Project 8: Use physiologically-based models to predict toxin exposure and toxin-dependent changes in energy availability. (Lead: Liu; Participants: Caughlin [early career], Forbey).

Predicting toxin exposure.

We use a mathematical pharmacokinetic model and relative values for rates of toxin absorption and metabolism (Project 6) to predict toxin exposure in an herbivore after a single meal of a toxic plant (Fig 3). For our models, we let I(t) be the food intake of an herbivore at time t. The parameter c is the concentration of toxin consumed. D(t) is the amount of toxin in the gut at time t, ka is the absorption rate of toxin from the gut compartment into the blood and m is the rate of toxin metabolized by both host and microbial enzymes in the gut prior to absorption. The variable D(t) satisfies the following differential equation:

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with initial condition D(0) = 0. This equation means the rate of change of toxins in the gut (estimated from Project 1) equals the amount of toxin absorbed from the gut compartment into the blood minus the amount of toxin metabolized by herbivore and microbial enzymes prior to absorption (estimated from Project 6A). Let C(t) denote the concentration of toxin in the blood, ke is the rate of toxin metabolized by the liver (estimated from Project 6B), V is the total volume of blood. The dynamics of C(t) can be described by the following differential equation:

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with initial condition C(0) = 0. This equation means that the rate of change of the total amount of toxin in the blood equals the amount of toxin absorbed from the gut compartment into the blood minus the amount of toxin metabolized by the liver.

8B: Predicting available energy.

We link predicted toxins exposure (Project 8A) to changes in the energy herbivores have available to grow, survive and reproduce (Fig 3). Here, I(t) is decided by the following

where, Cmax is the maximum toxin concentration an herbivore can tolerate and I0 is the food intake by an herbivore without toxin whose value can be taken as the ratio of the bite size of food without toxin and the time used to take this bite. The novel component is that we allow food intake of an herbivore to be instantaneously influenced by the toxin concentration [8, 11, 12, 14, 36].

We let E+(t) denote the energy intake at time t. The energy intake from food is decided by how much food is consumed, the concentration of toxin in food (Project 1), and the toxin-dependent changes in digestive function (Project 8). We assume the energy intake at time t is defined as:

where kd is the digestive efficiency of food without toxins in the gut, which is decreased by higher toxin concentrations in the gut [6] with a scaling parameter d. b is the energy metabolized from food without toxicant, which is decreased by higher toxin concentrations in the blood (D(t)) (e.g., [4]) with a scaling parameter q. The rate of change of total available energy E(t) equals the difference between energy intake E+(t) and the sum of: energy used to eliminate the toxins (before and after absorption), energy lost due to toxin-dependent reduction in digestive efficiency in the gut [6] and toxin-dependent reduction in energy metabolism [4], and energy allocated to maintain basal metabolic rate E0.

The second term on the right side of the equation is loss of endogenous energy associated with detoxification [4, 40] and a is the energy required to metabolize and eliminate each unit of toxin from the body. From the available energy E(t) we can predict relative toxin-dependent changes in body mass that determine demographic rates (Project 9). These equations are based on known energetic costs [14, 171] of consuming toxic plants that are linked to reproductive consequences [169, 170, 172]. While initial physiological models focus on energy, any nutritional currency that is known to change body mass could be modeled.

Project 9:

Predict toxindependent consequences in populations. (Lead: Caughlin [early career]; Participants: Liu). We use integral projection models (IPM) to predict population growth rate from body mass of focal species (Fig 4). IPMs are size-structured population models that have been widely used to quantify evolutionary fitness, forecast impacts of wildlife management, and to understand why population dynamics vary between geographicallyseparated populations [173, 174]. However, one limitation of IPMs is that physiological mechanisms are rarely incorporated into these demographic models. We bridge this gap by developing IPMs that predict demographic rates as a function of body mass. We fit IPMs with immediate short-term surrogates of demographic rates: body mass changes and energy loss. Body mass is estimated from available energy predicted from physiological-based models that account for toxin exposure (Project 8) or measured directly in the field (Project 10 below). We will apply a hierarchical Bayesian approach to combine experimental data from animals in captivity and in field enclosures as well as long-term data on population density and abundance. The Bayesian modeling approach provides an established framework for integrating various data sources to model wildlife population dynamics, while accounting for imperfect detection [175]. We will validate the mathematical models with independent data from population trends of wildlife populations. These include woodrat populations in known phytochemical environments monitored in Nevada by Matocq since 2005 or sage-grouse populations monitored by Forbey and Beck in Wyoming and Idaho since 2011. Finally, we will analyze the joint physiological-based model and the IPM using global sensitivity analysis [176].

This analysis allows us to quantify how variability in model input (parameters for toxin exposure, available energy, and body mass) translates into model output (population growth rate). The sensitivity analysis will directly address the genotype by environment conditions that best explain population growth rates. Project 10: Test and revise population model through manipulations of toxins and microbiome. (Co-Leads: Forbey, Matocq; Participants: Alves, Monteith, Scasta [all early career], Beck). We will iteratively test and improve models by using in vivo experiments that measure shortterm energetic and demographic consequences resulting from manipulation of mechanisms of toxin tolerance. We will manipulate the availability of toxins and microbial communities in individual herbivores using captive and field feeding trials previously used by the GUTT team [11, 52, 164]. To manipulate toxins, we provide creosote-tolerant populations of woodrats [11, 73, 177] with choices of sagebrush and creosote. We couple these dietary manipulations with manipulation of microbial communities of the gut following established protocols [25, 99]. To manipulate the gut microbiome, we provide woodrats with artificial food or leaves of whole plants that are mixed with feces collected from sage-grouse or pygmy rabbits consuming >90% sagebrush (Fig 2). Captive trials will include control animals where antibiotics are used (as in [100]). Using different toxin availability and microbial inoculation treatments, we compare changes in: 1) intake of food of known toxin composition (including feeding rates, interval, and duration from videos); 2) microbial communities from fecal collections (Project 3); 3) toxin exposure from concentrations of metabolites in feces and urine (Project 1); and 4) surrogates of available energy from energy and glucuronic acid in feces and urine [40, 171, 178]. In addition, we monitor changes in body mass [14, 78] as well as leptin levels and hypothalamic abundance of neuropeptides in plasma that are surrogates for available energy [162, 163]. We focus on manipulating availability of toxins and microbial communities because the GUTT team has experience conducting in vivo studies where these mechanisms cause changes in intake [11, 25], digestive efficiency [6], and available energy (energy excreted, body mass, [14, 78]) that are explicit parameters in our physiological-based model (Fig 3). However, alternative mechanisms of toxin tolerance may be manipulated based on mechanisms that best explain toxin tolerance identified in Themes 1 and 2.