Devils and Roadkill

CSSS Santa Fe 2010

Next Meeting: We'll meet in a couple of days over a meal to discuss progress, but feel free to discuss a time if need arises!

Impact of prey predictability on contact network dynamics of individual foragers

We are interested in using cellular automata/agent based modelling approaches to investigate how a predictable increase of prey density (from roadkill) impacts the contact network dynamics of a group of individual foragers (Tasmanian Devils). We are interested in how the frequency at which devils interact (and with whom) scales with the ratio of prey density on roads to background levels. (Gavin Fay)

The context for this foraging work is that determining how supplementing the prey base (from roadkill) might impact the transmission dynamics of Devil Facial Tumour Disease (DFTD) among the devil population. Additional interests of ours are therefore related to modelling dynamics of infection within the network, which could also be connected with population dynamics models, and changes in life history traits (infected populations are now semelparous, with a large drop in age of sexual maturity).

Working group / interest

Background

Tasmanian Devils, the largest marsupial carnivore, are currently experiencing a dramatic reduction in population due to DFTD, a rather nasty infectious cancer which has become prevalent through much of the state. DFTD infection relies on transmission of infected cells from contact, most likely due to biting, which these critters do a lot of during mating and around prey carcasses. A hot conservation topic right now is forestry plans to build roads opening up a wilderness area in the north of the state to ecotourism opportunities. The devil population in this area has until now remained disease free. There are concerns that the road will increase the likelihood that DFTD will spread to the diseasse-free population: Devils are scavengers and frequently feed on roadkill, the creation of a road may then provide an opportunity for increased frequency of contact between infected and disease-free devils. It might be interesting to investigate how introducing a fixed-location source of additional prey items (ie a road) to a devil population would change the contact network for Devils, and then also to what extent the increased contact frequency would have to be to facilitate transmission of DFTD from an infected devil population to a disease-free one.

Methods/Approach/Ideas

ABM approach - Model Devils as random walkers on a grid, that move diffusively toward prey locations. Use Devil densities from mark recapture estimates. Prey map is stochastic, with intensity of spatial process given by a base mortality rate. Parts of grid that are road have higher mortality rate (tunable ratio relative to base mortality rate). Keep track of who meets who, and how often. Build network, with weights of links driven by frequency of interaction. Analyse network structure when conducting simulations with/without a road. Other scenarios include, values for ratio of prey densities, how rapidly devils move toward prey, etc. (Gavin Fay)

Start off with random grid. Possible extensions could include importing GIS of parts of Tasmania for road locations. Approach above assumes that interaction occurs given same location - if we are going further with disease transmission etc, then we could have a probability of fighting/injury given an interaction.

From meeting on 06/14/10 (Megan Olsen):

Basic Model

The Basic model will NOT have disease, mating, natural death, etc. It will only have what is explicitly listed in this section.

The world:

Bounded grid (not a torus)
Overlap (multiple agents on a single grid point) is allowed
Essentially a Cellular Automata (decision rules are based on stochasticity and states in neighborhood)

Agents/Predators (Devils):

Moore neighborhood of interaction (8 neighbors, this includes cardinal points and diagonals)
Random walk on grid
If smell of prey is within neighborhood, will follow it with some (high) probability
Pr(Fight|Overlap) will be considered, but set to 1 (i.e. they will always fight if on same gridpoint)
Will follow strongest gradient of smell when there is a choice; if multiple directions are equivalent will choose randomly

Prey (Roadkill):

Have a defined "lifetime," the strength of their smell will decay with their lifetime until they disappear from end of lifetime or from being eaten
Smell diffuses within some radius; diffuses evenly in all directions

Start State:

Multiple populations of devils on grid
Random distribution of prey with higher likelihood where we want there to be a "road"

Timestep Includes:

Devils act (move, eat, fight)
- Devils can run in bursts at the impressive speed of 13 kilometers per hour (8.1 miles per hour). (Anne)
Diffusion of smell
Decay in prey lifetime

Necessary Parameters whose ranges should be determined through literature:

Size of home range for devils
* Some info: In my readings, I have found that devils will travel up to 20km each night searching for food. Their "home range" is not necessarily fixed. They will move towards a stronger smell. I have also read that the biting at feeding is much less than at mating, (Anne)
- They are predominantly solitary animals and do not form packs. They occupy territories of 8–20 km², which can overlap considerably amongst different animals.(Anne)
Densities of prey and predator
Distance smell can diffuse such that devil can still smell it
How quickly prey will decay if not eaten

Disease Model

This version of the model will be built on top of the basic model after we have analyzed the basic model dynamics (foraging).

Additional parameters needed:

Latency of disease (time to infectious state)
Time between when disease is obvious and when devil dies
Pr(transmission|bite)
Pr(bite|on same site)

There are few ways to approach the disease model. One way is to compare to tuberculosis literature as it has similar properties. Another is to find if there is literature on exactly how this disease propagates.

The goal in this version is to see how the disease spreads amongst the population, and how the density/location of prey affects the spread. Still not as realistic as we'd like as there is no natural death or birth.

I did a little reading on latency/disease progression. A paper by May and Anderson (J. Anim. Ecol 7 249–268, 1978) showed that time delays have a destabilizing influence host–parasite interactions. For the DFTD latency parameter, it doesn't look like a length for the latency period is well-known. MacCallum et al. (1997, EcoHealth 4:3) use a latent period of 12 months in their model, though based on other studies it looks like the period can be as low as 6 months. These authors found that a longer latent period led to extinction of the population, as opposed to a shorter latent period. In 2009, MacCullum et al. (Ecology 90:12) cite an anecdotal 10 month latent period examined in captivity. In this paper, MacCullum et al. also discuss the disease progression: tumors develop from small nodules to large tumors over 2–3 months, and once a visible tumor is present, death occurs ~6 months later.

- Julie Granka

Mating Model

This version would be built upon the disease model.

Additional parameters needed:

normal birth rate
- Females start to breed when they reach sexual maturity, typically in their second year. At this point, they become fertile once a year, producing multiple ova while in heat. Mating occurs in March, in sheltered locations during both day and night. Males fight over females in the breeding season, and female devils will mate with the dominant male. Devils are not monogamous, and females will mate with several males if not guarded after mating
- Gestation lasts 31 days, and devils give birth to 20–30 young, each weighing approximately 0.18–0.24 grams. When the young are born, they move from the vagina to the pouch. Once inside the pouch, they each remain attached to a nipple for the next 100 days. The female Tasmanian Devil's pouch, like that of the wombat, opens to the rear, so it is physically difficult for the female to interact with young inside the pouch. Despite the large litter at birth, the female has only four nipples, so that no more than four young can survive birth. On average, more females survive than males. Those who do not procure a nipple are typically eaten by the mother(Anne)
normal death rate
- The average life expectancy of a Tasmanian Devil in the wild is estimated at six years(Anne)
birth rate when infected
(death rate when infected is already incorporated from the disease version of the model)
could include the genetic change from mating, genetic network?

The goal in this version is to see how all of these different parameters affect the devil population, specifically in terms of the disease spread.

In terms of the mating model, I also read that you can have transmission of the disease during aggressive mating too, so that might be another interesting aspect to incorporate in the model: you have transmission by foraging and then you can have this extra layer of transmission where 2 individuals of opposite sex can meet in the grid and can get the disease from one-another. Might be interesting to see how this changes the dynamics of the model. Oana Carja