We developed an epidemiological model of avian malaria (Plasmodium relictum) across an altitudinal gradient on the island of Hawaii that includes the dynamics of the host, vector, and parasite. This introduced mosquito‐borne disease is hypothesized to have contributed to extinctions and major shifts in the altitudinal distribution of highly susceptible native forest birds. Our goal was to better understand how biotic and abiotic factors influence the intensity of malaria transmission and impact on susceptible populations of native Hawaiian forest birds. Our model illustrates key patterns in the malaria–forest bird system: high malaria transmission in low‐elevation forests with minor seasonal or annual variation in infection; episodic transmission in mid‐elevation forests with site‐to‐site, seasonal, and annual variation depending on mosquito dynamics; and disease refugia in high‐elevation forests with only slight risk of infection during summer. These infection patterns are driven by temperature and rainfall effects on parasite incubation period and mosquito dynamics across an elevational gradient and the availability of larval habitat, especially in mid‐elevation forests. The results from our model suggest that disease is likely a key factor in causing population decline or restricting the distribution of many susceptible Hawaiian species and preventing the recovery of other vulnerable species. The model also provides a framework for the evaluation of factors influencing disease transmission and alternative disease control programs, and to evaluate the impact of climate change on disease cycles and bird populations.

A fungicide resistance model (reported and tested previously) was amended to describe the development of resistance in Mycosphaerella graminicola populations in winter wheat (Triticum aestivum) crops in two sets of fields, connected by spore dispersal. The model was used to evaluate the usefulness of concurrent, alternating, or mixture use of two high-resistance-risk fungicides as resistance management strategies. We determined the effect on the usefulness of each strategy of (i) fitness costs of resistance, (ii) partial resistance to fungicides, (iii) differences in the dose-response curves and decay rates between fungicides, and (iv) different frequencies of the double-resistant strain at the start of a treatment strategy. Parameter values for the quinine outside inhibitor pyraclostrobin were used to represent two fungicides with differing modes of action. The effectiveness of each strategy was quantified as the maximum number of growing seasons that disease was effectively controlled in both sets of fields. For all scenarios, the maximum effective lives achieved by the use of the strategies were in the order mixtures ≥ alternation ≥ concurrent use. Mixtures were of particular benefit where the pathogen strain resistant to both modes of action incurred a fitness penalty or was present at a low initial frequency.

This paper reviews the evidence relating to the question: does the risk of fungicide resistance increase or decrease with dose? The development of fungicide resistance progresses through three key phases. During the 'emergence phase' the resistant strain has to arise through mutation and invasion. During the subsequent 'selection phase', the resistant strain is present in the pathogen population and the fraction of the pathogen population carrying the resistance increases due to the selection pressure caused by the fungicide. During the final phase of 'adjustment', the dose or choice of fungicide may need to be changed to maintain effective control over a pathogen population where resistance has developed to intermediate levels. Emergence phase: no experimental publications and only one model study report on the emergence phase, and we conclude that work in this area is needed. Selection phase: all the published experimental work, and virtually all model studies, relate to the selection phase. Seven peer reviewed and four non-peer reviewed publications report experimental evidence. All show increased selection for fungicide resistance with increased fungicide dose, except for one peer reviewed publication that does not detect any selection irrespective of dose and one conference proceedings publication which claims evidence for increased selection at a lower dose. In the mathematical models published, no evidence has been found that a lower dose could lead to a higher risk of fungicide resistance selection. We discuss areas of the dose rate debate that need further study. These include further work on pathogen-fungicide combinations where the pathogen develops partial resistance to the fungicide and work on the emergence phase.

This study used mathematical modeling to predict whether mixtures of a high-resistance-risk and a low-risk fungicide delay selection for resistance against the high-risk fungicide. We used the winter wheat and Mycosphaerella graminicola host-pathogen system as an example, with a quinone outside inhibitor fungicide as the high-risk and chlorothalonil as the low-risk fungicide. The usefulness of the mixing strategy was measured as the "effective life": the number of seasons that the disease-induced reduction of the integral of canopy green area index during the yield forming period could be kept <5%. We determined effective lives for strategies in which the dose rate (i) was constant for both the low-risk and high-risk fungicides, (ii) was constant for the low-risk fungicide but could increase for the high-risk fungicide, and (iii) was adjusted for both fungicides but their ratio in the mixture was fixed. The effective life was highest when applying the full label-recommended dose of the low-risk fungicide and adjusting the dose of the high-risk fungicide each season to the level required to maintain effective control. This strategy resulted in a predicted effective life of ≤ 12 years compared with 3 to 4 years when using the high risk fungicide alone.