model, including brief descriptor and equation number in which the parameters are found.

Parameters	Description	Equations	Mean	5% CI	95% CI
γ high elev.	K exponential decay	5	0.08	0.04	0.11
γ low, mid elev.	K exponential decay	5	0.09	0.07	0.12
r0	Max. growth rate week^−1	2, 4, 6	0.05	0.01	0.10
rimm	Immigration rate week^−1	7	0.03	<0.01	0.07
maxK high elev.	Max. carrying capacity	5	7.06	4.10	14.35
maxK low, mid elev.	Max. carrying capacity	5	17.70	10.81	23.38
kChangeDate	Week start K decline	5	38.10	25.00	50.00
immStart	Week start immigration	6	22.62	18.00	28.00
immEnd	Week end immigration	6	53.71	36	77
σ^2	Variance	3	0.31	0.17	0.55

• Abbreviation: elev., elevation.

The predicted carrying capacity differed for the two elevation classes in the model. The mean maxK was higher for the low- and mid-elevation grids (17.7 rats ha⁻¹) than for the high grids (7.1 rats ha⁻¹; Figure 3). The mean week in which the exponential decline of carrying capacity (kChangeDate) began was 38 weeks following an early mast date of 10 March (the austral autumn), which translates to the week of 1 December 2019 (the austral summer).

FIGURE 3

The mean and 90% credible intervals for ship rat carrying capacity over time for the high-elevation grids (blue) and the low- and mid-elevation grids (black) at Lake Alabaster, New Zealand following mast seeding in early 2019.

The mean start and end weeks for immigration were 23 and 54, respectively, which translates to the weeks of 18 August 2019 and 22 March 2020, respectively. This resulted in a rapid increase in emigration to the high grids from the mid-elevation grids directly below in late winter and early spring, which then slowly decreased into summer (Figure 4).

FIGURE 4

The mean predicted increase in density of ship rats per hectare per week due to emigration from mid-A grid to high-A grid (black) and from mid-B grid to high-B grid (red).

Assessment of model residuals using a variogram determined that grids were spatially independent at approximately 0.75 km. Given that the lowest separation distance among grids was 0.8 km, residual spatial autocorrelation was not present in the model results. Most of the variability in the density measurements was captured by the elevation effect and the autoregressive population model (Figure 5).

FIGURE 5

Predicted ship rat densities across all six grids using our best fitting model, which allowed for emigration from mid-grids to high grids.

We used the parameters from our best fitting model (the immigration model; Figure 5), but with immigration at zero, to estimate population growth at high-elevation grids if no immigration were to take place (i.e., a hypothetical scenario where rat control was applied to low and mid-elevations but not high elevations). Without immigration, ship rat densities were predicted to reach a peak density of 1.9 rats ha⁻¹ on each grid (maximum 95% CI limit of approximately 5 rats ha⁻¹: Figure 6) in January 2020, compared with the observed peaks of 10.6 and 6.3 rats ha⁻¹ (on high-B and high-A, respectively), that is, modeled density was about a quarter of that observed in the presence of immigration.

FIGURE 6

Predicted ship rat densities at high elevation using the parameters from our best fitting model, but with immigration set to zero. These results represent a scenario in which ship rats were controlled at low and mid-elevations to the extent that no immigration could occur.

DISCUSSION

Rat population dynamics

We found that rat emigration from mid- to high elevations best explained rapid population growth of rats in high-elevation habitat, enabling rats to go from densities of 0.6 to 10.6 rats ha⁻¹ (in the case of high-B grid) in just 6 months. This result is consistent with several molecular studies that have found substantial gene flow in ship rat populations within landscapes (Abdelkrim et al., 2010; King et al., 2011). In a mast year, increased food availability allows ship rats to breed through the winter (Clapperton et al., 2019), elevating densities at low and mid-elevations and presumably putting pressure on rats to disperse upslope to unoccupied habitat. Results from our best fitting model but with immigration set to zero suggested that without immigration high-elevation rat populations could have increased to densities of approximately 1.9 rats ha⁻¹ solely through in situ breeding, given the density of rats in that habitat when we began monitoring in winter 2019. Therefore, the population growth of rats at high elevation was probably driven both by immigration and by immigrants and residents breeding in the spring and summer of 2019. The breeding demographics of the rats trapped at high elevation between winter and spring 2019 support this finding (Carpenter et al., 2022). During this period, 86.4% of individuals trapped at high elevation were sexually mature, and over a quarter of the females were pregnant (Carpenter et al., 2022). In comparison, three to six months later, the proportion of sexually mature individuals had dropped to 74.3% and there were no pregnant females trapped.

Despite our results demonstrating that emigration from mid- to high elevations was important for rat population growth at high elevation, no movements between grids were detected from our tagged rats. Estimates of the spatial scale of detection derived from our SECR modeling suggested that home ranges of rats on middle elevation grids were reasonably small (radius of 47.8 m in July 2019, assuming a circular home range; Carpenter, unpublished data), as would be expected from a high-density population. In a south Westland beech forest with very low rat density, natal dispersal ranged from 128 to 675 m (Nathan et al., 2020), which implies that dispersing juvenile rats would be capable of moving the 550–650 m between our mid- and high grids. However, we hypothesize that the process was less one of long-distance dispersal of rats upslope and more one of rat individuals increasingly settling uphill as they occupied available habitat. Alternatively, our high-elevation grids (which were actually hollow grids; i.e., a 180 × 180 m² of 96 cage traps) may have been too small in the landscape to detect marked individuals dispersing from mid-elevation grids.

Because we only began monitoring 4 months after the beech seed fell, it is possible that two rats at high grids we detected in winter 2019 were early immigrants themselves, rather than a very-low-density resident population. Monitoring outside of beech mast years would be needed to confirm this, although data from inked tracking cards suggest that rats are never detected outside of mast years at high elevation in our study area (see supplementary material in Carpenter et al., 2022). Ship rats are captured in kill traps in high-elevation forest outside of beech mast years in other parts of Fiordland, although there is a strong negative relationship with elevation (Andrew Digby, unpublished data, 2022).

Our model demonstrated that even in a resource pulse year, high-elevation habitat has a lower carrying capacity for rats (7.1 rats ha⁻¹; 95% CI 4.1–14.4) than low- and mid-elevation habitat (17.7 rats ha⁻¹; 95% CI 10.8–23.4). This is unlikely to be due to differences in the amount of beech seed, because although beech trees often have the highest productivity at mid-slope (Wardle, 1984), seedfall data collected in the nearby Hollyford Valley during the first year of our study showed there was high beech seedfall at high elevation (>7500 seeds m⁻² at one 800 m asl seed trap; see Carpenter et al., 2022). Beech seed does fall later at high elevations compared with low elevations (and thereby could be available for a shorter window of time before rotting or germinating), but Wardle (1984) demonstrated this lag was only one or two months. Seed rain data collected at Lake Alabaster demonstrated that no significant seed rain fell after July 2019, and a seed rain study at a nearby site demonstrated that peak silver beech seedfall at mid- to high elevations (520–945 m asl) occurred in April and May (Burrows & Allen, 1991). Together, these findings suggest there was little variability in the timing of seedfall across the gradient as most falls between March and May. There may be more mice at high elevation, which may either increase food supply for ship rats (if rats feed on the mice; McQueen & Lawrence, 2008) or decrease food supply (if mice consume resources that rats would have otherwise eaten). There is a lower biomass of invertebrates at high elevation (Carpenter et al., 2022; Moeed & Meads, 1986), and invertebrates are important for reproduction in rats (Sweetapple & Nugent, 2007). The lower floristic diversity at high elevation may also mean less complex habitat to support nesting sites (Innes & Russell, 2021). Alternatively, the modeled difference in carrying capacity could be an artifact of ship rats having a delayed start at high elevations due to their very low starting densities, which meant the population had less time to grow before the resource presumably ran out. The only way to test this would have been to have other high-elevation plots with higher starting densities to see whether ship rat populations could reach higher densities at high elevation with sufficient starting numbers and time.

Our top model predicted that carrying capacity across both habitats declined from January 2020 onwards (38 weeks post-mast), which corresponds to both the time that beech seed germinates or rots and therefore becomes unavailable to rats (Wardle, 1984), and the time that stoats become abundant in response to increased rodent numbers (King, 1983). Although the model predicted that carrying capacity in both habitats declined to near zero by January 2021 (as per the densities of rats in these habitats at that time), this result probably reflects rat populations going through extreme delayed density dependence or potentially high levels of stoat predation following their peak in the summer. Other studies have shown that rodent populations can decline below their usual densities when they are in a decline phase following a peak (Sonerud, 1988; Wolff, 1996), and this process may explain what we observed. Similarly, tracking tunnel data from across the South Island of New Zealand suggests that ship rat populations crashed to very low densities following their peak in response to the 2019 mast event (Josh Kemp, unpublished data, 2022). Understanding what baseline carrying capacities are across the elevation gradient in nonmast years would be very useful, but our study began too late in the resource pulse year to assess this (i.e., rats were already responding to the beech mast).

Implications for control

Our results suggest that focusing control on lower elevations where rat densities are more consistently high may significantly suppress population growth at high elevations during beech mast years by preventing immigration. The density of rats at high elevation was very low when we began monitoring, and our model demonstrated that with no immigration occurring these populations were predicted to reach densities of only 1.9 rats ha⁻¹ before crashing post-summer. This is a reasonably low density compared with average ship rat densities in warmer, more floristically rich parts of New Zealand (which range from 1 to 12 rats ha⁻¹; Innes & Russell, 2021), although whether it is low enough to protect vulnerable biodiversity is uncertain, as few studies have characterized the necessary density-impact thresholds (Norbury et al., 2015). In addition, the upper confidence interval of this estimate was approximately 5 rats ha⁻¹, which would still represent a 10-fold increase.

As discussed in the previous section, it is possible that the rats we observed at high elevation in winter 2019 were very early immigrants in the mast cycle rather than residents. Our model results demonstrated that immigration increased significantly from mid-July onwards, so control would have to begin early in July to prevent most emigration to high elevations. Sustained control (e.g., using bait stations) may have to continue for some months to suppress the population enough to prevent immigration. However, the timing of immigration is likely to differ between sites, based on the size of the source population and the elevational gradient (i.e., it may take rats longer to traverse a flatter gradient as there would be more distance to cover). Changes in the timing of immigration may also have a substantial effect on the peak densities at high elevation, as more immigration earlier in the mast cycle will mean there is a larger initial population available to respond exponentially to the food pulse in the limited period it is available.

Almost no rat control operations kill 100% of individuals, so applying one-off control to low and mid-elevations only is unlikely to eradicate these populations entirely. An analysis of rat kill results from the Department of Conservation's large-scale “Battle for Our Birds” response to the 2015 beech forest mast (Elliott & Kemp, 2016) found that only 76% of operations suppressed rats below a 10% rat-tracking rate (an index of rat activity based on the proportion of inked tunnels that detect a rat). According to the relationship between tracking tunnels and density found by Brown et al. (1996) in North Island podocarp-broadleaf forest, a residual tracking rate below 10% would equate to approximately 1.5 rats ha⁻¹ or less. As emigration is often positively density-dependent (Matthysen, 2005), rats in a low-density population are probably unlikely to emigrate to upper elevations, so very high kill rates may not be necessary to prevent immigration. We know of only one published study that has tested how resident ship rat movements change following large-scale control operations that result in the loss of most of their neighbors, which found that movement (as measured by SECR) did not significantly change (O'Malley et al., 2022). However, it is possible that over time, these survivor rats may move large distances as they search for conspecifics, as has been found for rats placed in novel environments with low rat densities (e.g., Nathan et al., 2020; Russell et al., 2010). In addition, one-off control early in the irruption may mean that low- and mid-elevation rats that survive the operation have enough time and resources available for the population to regrow rapidly and reach high densities by the spring, when nesting birds are vulnerable. For this reason, current best practice is for aerial control operations to occur between July and November of the mast year (Elliott & Kemp, 2016).

Although our results showed a significant difference in ship rat density at mid- and high elevations when we began monitoring in July of the mast year, we do not know exactly how density changes with elevation between 500 and 800 m asl. Our mid-elevation grids were just below the threshold where more complex forest grades into floristically simple silver beech, so this shift in vegetation communities may have also delimited where ship rat density went from high to low. More spatially explicit, albeit less intensive, monitoring (e.g., using inked tracking tunnels) would help ascertain this, and how this threshold might vary across different habitat types and latitudes. For example, ship rats were detected up to 1200 m asl in a floristically diverse Westland valley dominated by the three tree species rātā (Metrosideros umbellata), rimu (Dacrydium cupressinum), and kāmahi (Nichols et al., 2021), although there was still a negative relationship between detections and elevation. Our results suggest that attempting to control rats at low and mid-elevations in mast years may work in beech-dominated, deeply incised river valleys bounded by high mountains, but this strategy is unlikely to work at sites that do not have such extreme topography, or have more resource-rich forest at high elevations.

In summary, our results suggest that immigration from higher quality, lower elevation sites to more marginal, high-elevation sites is a key process enabling ship rat irruptions to propagate across a landscape in response to a pulsed resource. Because most population growth in high-elevation habitats is driven by immigrants from lower down, control of rat source populations at lower elevations before they emigrate may be sufficient to prevent outbreaks in these habitats.

ACKNOWLEDGMENTS

We thank all the field workers who collected data for this study. Thanks also to Josh Kemp, Graeme Elliott, and Susan Walker for insightful discussions about ship rats, and to Mandy Barron and two anonymous reviewers for reviewing this manuscript. We are grateful for support from Department of Conservation Te Anau, especially Jamie McAulay and Bex Jackson (for providing tracking data). We acknowledge the use of New Zealand eScience Infrastructure (NeSI) high-performance computing facilities, consulting support, and training services as part of this research. New Zealand's national facilities are provided by NeSI and funded jointly by NeSI's collaborator institutions and through the Ministry of Business, Innovation and Employment's Research Infrastructure programme (https://www.nesi.org.nz). This research was funded by the New Zealand Ministry for Business, Innovation and Employment through an Endeavour Grant (contract C09X1805) as part of the “More Birds in the Bush” program.

CONFLICT OF INTEREST STATEMENT

The authors have no conflict of interest to declare.

Open Research

DATA AVAILABILITY STATEMENT

Data (Carpenter, 2022) are available from Landcare Research: https://datastore.landcareresearch.co.nz/en_LRNZ/dataset/ship-rat-density-data-from-lake-alabaster.