Brood size in an uncertain world.

Reproduction in an uncertain world is fraught. The consequences of investing in too many offspring in a resource poor season can be disastrous but so too is missing the opportunity of a resource rich year. We consider a simple population and individual growth model and use Lyapunov exponents to find analytical results for the optimum brood size under stochastic environmental conditions. We show that if the environment shows dramatic changes between breeding seasons choosing a smaller brood size is more likely to be successful but the best strategy is to synchronize your reproduction to the food availability. Finally, we show that if the cost of having offspring is high it can be better to live in a highly varying world with a plastic strategy that synchronizes to the environment than to live in a deterministic world with a constant strategy, a finding with implications for invasive species and climate change.

What are mycorrhizal traits?

Traits are inherent properties of organisms, but how are they defined for organismal networks such as mycorrhizal symbioses? Mycorrhizal symbioses are complex and diverse belowground symbioses between plants and fungi that have proved challenging to fit into a unified and coherent trait framework. We propose an inclusive mycorrhizal trait framework that classifies traits as morphological, physiological, and phenological features that have functional implications for the symbiosis. We further classify mycorrhizal traits by location - plant, fungus, or the symbiosis - which highlights new questions in trait-based mycorrhizal ecology designed to charge and challenge the scientific community. This new framework is an opportunity for researchers to interrogate their data to identify novel insights and gaps in our understanding of mycorrhizal symbioses.

Optimal control of irrupting pest populations in a climate-driven ecosystem.

Irruptions of small consumer populations, driven by pulsed resources, can lead to adverse effects including the decline of indigenous species or increased disease spread. Broad-scale pest management to combat such effects benefits from forecasting of irruptions and an assessment of the optimal control conditions for minimising consumer abundance. We use a climate-based consumer-resource model to predict irruptions of a pest species (Mus musculus) population in response to masting (episodic synchronous seed production) and extend this model to account for broad-scale pest control of mice using toxic bait. The extended model is used to forecast the magnitude and frequency of pest irruptions under low, moderate and high control levels, and for different timings of control operations. In particular, we assess the optimal control timing required to minimise the frequency with which pests reach 'plague' levels, whilst avoiding excessive toxin use. Model predictions suggest the optimal timing for mouse control in beech forest, with respect to minimising plague time, is mid-September. Of the control regimes considered, a seedfall driven biannual-biennial regime gave the greatest reduction in plague time and plague years for low and moderate control levels. Although inspired by a model validated using house mouse populations in New Zealand forests, our modelling approach is easily adapted for application to other climate-driven systems where broad-scale control is conducted on irrupting pest populations.

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.

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 modelling framework for predicting the optimal balance between control and surveillance effort in the local eradication of tuberculosis in New Zealand wildlife.

Bovine tuberculosis (TB) impacts livestock farming in New Zealand, where the introduced marsupial brushtail possum (Trichosurus vulpecula) is the wildlife maintenance host for Mycobacterium bovis. New Zealand has implemented a campaign to control TB using a co-ordinated programme of livestock diagnostic testing and large-scale culling of possums, with the long-term aim of TB eradication. For management of the disease in wildlife, methods that can optimise the balance between control and surveillance effort will facilitate the objective of eradication on a fixed or limited budget. We modelled and compared management options to optimise the balance between the two activities necessary to achieve and verify eradication of TB from New Zealand wildlife: the number of lethal population control operations required to halt the M. bovis infection cycle in possums, and the subsequent surveillance effort needed to confidently declare TB freedom post-control. The approach considered the costs of control and surveillance, as well as the potential costs of re-control resulting from false declaration of TB freedom. The required years of surveillance decreased with increasing numbers of possum lethal control operations but the overall time to declare TB freedom depended on additional factors, such as the probability of freedom from disease after control and the probability of success of mop-up control, i.e. retroactive culling following detection of persistent disease in the residual possum population. The total expected cost was also dependent on a number of factors, many of which had wide cost ranges, suggesting that an optimal strategy is unlikely to be singular and fixed, but will likely vary for each different area being considered. Our approach provides a simple framework that considers the known and potential costs of possum control and TB surveillance, enabling managers to optimise the balance between these two activities to achieve and prove eradication of a wildlife disease, or the pest species that transmits it, in the most expedient and economic way. This cost- and risk-evaluation approach may be applicable to other wildlife disease problems where limited management funds exist.

Climate-based models for pulsed resources improve predictability of consumer population dynamics: outbreaks of house mice in forest ecosystems.

Accurate predictions of the timing and magnitude of consumer responses to episodic seeding events (masts) are important for understanding ecosystem dynamics and for managing outbreaks of invasive species generated by masts. While models relating consumer populations to resource fluctuations have been developed successfully for a range of natural and modified ecosystems, a critical gap that needs addressing is better prediction of resource pulses. A recent model used change in summer temperature from one year to the next (ΔT) for predicting masts for forest and grassland plants in New Zealand. We extend this climate-based method in the framework of a model for consumer-resource dynamics to predict invasive house mouse (Mus musculus) outbreaks in forest ecosystems. Compared with previous mast models based on absolute temperature, the ΔT method for predicting masts resulted in an improved model for mouse population dynamics. There was also a threshold effect of ΔT on the likelihood of an outbreak occurring. The improved climate-based method for predicting resource pulses and consumer responses provides a straightforward rule of thumb for determining, with one year's advance warning, whether management intervention might be required in invaded ecosystems. The approach could be applied to consumer-resource systems worldwide where climatic variables are used to model the size and duration of resource pulses, and may have particular relevance for ecosystems where global change scenarios predict increased variability in climatic events.

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

Patterns of herbivore browse at small scales, such as the rate of leaf consumption or plant preferences, drive the impact of herbivores on whole-plant processes, such as growth or survival, and subsequent changes in plant population structure. However, herbivore impacts are often non-linear, highly variable and context-dependent. Understanding the effect of herbivores on plant populations therefore requires a detailed understanding of the relationships that drive small-scale processes, and how these interact to generate dynamics at larger scales. We derive a mathematical model to predict annual rates of browse-induced tree mortality. We model individual plant mortality as a result of rates of foliage production, turnover and herbivore intake, and extend the model to the population scale by allowing for between-tree variation in levels of herbivore browse. The model is configurable for any broadleaved tree species subject to vertebrate or invertebrate browse, and is designed to be parameterized from field data typically collected as part of browse damage assessments. We parameterized and tested the model using data on foliage cover and browse damage recorded on kamahi trees (Weinmannia racemosa) browsed by possums (Trichosurus vulpecula) in New Zealand forests. The model replicated observed patterns of tree mortality at 12 independent validation sites with a wide range of herbivore densities and browse damage. The model reveals two key thresholds; in plant foliar cover, indicating when individual trees may be at high risk from browse-induced mortality, and in herbivore intake, leading to high rates of mortality across the whole population.

On the growth of locally interacting plants: differential equations for the dynamics of spatial moments.

Ecologists are faced with the challenge of how to scale up from the activities of individual plants and animals to the macroscopic dynamics of populations and communities. It is especially difficult to do this in communities of plants where the fate of individuals depends on their immediate neighbors rather than an average over a larger region. This has meant that algorithmic, agent-based models are typically used to understand their dynamics, although certain macroscopic models have been developed for neighbor-dependent, birth death processes. Here we present a macroscopic model that, for the first time, incorporates explicit, gradual, neighbor-dependent plant growth, as a third fundamental process of plant communities. The model is derived from a stochastic, agent-based model, and describes the dynamics of the first and second spatial moments of a multispecies, spatially structured plant community with neighbor-dependent growth, births, and deaths. A simple example shows that strong neighborhood space-filling during tree growth in an even-aged stand of Scots pine is well captured by the spatial-moment model. The space-filling has a spatial signature consistent with that observed in several field studies of forests. Small neighborhoods of interaction, nonuniform spacing of trees, and asymmetric competition all contribute to the buildup of a wide range of tree sizes with some large dominant individuals and many smaller ones.

Landscape as a model: the importance of geometry.

In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models that are used in decisionmaking.