Maslo and Fefferman (2015) recently modeled the population dynamics of Myotis lucifugus undergoing responsive immunity or evolutionary rescue in the face of WNS (summarized below). The evolutionary rescue model makes the conservative assumption that phenotypic robustness to WNS was based upon a Boolean protective genetic profile. Bats within an uninfected population were either entirely robust, r, or susceptible, wt, to WNS-induced mortality. Using published or estimated vital rates from before (M¯wt and M¯r) and after (Mwt+ and Mr+) P. destructans introduction (Frick et al., 2010b; Maslo et al., 2015), Maslo and Fefferman (2015) parameterized four two-stage Lefkovitch matrices (Morris and Doak, 2002), each representing population growth of one genetic segment of the population in both the uninfected and infected state:

where S represents survival of M. lucifugus; B represents the proportion of females breeding; and the subscripts j and a indicate values for 1st-year or adult bats, respectively. They set 1st-year bat survival as a constant proportion (0.47) of adult survival (Frick et al., 2010b), and held maternity (m) constant at F = 1, as M. lucifugus typically produce a single pup per year (Barclay et al., 2003).

Starting with an initial population vector of 5,000 total individuals, they estimated initial prevalence of the robust genetic profile in the population to be ρ₀ and then split the initial demography υ-total, 0 into two corresponding initial vectors υ-wt, 0  and υ-r, 0  such that υ-r, 0=ρ0υ-total, 0 and υ-wt, 0=(1-ρ0)υ-total, 0. This approach deviated from traditional PVA, which would apply a single population projection matrix to a single state vector representing the current stage-based demography of the population. Maslo and Fefferman (2015) then projected population growth in the absence of disease by independently applying the appropriate matrix to each vector to obtain the population vector for the next year: M¯wtυ-wt, t=υ-wt, t+1 and M¯rυ-r, t=υ-r, t+1. Maslo and Fefferman (2015) then computed the realized total population vector υ-wt, t+1+υ-r, t+1, and resulting growth rate.

The model assumes environmental contamination for an entire habitat (e.g., hibernaculum) with 100% infection following contamination. They define I_t to be the percent of the population infected in year t and assume that the rate of exposure/infection in a hibernaculum is independent of genetic robustness. Using these probabilities and matrices, they then computed the subpopulations in year t + 1 within a single population as the sum of individuals that are wild type and uninfected: (1-It)M¯wtυ-wt, t, robust and uninfected: (1-It)M¯rυ-r,t, wild type and infected: ItMwt+ υwt, t, and robust and infected:  ItMr+ υr, t.

Additionally, 0.1% of the offspring from same profile pairs spontaneously mutate to the other profile (i.e., wt × wt results in a Robust offspring), and r × wt results in 50% of each profile. Assuming random mating among adults Maslo and Fefferman (2015) “corrected” each of the projected population vectors by subtracting the offspring with different genetic profiles from the projected population vector associated with the matrix relevant for the parents, and adding them to the offspring in the vector associated with the appropriate subpopulation for the resulting juvenile.

Under evolutionary rescue, the resulting total population vector in each year was the sum of the individuals within each subpopulation, and the stabilized growth rate (λ = 1.05) was representative of the shifting proportion of genetic robustness within the population (Maslo and Fefferman, 2015). Under responsive immunity, the model projected a single state vector (N = 5000) representing pre-WNS stage-based demographic structure through a single projection matrix (parameterized with survival estimates generated from population counts of multiple infected hibernacula within the first three years of WNS emergence; Frick et al., 2010a). The model output predicted continued population declines stabilizing at λ = 0.89 after 3 years.

For the current analysis, we separated the acquired immune response into adaptive and innate immunity and used both published and estimated vital rates. Both provide protection against mortality for individuals that survived initial exposure, but adaptive immunity confers life-long individual protection, whereas the innate immune protection is lost in the absence of continued pathogen exposure. Individuals with adaptive immunity were therefore modeled in the same way as (Maslo and Fefferman, 2015). In contrast, treated and re-exposed individuals with innate immunity suffered the same initial mortality risks from re-exposure as though they had never previously been immune (though if they survived, they would again be protected throughout the duration of their continuous exposure). In all other ways, this population was also modeled as in Maslo and Fefferman (2015) (Figure 1). Note that this representation of innate immunity can vary either in dose-response curves, or in physiological state of the individuals. However, we do assume that rapidity of the innate response is not itself consistent for an individual over time. We make this assumption because such a consistent response would likely have a genetic component and be considered a potential mechanism for evolutionary rescue, thus covered by that scenario.

We applied a suite of treatment regimes to the three host response scenarios (Figure 2), making the following assumptions based on current treatment research: (1) treatment application occurs just prior to or during the hibernation period; (2) no immigration/emigration occurs after treatment deployment; and (3) treatment suppresses P. destructans growth for a single hibernation season. In the pulsed model (Figure 2), bats are treated in the 1st, 5th, and 10th year following WNS arrival. We modeled constant treatment application regimes, beginning 5 or 15 years following WNS arrival at a site. We also examined the impacts of an interval treatment regime, where bats are treated annually between 5 and 15 years following WNS arrival. We modeled the demographic impacts of each treatment regime for treatments that were 25, 50, 75 or 100% effective and were applied to 25, 50, 75 or 100% of the population. We assumed a quasi-extinction threshold of 150 individuals, below which a population was considered extirpated. If a population reverted to positive growth, we calculated the time required for the abundance to reach its minimum viable population size (assumed to be 2,500 individuals based upon a review of finite rates of increase at WNS-infected hibernacula of various sizes; Maslo and Fefferman, 2015).

For bats undergoing either type of immune response, annual treatment beginning early in the disease phase may be extremely effective in reversing demographic decline and creating a positive growth trajectory. However, long-term treatment of multiple bat populations presents several logistical challenges. Treatments applied directly to bats would require significant numbers of individuals to be captured at least once each year (treatments may not last a full hibernation season). Traditional bat capture methods (e.g., harp traps, mist nests) may not guarantee treatment of even 25% of the population in any given year. Actively treating bats during the hibernation period would increase the likelihood that the appropriate threshold number of bats are treated but would disturb hibernating populations unless a passive delivery system is implemented. Hibernaculum treatments (e.g., antifungal treatment of surfaces, VOC treatment of air) may offer a more practicable approach, but treating every infected North American hibernaculum in perpetuity is not sustainable. Identifying the appropriate treatment approach becomes important when monetary and physical feasibility is taken into account. Furthermore, different bat species may be responding to the disease differently, understanding the host response will help to prioritize treatment of species and determine whether one treatment regime is appropriate for all species or if individual treatment plans should be developed.

Understanding a host's response to a pathogen prior to intervention is critical to success. While it is tempting to assume that any decrease in pathogen load would be beneficial, the physiology of natural immunity may not always allow such black-and-white solutions. As we have shown, if individuals upregulate physiologically costly innate immune protections only during pathogen exposure and downregulate them once the threat is passed, removal of the trigger for protection can cause a protected population to revert to vulnerability. In these cases, treatment in the absence of reasonable belief that the pathogen will not be reintroduced until after the population has recovered to pre-infection sizes (or beyond) could be catastrophic. Of course, the disease in the absence of treatment may itself be catastrophic. If the ongoing mortality is sufficiently high to compromise the long-term population growth rates, treatment may be the only option. In this case, if innate immunity is providing protection, we must recognize the risks of inconsistent treatment regimes and commit to constant efforts. There is still a point of no return beyond which even constant treatment cannot guarantee the persistence of the population (e.g., small population paradigm, Allee effects, etc.). If the only mechanisms of protection are from immunity and not evolutionary rescue, treatment must begin early enough to preserve a sufficient number of mostly healthy, breeding individuals. Models of this sort will be a critical tool in evaluating when this point-of-no return might happen, what level of efficacy is required and what treatment regime will ensure survival.

The prospects for a population are better under the processes of evolutionary rescue even without intervention. In these cases, treatment becomes a beneficial mechanism for support of the population to mitigate the initial drop in population size as infection decimates individuals without protective genotypes. Increasing the survival of unprotected individuals can prevent the population from growing too small, or being moderately low for too long. However, treatment will also ease the intensity of the selective pressure, slowing the rate of replacement of unprotected individuals by protected individuals. The simulations presented here assumed 50% probability of protection for the offspring of mating between protected and unprotected individuals (i.e., a dominant trait on a single locus that assorts independently). In reality, genetically-derived protection against infection is likely due to a suite of genes that do not assort simply, and dilution of selective pressure must therefore also be considered.

Lastly, evolutionary rescue is not mutually exclusive with either immune protection, meaning that the impact of treatment on real-world population persistence will entail a complicated trade-off between the dilution of selective forces, the mitigation of mortality costs from new infections due to ongoing transmission, and the potential for compromising ongoing innate immune protection in already-exposed individuals. By tailoring models to reflect the genetic and immunological processes of particular systems, we can begin to consider certain treatment strategies, weighing these impacts explicitly, and discovering how best to manage populations under threat.

The implications of these models extend beyond the WNS epizootic. For the increasing numbers of emerging wildlife diseases, such as the recently discovered snake fungal disease (Tetzlaff et al., 2015) or the multiple etiologically complicated coral diseases (Weil and Rogers, 2011; Sutherland et al., 2016), our study underscores the importance of studying the host response concurrently to investigating mechanisms of infection and transmission. The fungus Batrachochytrium dendrobatidi has caused worldwide declines in amphibian populations, leading to coordinated efforts to control pathogen spread, understand mechanisms of transmission and infection, and treat the disease (Whilde et al., 2017). However, efforts to treat infection have been largely unsuccessful and different species have varying degrees of susceptibility (Heard et al., 2011; Woodhams et al., 2012). Recent evidence shows that immunosuppression of the host by the pathogen may play a critical role in its ability to infect hosts (Savage et al., 2016) indicating that a better understanding of the host response(s) will help to elucidate a successful treatment plan for this disease. For more well-characterized diseases, such as Dermo in oysters (Burge et al., 2014) or chronic wasting disease in cervids (Williams et al., 2002), where the host response may be better understood, our study demonstrates the necessity of incorporating what is known of the host response into an efficient and effective treatment plan.

The implications of these models extend beyond the WNS epizootic. For the increasing numbers of emerging wildlife diseases, such as the recently discovered snake fungal disease (Tetzlaff et al., 2015) or the multiple etiologically complicated coral diseases (Weil and Rogers, 2011; Sutherland et al., 2016), our study underscores the importance of studying the host response concurrently to investigating mechanisms of infection and transmission. The fungus Batrachochytrium dendrobatidi has caused worldwide declines in amphibian populations, leading to coordinated efforts to control pathogen spread, understand mechanisms of transmission and infection, and treat the disease (Whilde et al., 2017). However, efforts to treat infection have been largely unsuccessful and different species have varying degrees of susceptibility (Heard et al., 2011; Woodhams et al., 2012). Recent evidence shows that immunosuppression of the host by the pathogen may play a critical role in its ability to infect hosts (Savage et al., 2016) indicating that a better understanding of the host response(s) will help to elucidate a successful treatment plan for this disease. For more well-characterized diseases, such as Dermo in oysters (Burge et al., 2014) or chronic wasting disease in cervids (Williams et al., 2002), where the host response may be better understood, our study demonstrates the necessity of incorporating what is known of the host response into an efficient and effective treatment plan.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.