Climate change has physiological consequences on organisms, ecosystems, and human societies, surpassing the pace of organismal adaptation. Hibernating mammals are particularly vulnerable as winter survival is determined by short-term physiological changes triggered by temperature. In these animals, winter temperatures cannot surpass certain threshold, above which hibernators arouse from torpor, increasing several fold their energy needs when food is unavailable. Here, we parameterized a numerical model predicting energy consumption in heterothermic species, and modeled winter survival at different climate change scenarios. As a model species, we used the arboreal marsupial monito del monte (genus Dromiciops) which is recognized as one of the few South America hibernators. We modeled four climate change scenarios (from optimistic to pessimistic), based on IPCC projections, predicting that northern and coastal populations (Dromiciops bozinovici) will decline because the minimum number of cold days needed to survive the winter will not be attained. These populations are also the most affected by habitat fragmentation and change in land use. Conversely, Andean and other highland populations at cooler environments, are predicted to persist and thrive. Given the widespread presence of hibernating mammals around the world, models based on simple physiological parameters such as this one, are becoming essential for predicting species responses to warming in the short term.

During hibernation, animals reduce their metabolic rate up to 95%, and do not ingest food, thus relying completely on accumulated fat. An hibernating Dromiciops consumes about 0.09 g of fat per day, thus it would need to accumulate about 13.5g of fat to survive 150 days of hibernation. Then, it is possible to estimate winter survival (in days) by measuring the amount of body fat, and knowing the rate of energy consumption in hibernation, assuming that 100% of nutritional needs are covered by body fat. In this study, we calculated how much days would survive an animal that is exposed to a small increase in winter temperatures and transformed this in a survival function by a numerical model. Our model has the following assumptions:

1.     Cold is the main trigger of hibernation.

2.     Animals rely 100% on body fat during hibernation.

3.     Seasonal food provision will not change with warming.

4.     Animals do not ingest food, at least during the four months of deep hibernation (May to August).

The model

            The model we used predicts daily energy consumption in active and torpid animals, for which we used the proportion of torpid individuals in the field, by re-analyzing Nespolo et al. (2021) dataset, which included time-series of T_B and T_A recorded by intra-peritoneal and environmental data loggers, during one winter. Then, this is an individual-based model aimed at predicting population-level parameters, thus it assumes that the environment is static.

Thus, we codified each datapoint as "torpid" or "active" assuming that below 25ºC of T_B the animal is torpid, and above this value the animal is active. This threshold was set, based on several previous records showing a broad thermal range of activity for this species. Then, we generated a frequency distribution of torpor events, denoting with zero (active) or one (torpid) each hour of the day, and this was associated with a given T_A. Thus, the probability of being torpid, p(torpor) as function of T_A, can be estimated from these time-series, and included in the expression for daily energy expenditure (DEE, kJ d^-1) as:

DEE = p(torpor)TMR + p(active)MR                                  (1)

, where TMR is torpor metabolic rate and MR is the metabolic rate of euthermic animals, which is equivalent to:

DEE = p(torpor)TMR + [1-p(torpor)]MR                            (2)

And given that torpor probability is negatively related with T_A, it can be described with a logistic equation (="torpor incidence equations", hereafter) of the form:

           p(torpor) = 1 / 1+e^-(L0+LX)     (3)

, where L₀ is the intercept, L is the slope, and X is ambient temperature. The empirical values for L₀ and L, obtained by logistic regressions adjusted to the data.

            Below torpor critic temperature (C₁) (the temperature below which heterothermic animals start thermoregulating in torpor), animals generate metabolic heat proportionally to the decrease in ambient temperature, according to the following linear equation (="torpor thermoregulation equation"):

            TMR = M₀(T₀+TX)                        [C₀ < X < C₁]    (4)

, where M₀ is the metabolically active tissue (lean mass, in grams); T₀ the y-intercept of the metabolic curve in torpor (kJ g^-1 d^-1) and T is the slope of this curve (kJ g^-1 d^-1 ºC^-1). Also, C₀ is the lower lethal temperature (ºC), which for Dromiciops is about -5ºC . Above C₁, metabolic rate in torpor is approximately constant and independent of T_A, which we denoted here as i (kJ g^-1 d^-1). Thus, in this range eq. (4) could be reduced to:

            TMR =  M₀i                                       [C₁ < X < C₂] (5)

, where C₂ represents the lower limit of thermoneutrality.

Below the thermoneutral zone, active metabolic rate (MR) behaves as the standard metabolic curve of endotherms (inversely linear with temperature). Expressing this as whole animal values, gives:

MR = M₀(E₀ + EX + Rn)                   [C₁ < X < C₂]            (6)

, where E₀ is the y-intercept of the euthermic curve (kJ g^-1 d^-1), and E is the slope (kJ g^-1 d^-1 ºC^-1, also known as minimum thermal conductance, which is roughly constant for a given body mass and below C₂. The term Rn represents activity, where R is the basal rate of metabolism (kJ g^-1 d^-1) and n is an integer, representing the factorial aerobic scope (or aerobic capacity). Rearranging on a single expression for DEE below C₁ gives:

DEE =  M₀(T₀+TX) + [(1-  )M₀(E₀ + EX + Rn)   [C₀<X< C₁] (7)

, and between C₁ and C₂ gives:

DEE =  M₀i + [(1-  )M₀(E₀ + EX + Rn)                [C₁<X< C₂] (8)

The resulting relationship between DEE and temperature (between C₁ and C₂) represents the percentage of individuals in torpor. The model predictions of torpor probability and DEE. Finally, we estimated winter survival in days, by dividing the standard content of energy for animal fat of 39.7kJg^-1, by the DEE expression, assuming an animal with 20g of body fat, and predicting survival at several fat contents. Parameters of the model, definitions and sources are presented in Table 1. The model is provided as an R script (available from this repository. This modeling approach, along with its assumptions and the derived predictions, are an exploratory exercise, in which we assume that any other factors are kept constant.

IPCC climatic scenarios

To evaluate the survival function, we used the current mean winter temperatures across the geographic area of Dromiciops, and downloaded climatic projections for 2050, 2080, and 2100, for the four common representative concentration pathways (RCPs), at WorldClim (https://www.worldclim.org/data/cmip6/cmip6climate.html). This dataset includes an optimistic scenario (referred as RCP2.6 or ssp126), where emissions are kept constant until 2060, a moderately pessimistic scenario (RCP4.5 or ssp245), where emissions continue to increase at a constant rate, a pessimistic scenario (RCP6.0 or ssp370), and a catastrophic scenario, where emissions increase exponentially (RCP8.5 or ssp585). For simplicity, hereafter we refer to these scenarios using the second nomenclature ("ssp...").  These projections have a resolution of 500 m and every 1,000 m of elevation bands, which we downloaded as raster layers and used with a resolution of 2.5 min (about 5 km per side).