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Invasive plant species that have the potential to alter fire regimes have significant impacts on native ecosystems. Concern that pine invasions in the Southern Hemisphere will increase fire activity and severity and subsequently promote further pine invasion prompted us to examine the potential for feedbacks between Pinus contorta invasions and fire in Patagonia and New Zealand. We determined how fuel loads and fire effects were altered by P. contorta invasion. We also examined post-fire plant communities across invasion gradients at a subset of sites to assess how invasion alters the post-fire vegetation trajectory. We found that fuel loads and soil heating during simulated fire increase with increasing P. contorta invasion age or density at all sites. However, P. contorta density did not always increase post-fire. In the largest fire, P. contorta density only increased significantly post-fire where the pre-fire P. contorta density was above an invasion threshold. Below this threshold, P. contorta did not dominate after fire and plant communities responded to fire in a similar manner as uninvaded communities. The positive feedback observed at high densities is caused by the accumulation of fuel that in turn results in greater soil heating during fires and high P. contorta density post-fire. Therefore, a positive feedback may form between P. contorta invasions and fire, but only above an invasion density threshold. These results suggest that management of pine invasions before they reach the invasion density threshold is important for reducing fire risk and preventing a transition to an alternate ecosystem state dominated by pines and novel understory plant communities.

The quantification of invader impacts remains a major hurdle to understanding and managing invasions. Here, we demonstrate a method for quantifying the community-level impact of multiple plant invaders by applying Parker et al.'s (1999) equation (impact = range × local abundance × per capita effect or per unit effect) using data from 620 survey plots from 31 grasslands across west-central Montana, USA. In testing for interactive effects of multiple invaders on native plant abundance (percent cover), we found no evidence for invasional meltdown or synergistic interactions for the 25 exotics tested. While much concern exists regarding impact thresholds, we also found little evidence for nonlinear relationships between invader abundance and impacts. These results suggest that management actions that reduce invader abundance should reduce invader impacts monotonically in this system. Eleven of 25 invaders had significant per unit impacts (negative local-scale relationships between invader and native cover). In decomposing the components of impact, we found that local invader abundance had a significant influence on the likelihood of impact, but range (number of plots occupied) did not. This analysis helped to differentiate measures of invasiveness (local abundance and range) from impact to distinguish high-impact invaders from invaders that exhibit negligible impacts, even when widespread. Distinguishing between high- and low-impact invaders should help refine trait-based prediction of problem species. Despite the unique information derived from evaluation of per unit effects of invaders, invasiveness scores based on range and local abundance produced similar rankings to impact scores that incorporated estimates of per unit effects. Hence, information on range and local abundance alone was sufficient to identify problematic plant invaders at the regional scale. In comparing empirical data on invader impacts to the state noxious weed list, we found that the noxious weed list captured 45% of the high-impact invaders but missed 55% and assigned the lowest risk category to the highest-impact invader. While such subjective weed lists help to guide invasive species management, empirical data are needed to develop more comprehensive rankings of ecological impacts. Using weed lists to classify invaders for testing invasion theory is not well supported.

Ambrosia artemisiifolia is a highly invasive weed. Identifying the characteristics and the factors influencing its establishment and population growth may help to identify high invasion risk areas and facilitate monitoring and prevention efforts. Six typical habitats: river banks, forests, road margins, farmlands, grasslands, and wastelands, were selected from the main distribution areas of A. artemisiifolia in the Yili Valley, China. Six propagule quantities of A. artemisiifolia at 1, 5, 10, 20, 50, and 100 seeds m -2 were seeded by aggregation, and dispersion in an area without A. artemisiifolia . Using establishment probability models and Allee effect models, we determined the minimum number of seeds and plants required for the establishment and population growth of A. artemisiifolia , respectively. We also assessed the moisture threshold requirements for establishment and survival, and the influence of native species. The influence of propagule pressure on the establishment of A. artemisiifolia was significant. The minimum number of seeds required varied across habitats, with the lowest being 60 seeds m -2 for road margins and the highest being 398 seeds for forests. The minimum number of plants required for population growth in each habitat was 5 and the largest number was 43 in pasture. The aggregation distribution of A. artemisiifolia resulted in a higher establishment and survival rate. The minimum soil volumetric water content required for establishment was significantly higher than that required for survival. The presence of native dominant species significantly reduced the establishment and survival rate of A. artemisiifolia . A. artemisiifolia has significant habitat selectivity and is more likely to establish successfully in a habitat with aggregated seeding with sufficient water and few native species. Establishment requires many seeds but is less affected by the Allee effect after successful establishment, and only a few plants are needed to ensure reproductive success and population growth in the following year. Monitoring should be increased in high invasion risk habitats.

Highly active antiretroviral therapy has successfully controlled HIV replication in many patients. The treatment effectiveness may depend on the pharmacodynamics of antiretroviral drugs. In this paper, we integrate several drug-related parameters into an HIV infection model to investigate the effects of drug pharmacodynamics on the HIV latent reservoir and viral load dynamics. We showed that pharmacodynamic characteristics of drugs and the dosing schedule can significantly affect the outcome of either early or late treatment. Variations in each of the four studied parameters (the slope of the dose-response curve, the ratio of the maximum dosage to the 50% inhibitory concentration, the drug's half-life, and the dosing interval) can generate either an infection-free steady state or persistent infection when the other parameters remain unchanged. The global stability of the infection-free steady state and the viral persistence are shown to be governed by a viral invasion threshold that depends on the drug pharmacodynamics. Our results highlight that success of treatment, particularly pre-exposure prophylaxis or early treatment, may be determined by the choice of antiretroviral drugs in the treatment regimen; prophylaxis or very early treatment using drugs with a good pharmacodynamic profile has the potential to prevent or postpone the establishment of viral infection. In patients with established latent reservoir, late treatment can suppress the viral load to an undetectable level but cannot eradicate the virus. In this scenario, pharmacodynamic parameters and the dosing schedule can moderately change the viral load dynamics. However, the latent reservoir is hardly affected by them because it can be maintained by homeostasis of latently infected cells or other mechanisms rather than ongoing residual viral replication. These results support that drug pharmacodynamics need to be considered in studying HIV dynamics and in developing antiretroviral therapy against HIV infection.

What is the effect of landscape heterogeneity on the spread rate of populations? Several spatially explicit simulation models address this question for particular cases and find qualitative insights (e.g., extinction thresholds) but no quantitative relationships. We use a time-discrete analytic model and find general quantitative relationships for the invasion threshold, i.e., the minimal percentage of suitable habitat required for population spread. We investigate how, on the relevant spatial scales, this threshold depends on the relationship between dispersal ability and fragmentation level. The invasion threshold increases with fragmentation level when there is no Allee effect, but it decreases with fragmentation in the presence of an Allee effect. We obtain simple formulas for the approximate spread rate of a population in heterogeneous landscapes from averaging techniques. Comparison with spatially explicit simulations shows an excellent agreement between approximate and true values. We apply our results to the spread of trees and give some implications for the control of invasive species.

The theory of resource competition in spatially extended systems with resources and biomass fluxes is far from trivial. Here, we analyze the competition between two phytoplankton species for light and a nutrient in a weakly mixed water column. We develop a general framework for such an analysis and show that the competition outcome can be largely understood from a single parameter, the slope of the invasion threshold in the plane of resources. Using this approach, we show that the competition outcome crucially depends on the depth of the biomass maximum. Under eutrophic conditions, when the phytoplankton production peaks on the surface, species composition depends on the ratio of resource supplies, and the competition outcome follows the “classic” rule: coexistence is possible if each competitor has the greatest effect on its most limiting resource. By contrast, in oligotrophic systems, characterized by deep biomass maxima, the absolute level of resource supplies drives species composition, and coexistence becomes more feasible if each competitor mostly consumes its least limiting resource. Finally, when the production peaks in the subsurface, good nutrient competitors are favored. Our findings are supported by empirical data.

Since wild birds are the major natural reservoir for all known influenza A viruses, understanding the ecology of avian influenza (AI) viruses circulating in wild birds is critical to predicting disease risk in wild and domestic birds and preventing transmission to humans. AI virus which is shed by infected birds into aquatic environments plays a pivotal role in the sustained transmission of AI. Recent laboratory experiments, however, show that viral persistence in water is highly sensitive to environmental conditions such as temperature, which varies seasonally and geographically. Here, we develop mathematical models to study the effects of time-varying environmental conditions on AI dynamics, deriving the effects of temperature on the basic reproductive number (𝓡0), the final outbreak size, and the effective reproductive number (𝓡e). For periodic environmental temperatures, we derive a mathematical formulation of an AI invasion threshold (𝓡i) and conclude that apart from the mean temperature, the amplitude of the periodic temperature profile plays a significant role in the invasion of wild bird populations by AI. In particular, both higher means and higher amplitudes (warmer and more variable temperatures) reduce the likelihood of AI invasion. We also analyze the global dynamics of the model proving that AI is uniformly persistent in the wild bird population if 𝓡i > 1. In numerical work, we fit the model to recent experimental data and field survey data from Northern Europe. Two important and robust quantitative conclusions emerge: that direct transmission is negligible compared to indirect and that immunity wanes within about 4 weeks. The latter conclusion is of particular interest since many previous models assume lifetime immunity. We also demonstrate that time-varying temperature may be the underlying cause of several features of AI dynamics which are observed in real data. In particular, AI prevalence is observed to peak in spring and fall but to wane in summer; this behavior naturally emerges from our model under a wide range of conditions.

The discrepancy in the turnover of cells and virus in different organs or viral reservoirs necessitates the investigation of multiple compartments within a host. Establishing a multi-compartmental structure that describes the complexity of various organs, where viral infection comprehensively proceeds, provides a modeling framework for exploring the effect of spatial heterogeneity on viral dynamics. To successfully suppress within-host viral replication, it is imperative to determine drug administration during therapy, particularly for a combination of antiretroviral drugs. The proposed model provides quantitative insights into pharmacokinetics and the resulting virus population, which substantially relates to environmental heterogeneity. The main results are the following: (1) A model incorporating drug treatment admits threshold dynamics, driving to either viral extinction or uniform persistence, regardless of non-trivial initial infection, in the entire system. (2) Viral infection may be underestimated if a well-mixed (single-compartmental) model is used. (3) Optimal drug administration depends not only on the drug distribution over various compartments but also on the timing, described by phase shifts, of the administration of different drugs in a combined therapy.

• The ability to forecast invasion of harmful and beneficial organisms is becoming increasingly important in agricultural and horticultural production systems as well as in natural plant communities. • In this paper we examine the spread of a fungus through a population of discrete sites on a lattice, using replicable, yet stochastically variable experimental microcosms. • We combine epidemiological concepts to summarise fungal growth dynamics with percolation theory to derive and test the following hypotheses: first fungal invasion into a population of susceptible sites on a lattice can be stopped by a threshold proportion of randomly removed sites; second random removal of susceptible sites from a population introduces a shield which can prevent invasion of unprotected sites; and third the rate at which a susceptible population is invaded reduces with increasing number of randomly protected sites. • The broader consequences of thresholds for fungal invasion in natural and agricultural systems are discussed briefly.

Tospoviruses are plant viruses in the genus Bunyaviridae transmitted in a persistent–propagative manner by a range of thrips species and cause disease in wide range of cultivated crops and wild hosts. The viruses in this genus are the only plant-infecting members of the Bunyaviridae. A distinguishing feature, of tospoviruses, from other persistent–propagative plant viruses is that acquisition from infected host plants only occurs by larvae of thrips species. This transmission characteristic is modelled generically as acquisition by juveniles, an invasion threshold is derived, and the dynamics of the system are compared with systems where adults only are involved in acquisition and inoculation. The comparison suggests that in the model disease develops faster and to a greater extent where adults are involved in both acquisition and inoculation. In that case, mobile non-viruliferous adults visit infected plants to acquire virus and in turn visit healthy plants to inoculate virus, whereas acquisition by non-mobile juveniles depends firstly on eggs being laid on an infected plant and then on the virus passaging trans-stadially from the juvenile to the mobile adult form: other factors being equal, the greater the mobility of vectors the greater the probability of both acquisition and inoculation. Where acquisition is by both juvenile and adult forms of the vector, the derived invasion threshold is simply the sum of the component thresholds for each life stage; however, there may be a fitness cost on combining these characteristics expressed as a trade-off between optimising the life history parameters involved in each acquisition route.