Wild Life Model (WildLife)

The wildlife model use in the TaigaClimate project

The TaigaClimate project

Boreal forest is a basis for many societies in the taiga zone where natural and cultural heritage is tightly connected to forests and wildlife. It is home to a high diversity of species, ecological processes and functions. However, exploitation of forest resources strongly influences and shapes today’s forests, with the forestry sector being the key player of forest-based economy. In addition, hunting is of economic importance, with potentials for further economic growth, as well as having essential recreation values. However, moose can cause damage to forest production, leading to conflicts of interests between different actors and a preference for planting spruce instead of pine to avoid damages; this in turn alters biodiversity and recreational value. These interactions are further complicated by the recent return of top predators. No single component (e.g., climate - forest – moose – wolf - biodiversity) can be understood and successfully managed in isolation. Many studies and ongoing research projects address one or two components, such as climatic effects on forests and management, predators, deer populations, impacts of moose on forests, and spread of diseases and parasites, such as CWD, tick-borne anaplasmosis, or deer ked, along with potentially zoonotic consequences. However, to understand and manage the system as a whole remains a formidable challenge. One of the key questions is how to utilize and manage boreal forest resources in a way that is maximizing the economic output, while minimizing negative ecological impacts. It is also important to consider stakeholder preferences and goals for future forests that go beyond economic and ecological considerations, such as aesthetical or recreational values.

While current policies for wildlife management often follow a reactive, rather than predictive, strategy based on experience from past conditions, a longer-term forward-looking strategy would be more desirable. Climate change is now forcing the ecosystems into new alternative states. Because of the changing environmental conditions, the future behaviour of the system can no longer be projected based on extrapolation of historical observations. Instead, we need a model based on universal mechanisms, able to predict the long-term effects of dynamically changing conditions. It is this type of model that we propose to develop – the first of its kind that enables forest and wildlife management to be based on quantitative projections of the system as a whole, including feedbacks and interactions. Because environmental conditions and society vary geographically and because animal and plant species change in distribution and abundance due to climate change, the model should be spatially explicit. We will minimize model complexity by not attempting to maximize the sophistication of each process but strive for a balanced, low level of complexity for all processes. Nevertheless, computation time will always be a critical limitation to evaluation of large-scale models, especially for multiple scenario runs and optimization. To overcome this problem, we will create a user tool that emulates the detailed process-based model using machine learning (deep neural networks) approach, which reduces calculation time by orders of magnitude with negligible loss in accuracy. To ensure the model remains both scientifically and socially relevant, key stakeholders will give inputs throughout the project.

In summary the project will have the following main objectives:

1. Define the goals of the stakeholders, how they are linked with ecosystem properties and services (forest production, wildlife, hunting, recreation), and the relevant management options and scenarios (WP1)
2. Assess impacts of the scenarios developed in WP1 on the Norwegian forest sector, in terms of demand for products and ecosystem services (WP2)
3. Bring together and structure the current scientific understanding of ecology and management of wildlife and forests, in terms of key mechanisms that determine effects of and responses to climate change (WP3)
4. Integrate the key components and mechanisms into a systems model and a user tool that are co-designed with key stakeholders and provide a quantitative evaluation of the long-term consequences of different management options and scenarios, including the supply of forest products and ecosystem services that matches the demand (WP3)
5. Delineate trade-offs between conflicting goals and preferences. Discuss and find acceptable solutions among the possible policy and management options together with stakeholders (WP1).

The TaigaClimate modeling overview

The models used in the project can be divided into two types: (i) dynamic models subject to feedbacks and (ii) models using output from the dynamic models but which do not feed back (fig. 1). The dynamic models will be integrated and interdependent. The resulting integrated model will be run for 100 years scenarios over a large number of interacting spatial gridcells, which means that computational speed is important.

Fig. 1. Overview of the modeling in the TaigaClimate project. The Dynamic models will all be integrated into an integrated ecosystem model.

Deer and food-plants model overview

The forest and its management are modelled separately from the wildlife in the TaigaClimate project (Fig. 1). The forest model variables such as number of trees per hectare of different diameters cannot directly be used as food availability for wildlife. Instead, a food-plants model is used to calculate food availability based on the input from the forest model. While the forest model produces yearly mean biomass and growth rates, food plant availability and growth is calculated on a weekly time scale by accounting for the relative variation in growth over the year and the plant consumption by the animals (Fig. 2).

Fig. 2. The deer model structure. The forest model and provide the yearly input of biomass, growth, and densities (number of plants per area) to the food plant model. Food plants include at least 5 species of which the trees are separated into height classes. If there are 3 tree species with different height classes and 2 other plants, there will be 3*4+2 = 14 different plant types. Plant availability (biomass and density) and quality (digestibility and energy) influence the foraging by the deer. We model 3 deer species which are separated into calves, females with and without calves, and males = 12 different deer types. 

The Food-plants model

The food plants model accounts for the growth and mortality of the plants, as well as the browsing by deer, which is modelled by the deer model (see below). The mortality and biomass loss of the plants due to browsing is fed back to the forest model.

The plant growth and deer-independent mortality are estimated for each year in advance on weekly resolution based on the yearly values produced by the forest model. The weekly distribution of growth and mortality is determined based on start and end of the growing season, assuming an initially high growth which declines towards the end of the season. The quality of the plants influences the nutritional benefits for the deer and is assumed to vary in proportion to the growth rate, because high growth requires high nutrient and carbohydrate content.

The properties of the food plants (to determine their value for the deer) are defined by the following variables and parameters:

• Spatial density (numbers/ ha) = used to calculate how long it takes to find each plant.
• Biomass (kg) = Edible biomass of each plant
• Energy (J/kg) = Effective energy content the animals obtain, adjusted for its nutritious benefits or adversity for each animal. If a plant is avoided by a animal we assume that this is because of adverse effects that reduce the potential energy gain.
• Digestibility (%) = Fraction of plant biomass that can be digested. Also influence the time it takes to digest and ruminate.
• Quality (relative to seasonal mean) = Relative variation in effective energy content over the season. Varies in proportion to growth rate.

The Deer model

Main assumptions

Deer survival and reproduction is mainly affected by their energy balance, which is represented as fat content (as energy storage). Fat gain = energy uptake – energy use. Energy uptake is determined by food consumption and the properties of the food (see plant model above). We assume that deer distribute their time foraging on different food plants in proportion to the relative net energy gain obtained from each plant.

Feeding: Searching, eating, and rumination

Searching time per food plant depends on the density of plants in the forest (D_plant 1/ha), the biomass eaten per plant or vegetation patch (B_plant, kg), and the speed the animal moves between food plants (v, m/minute).

Plant biomass consumption rate (intake, Br_c, kg/minute) depends on the animal’s maximal eating capacity. As a plant is consumed, the accessibility of its remaining edible biomass declines with the fraction plant consumed which slows the eating rate Br_c.

Because the intake rate declines with time, eventually it is better to go for a new plant. We assume that the deer optimize the time spent eating on each plant.

max⁡0te.optBrcte dte

Fig. 3. Modelled optimal eating time for different plant sizes and animal sizes (affects the maximal food consumption rate).

Rumination time depends on digestibility of the food plants (d_plant) and the rumination capacity of the animal (R_animal), which is a function of body size (B_animal).  t_r=1dplantxdRanimal                                                                            

Because the deer cannot ruminate and consume new food at the same time, the food intake rate (Br_in) is limited by the sum of rumination time and consumption time per biomass.

Digestion

We assume that digestion is limited by the rumen (and not other parts of the digestive system). The digestible fraction of the food (Br_in d) is digested at a rate r_dig (1/hour) and the rest is not digested. All the food is passing through the rumen with a rate r_pass (1/hour).

The maximal energy gain (food digestion) is obtained if the rumen is full (operating at maximum food content). Thus, we assume that the turnover rate (r_pass) is adjusted to maintain a full rumen.

Fig 4. Model results for optimal digestion. (a) Food digestion rate.  (b, c) rumen turnover time = 1/r_pass for high (blue) vs low (red) food digestibility. (c) modeled (blue) vs measured (red) values

Energy budget

Energy intake per foraging time (E_in, J/hour) depends on digestion (Br_dig ) and energy concentration of the digested plants adjusted for relative seasonal quality (e_plant, J/kg). Digestion depends on biomass consumption Br_in , which depends on time to find and eat per plant biomass and time for rumination per biomass  Ein=eplant Brdig Brin, rpass…                                                                                                                                               

Energy use depends on metabolic rate, which is a function of body size and basal metabolic rate (C₀) and the energy cost of movement C_move, which can increase with snow depth. Euse=  Cmovev, snow,Banimal tmoving+ C0(Banimal, season)                                                                                                                                                           

The basal metabolic rate varies over the season to save energy in winter and to enable growth in summer. It is about twice as high in summer as in winter.

The total daily foraging time is distributed towards the different food plants according to their benefits.

The net energy gain (E_net , J/day) is the sum of eating on all plants. In addition to foraging, calves get energy from milk from their mothers at the rate that depends on the fat status of the mother.

The net energy gain affects the fat storage in the next time step, F_t+1 =F_t + E_net

Deer population model

We assume that a fraction of the adult female deer (reproductive life span/total adult life span) reproduce at a certain time every year. The probability and number of offspring depends on the species-dependent maximum number, and the fat status at the time of conception (in autumn the year before giving birth). Initial suggested model.

There is a basic constant mortality risk (p_m0) that is related to max lifespan, mortality from predators (modelled by wolf and bear model), and mortality related to starving (p_starve ) as represented by low fat (F, energy store). Total (non-predator) mortality risk is p_m = 1 – ((1-p_m0) (1-p_m.starve)). The number of dead deer is determined by a binomial function N_m= B(p_m, N_deer)

Deer movement model

We don’t explicitly model movement within each grid cell, but assume that the deer will be able to find the food plants. Between grid cells deer are assumed to move towards higher food availability, which will lead to migration in winter when some food sources are no longer available. The probability that a deer moves to a neighboring grid cell depends on the difference in food availability, the movement speed, and the distance between grid cells.

The wolf model

Wolves live in packs which have territories that they defend against other wolves. There are also solitary wolves, usually wolves that are dispersing from a pack. The wolf grid cells are larger than a typical territory, so there can be more than one territory in the cell.

Wolf hunting and eating model

Wolves tend to catch more prey and consume a smaller fraction of each prey the more prey are available. Parts of the prey can also be lost to scavengers. Assuming that the hunting rate and prey utilization (functional response) is adaptive (Vucetich et al., 2012; Zimmermann et al., 2015), it can be explained by some fitness maximizing criterion. Our model assumes that the wolves optimize their eating time per prey (t_e) in order to maximize their rate of energy gain.

Our model results show that the longer it takes to find a new prey the longer the wolves eat on each prey and the larger the fraction they consume. More scavengers mean less fraction consumed by wolves and shorter eating time on one prey. A smaller prey is consumed more completely by the wolves because there is less time for scavengers to eat.

Fig. 5. Optimal time spent eating on a prey (handling time, t_s) and fraction of the prey consumed by a wolf pack versus the expected time to capture a new prey. The lines are preys with different amount of edible biomass: red line = moose calf (100 kg), blue line = roe deer (18 kg).

Wolf population dynamics

Reproduction and survival depend on food consumption. We use similar principle for the dependence on energy status as in the deer model but replace fat status with food consumption (Gr per wolf) relative to maximum food consumption (Gr_max per wolf)

Probability of starving mortality is pm.starve  and the basic mortality rate is determined by mean life span, p_m0 = 1/13.  Total (non-violent) mortality risk is p_m = 1 – ((1-p_m0) (1-p_m.starve)) and number of dead wolf is determined by a binomial function N_m= B(p_m, N_wolf)

We assume that the main wolf couple in each pack reproduce at a certain time every year. The number of offspring depends on the species-dependent maximum and the energy status at the time of conception (in autumn the year before giving birth).

Pack dynamics

A wolf pack grows by reproduction (see above) and declines by dispersal of young wolves or mortality (see above). 75% of cubs disperse after one year and 100% have dispersed after 2 years, which means that on average they stay in the pack 1.25 years and the dispersal rate of cubs is 0.8 per year.

Wolf territory size

The territory size (S_t) decreases with habitat suitability (H, an index between 0 and 1) as the wolves need to cover less area to have enough suitable area. Habitat suitability is a function of vegetation and landscape properties. S_t also decreases at high density of roe deer - the most preferred prey – as they do not have to go as far to find them.   

Wolf movement and territory establishment

Dispersing wolves will move in the landscape. The probability that a wolf moves to a neighboring grid cell (p_move) depends on the difference in habitat suitability, presence of established territories (space for new territory), and the movement speed (v) relative to the distance between origin and neighbor grid cell

If two of more solitary wolves are in the same grid cell and there is space ( for a new territory, a territory will be formed if there is at least one male and one female, which has a probability pT=1-0.5Ns-1 .

The bear model

External = constant bear density and predation rate.