Thresholds in plant–herbivore interactions: predicting plant mortality due to herbivore browse damage

GIRAE: a generalised approach for linking the total impact of invasion to species' range, abundance and per-unit effects

The total impact of an alien species was conceptualised as the product of its range size, local abundance and per-unit effect in a seminal paper by Parker et al. (Biol Invasions 1:3-19, 1999). However, a practical approach for estimating the three components has been lacking. Here, we generalise the impact formula and, through use of regression models, estimate the relationship between the three components of impact, an approach we term GIRAE (Generalised Impact = Range size × Abundance × per-unit Effect). We discuss how GIRAE can be applied to multiple types of impact, including environmental impacts, damage and management costs. We propose two methods for applying GIRAE. The species-specific method computes the relationship between impact, range size, abundance and per-unit effect for a given species across multiple invaded sites or regions of different sizes. The multi-species method combines data from multiple species across multiple sites or regions to calculate a per-unit effect for each species and is computed using a single regression model. The species-specific method is more accurate, but it requires a large amount of data for each species and assumes a constant per-unit effect for a species across the invaded area. The multi-species method is more easily applicable and data-parsimonious, but assumes the same relationship between impact, range size and abundance for all considered species. We illustrate these methods using data about money spent managing plant invasions in different biomes of South Africa. We found clear differences between species in terms of money spent per unit area invaded, with per-unit expenditure varying substantially between biomes for some species-insights that are useful for monitoring and evaluating management. GIRAE offers a versatile and practical method that can be applied to many different types of data to better understand and manage the impacts of biological invasions.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10530-022-02836-0.

Stochastic plant-herbivore interaction model with Allee effect

Environmental noises often affect population dynamics, and hence many benefits are gained in using stochastic models since real life is full of stochasticity and randomness. In this paper a stochastic extension of a model by Asfaw et al. (Int J Biomath 11:1850057, 2018) is considered. Due to the non-linearity of the model, first, a simplified stochastic plant-herbivore model is formulated and analyzed for its global Lipschitz continuity, positivity, existence and uniqueness of solutions. Second, the analysis is extended to a more complex and realistic model. Numerical simulations using Euler-Maruyama method are employed to demonstrate the long term dynamics. It was found that the noise added to the herbivore population resulted more change in the dynamics than the noise added to the plant population (food source). Ignoring the environmental noise could make the land management and wild life conservation not to maintain their goals.

A New Flexible Sigmoidal Growth Model

Biological growth is driven by numerous functions, such as hormones and mineral nutrients, and is also involved in various ecological processes. Therefore, it is necessary to accurately capture the growth trajectory of various species in ecosystems. A new sigmoidal growth (NSG) model is presented here for describing the growth of animals and plants when the assumption is that the growth rate curve is asymmetric. The NSG model was compared with four classic sigmoidal growth models, including the logistic equation, Richards, Gompertz, and ontogenetic growth models. Results indicated that all models fit well with the empirical growth data of 12 species, except the ontogenetic growth model, which only captures the growth of animals. The estimated maximum asymptotic biomass wmax of plants from the ontogenetic growth model was not reliable. The experiment result shows that the NSG model can more precisely estimate the value and time of reaching maximum biomass when growth rate becomes close to zero near the end of growth. The NSG model contains three other parameters besides the value and time of reaching maximum biomass, and thereby, it can be difficult to assign initial values for parameterization using local optimization methods (e.g., using Gauss–Newton or Levenberg–Marquardt methods). We demonstrate the use of a differential evolution algorithm for resolving this issue efficiently. As such, the NSG model can be applied to describing the growth patterns of a variety of species and estimating the value and time of achieving maximum biomass simultaneously.

Co-existence thresholds in the dynamics of the plant–herbivore interaction with Allee effect and harvest

In the interaction between plants and herbivores that live in the same ecosystem, understanding the conditions in which co-existence equilibrium occurs answers a major question in Ecology. In this interaction, plants serve as food for herbivores on the food chain. Then the livelihood of herbivores highly depends on the availability of food, in this case the availability of plants. Moreover, the abundance of the plant density alone does not guarantee the non-extinction of the herbivore population as they are assumed to reproduce sexually. With this motivation, in this paper a predator–prey mathematical model is reformulated such that the death rate of the herbivore population is dependent on the plant density and their emergence is also governed by the Allee effect. Using the mathematical theory of dynamical system, threshold conditions are obtained for the non-extinction of the herbivore population and a trapping region is obtained to ensure co-existence of the population. Moreover, it has been shown that the dynamics of the population is significantly sensitive to the feeding rate and the harvest rate of the herbivore population.

Multi-scale dynamic maps for the management of invading and established wildlife populations: brushtail possums in New Zealand

Context The abundance and distribution of mammalian species often change in response to environmental variability, losses or gains in suitable habitat and, in the case of pest species, control programs. Consequently, conventional distribution maps rapidly become out of date and fail to provide useful information for wildlife managers. For invasive brushtail possum populations in New Zealand, the main causes of change are control programs by central and local government agencies, and post-control recovery through recolonisation and in situ recruitment. Managers need to know current, and likely future, possum population levels relative to control targets to help assess success at preventing the spread of disease or for protecting indigenous species. Information on the outcomes of government-funded possum control needs to be readily available to members of the general public interested in issues such as conservation, disease management and animal welfare. Aims To produce dynamic, scalable maps of the current and predicted future distribution and abundance of possums in New Zealand, taking into account changes due to control, and to use recent visualisation technology to make this information accessible to managers and the general public for assessing control strategies at multiple spatial scales. Methods We updated an existing individual-based spatial model of possum population dynamics, extending it to represent all individuals in a national population of up to 40 million. In addition, we created a prototype interface for interactive web-based presentation of the model’s predictions. Key results The improved capability of the new model for assessing possum management at local-to-national scales provided for real-time, mapped updates and forecasts of the distribution and abundance of possums in New Zealand. The versatility of this platform was illustrated using scenarios for current and emerging issues in New Zealand. These are hypothetical incursions of possums, reinvasion of large areas cleared of possums, and impacts on animal welfare of national-scale management of possums as vectors of bovine tuberculosis (TB). Conclusions The new individual-based spatial model for possum populations in New Zealand demonstrated the utility of combining models of wildlife population dynamics with high-speed computing capability to provide up-to-date, easily accessible information on a species’ distribution and abundance. Applications include predictions for future changes in response to incursions, reinvasion and large-scale possum control. Similar models can be used for other species for which there are suitable demographic data, typically pest species, harvested species or species with a high conservation value. Implications Models such as the spatial model for possums in New Zealand can provide platforms for (1) real-time visualisation of wildlife distribution and abundance, (2) reporting and assessing progress towards achieving management goals at multiple scales, (3) use as a decision-support tool to scope potential changes in wildlife populations or simulate the outcomes of alternative management strategies, and (4) making information about pest control publicly available.

How Herbivore Browsing Strategy Affects Whole-Plant Photosynthetic Capacity

If a browse damage index indicates that a tree has been 50% browsed by herbivores, does this mean half the leaves are entirely eaten or are all the leaves half eaten? Were the affected leaves old or young? Large or small? In sunshine or shade? Understanding what effect browsing will have on the photosynthetic capacity and the plant's survival ability clearly requires a greater understanding of browsing strategy across the canopy than can be given by a single index value. We developed stochastic models of leaf production, growth and consumption using data from kamahi (Weinmannia racemosa) trees in New Zealand which have been browsed by possums (Trichosurus vulpecula), to ascertain which of six feasible browsing strategies possums are most likely to be employing. We compared the area distribution of real fallen leaves to model output in order to select the best model, and used the model to predict the age distribution of leaves on the tree and thus infer its photosynthetic capability. The most likely browsing strategy that possums employ on kamahi trees is a preference for virgin (i.e. previously unbrowsed) leaves, consistent with the idea that browsing increases the production of chemical plant defences. More generally, our results show that herbivore browsing strategy can significantly change the whole-plant photosynthetic capability of any plant and hence its ability to survive, and therefore, herbivore damage indices should be used in conjunction with more detailed information about herbivore browsing strategy.

Investigating brushtail possum (Trichosurus vulpecula) home-range size determinants in a New Zealand native forest

Context The Australian brushtail possums (Trichosurus vulpecula) introduction to New Zealand has exacted a heavy toll on native biodiversity and presented the country with its greatest wildlife reservoir host for bovine tuberculosis (TB). Management efforts to control both possums and TB have been ongoing for decades, and the biology of possums has been studied extensively in Australia and New Zealand over the past 50 years; however, we still do not have a clear understanding of its home-range dynamics. Aims To investigate determinants of home range size by using a uniquely large dataset in the Orongorongo Valley, a highly monitored research area in New Zealand and compare our findings with those of other studies. Methods Possum density was estimated, for subpopulations on four 13-ha cage-trap grids, by the spatially explicit capture–mark–recapture analysis of trapping data from 10 consecutive months. Home ranges were estimated from trap locations using a 100% minimum convex polygon (MCP) method for 348 individuals and analysed with respect to grid, age and sex. Key results Mean (standard error) possum density, estimated as 4.87 (0.19), 6.92 (0.29), 4.08 (0.21) and 4.20 (0.19) ha–1 for the four grids, was significantly negatively correlated with mean MCP home-range size. Grid, age, and the interaction of age and sex were significantly related to home-range size. Older possums had larger home ranges than did younger possums. When ‘juvenile cohort’ and ‘adult cohort’ data were analysed separately, to investigate the significant interaction, males in the ‘adult cohort’ had significantly larger home ranges than did females, with the grid effect still being apparent, whereas neither sex nor grid effects were significant for the ‘juvenile cohort’. Conclusions Our findings indicate that, in addition to density, age and sex are likely to be consistent determinants of possum home-range size, but their influences may be masked in some studies by the complexity of wild-population dynamics. Implications Our findings have strong implications regarding both disease transmission among possums and possum management. The fact that adult males occupy larger home ranges and the understanding that possum home range increases as population density decreases are an indication that males may be the primary drivers of disease transmission in possum populations. The understanding that possum home range increases as population density decreases could be a direct reflection of the ability of TB to persist in the wild that counteracts current management procedures. If individuals, and particularly males, infected with TB can withstand control measures, their ensuing home-range expansion will result in possible bacteria spread in both the expanded area of habitation and new individuals becoming subjected to infection (both immigrant possums and other control survivors). Therefore, managers should consider potential approaches for luring possum males in control operations.

Foliar Nutritional Quality Explains Patchy Browsing Damage Caused by an Invasive Mammal

Introduced herbivores frequently inflict significant, yet patchy damage on native ecosystems through selective browsing. However, there are few instances where the underlying cause of this patchy damage has been revealed. We aimed to determine if the nutritional quality of foliage could predict the browsing preferences of an invasive mammalian herbivore, the common brushtail possum (Trichosurus vulpecula), in a temperate forest in New Zealand. We quantified the spatial and temporal variation in four key aspects of the foliar chemistry (total nitrogen, available nitrogen, in vitro dry matter digestibility and tannin effect) of 275 trees representing five native tree species. Simultaneously, we assessed the severity of browsing damage caused by possums on those trees in order to relate selective browsing to foliar nutritional quality. We found significant spatial and temporal variation in nutritional quality among individuals of each tree species examined, as well as among tree species. There was a positive relationship between the available nitrogen concentration of foliage (a measure of in vitro digestible protein) and the severity of damage caused by browsing by possums. This study highlights the importance of nutritional quality, specifically, the foliar available nitrogen concentration of individual trees, in predicting the impact of an invasive mammal. Revealing the underlying cause of patchy browsing by an invasive mammal provides new insights for conservation of native forests and targeted control of invasive herbivores in forest ecosystems.

Species- and site-specific impacts of an invasive herbivore on tree survival in mixed forests

Invasive herbivores are often managed to limit their negative impact on plant populations, but herbivore density - plant damage relationships are notoriously spatially and temporally variable. Site and species characteristics (both plant and herbivore) must be considered when assessing the potential for herbivore damage, making it difficult to set thresholds for efficient management. Using the invasive brushtail possum Trichosurus vulpecula in New Zealand as a case study, we parameterized a generic model to predict annual probability of browse-induced mortality of five tree species at 12 sites. We compared predicted and observed tree mortality for each species + site combination to establish herbivore abundance - tree mortality thresholds for each site on a single and combined tree species basis. Model results indicated it is likely that possum browse was the primary cause of all tree mortality at nine of the 12 species-site combinations, allowing us to estimate site-specific thresholds below which possum population numbers should be reduced and maintained to keep tree mortality under a predetermined level, for example 0.5% per year. The browse model can be used to set site- and species-specific management action thresholds, and can be adapted easily for other plant or herbivore species. Results for multiple plant or herbivore species at a single site can be combined to create conservative, site-wide management strategies, and used to: determine which sites will be affected most by changes in herbivore abundance; quantify thresholds for herbivore management; and justify expenditure on herbivore control.

A review of biodiversity outcomes from possum-focused pest control in New Zealand

Worldwide, introduced vertebrate pests impact primary production, native biodiversity, and human health. In New Zealand, extensive pest control (~10 million ha) is undertaken to protect native biota and to prevent losses to the primary sector from wildlife vectors of bovine tuberculosis (TB), primarily possums (Trichosurus vulpecula). Control is conducted by TBfree New Zealand and by conservation agencies. Remote, forested terrain is treated using the toxin 1080 via aerial delivery in bait with a return time of ~5 years. Ground-based control is conducted annually using traps and/or poison bait. Possums are controlled to very low abundance by these operations. Aerial 1080 is effective against another forest-dwelling vertebrate pest, the ship rat (Rattus rattus). Possum control has reduced TB rates, but collateral benefits for native biodiversity have not been quantified, making it difficult to demonstrate a return on investment. We review information from 47 accounts of responses of native biota to possum control. Of these, 60% quantified responses to aerial 1080; the remainder were ground-based. Possum control benefited vegetation by increasing foliage and fruit production, and by reducing tree mortality. Controlling ship rats and possums together improved bird populations, but rats recovered rapidly and long-term outcomes for rat-vulnerable birds are unknown.Large-bodied invertebrates also benefited from extensive pest control. We conducted a meta-analysis of 84 response measures from 35 of these 47 studies in order to provide a quantitative assessment of these findings. The analysis demonstrated that both ground and aerial control of this invasive pest in New Zealand has provided substantial collateral benefits for native biota. Few studies have taken advantage of decades of extensive pest control in New Zealand to monitor ecosystem-level outcomes, which have received only short-term attention thus far. Non-treatment experimental controls and replicate sites that enable validated assessments of outcomes for native biota are vital. Future studies would benefit from a standardised set of biodiversity indicators from a range of taxonomic and functional groupings, and from standardising experimental designs so individual studies can contribute to future meta-analyses, to strengthen the evidence base for the impacts of invasive pests on native biota in New Zealand and worldwide.