Jaguars: the next step

So what I should have explained by now is that I've moved on from the initial 'lets get a model of jaguar movement in an abstract world working' to "lets validate how jaguars move around in a real-landscape using real data'.

But I should first add some results from the initial 'abstract' model. Not only are territories clearly defined (see post 'habitat preference and territory development' from september '11) and habitat preferences clearly working, but I made a first attempt to investigate some questions about landscape-level population effects of fragmentation and landscape structure. I outlined the model in brief in a previous post ('1st jaguar simulation model' from november '11) and chose to focus on two key questions:

1. What is the effect of landscape structure on the population?

2. How well do corridors connect discrete habitat patches?

So, to answer question 1. I looked at the 'happiness' of individuals in the population over the 9 different landscape designs. 'Happiness' here is defined as the inverse of the cost per time step per individual, where cost is defined as the combination of cost of the habitat (via the least-cost model) and cost of encountering another individuals territory (defined via 'pheromones' which are deposited when an individual moves into a cell and degrade over time). The lower the cost per time step, the happier the individual.

Figure 1. The mean cost per time step for populations within each of the 9 landscapes.

The primeval design is the clear winner here, but this tells us nothing interesting. This design is all forest and so tells us nothing about the effect of landscape structure on the population. By removing this from the figure, we see the results much more clearly:

Figure 2. The mean cost per time step for populations within each of the 8 landscapes that have some amount of matrix habitat.

Now we can see that there is a much clearer difference between those landscape with a corridor and those without. But what is really noticeable is that the happiness of the population relies on how much pure forest habitat there is rather than the structure of the landscape. The Random Islands design includes island of forest that are so small, they are effectively all edge and so this landscape contains less pure forest than all of the other landscape except for the No Corridor design.

To answer question 2. I looked at the proportion of individuals that were able to migrate from one side of the world to the other, in short, the proportion that started in one habitat patch and ended up in the other. This represents the ability of the corridor design to facilitate movement of individuals through the landscape.

Figure 3. The proportion of individuals that moved from one side to the other by the end of the simulation.

Again, clearly the primeval landscape wins, but that tells us nothing interesting. There are no barriers to movement in this design. But there is clearly some big differences between the other 8 landscapes. In fact there is a three-fold difference in the proportions vs a 10% difference found when looking at the happiness of individuals. Clearly, it is the ability to facilitate movement across the landscapes that really differentiates  landscapes in terms of their structure. Connected corridors (represented by One Corridor, Three Corridors and Five Corridors) all increase the proportion of individuals that successfully switches sides during the simulation. What is interesting is that there is such a big difference between these three corridor designs. This surprised me at first until I started to think more about the problem.

One big fat corridor limits the ability of an individual to randomly find it, given that individuals are spread through the entire forest block. Having more corridors increases the chances that any individual will find it. Not only this, but having a corridor that is large enough to support resident individuals means that others may be prevented from travelling through the corridor. It seems to me that the optimum corridor design differs depending on what you want to maximise. A single fat corridor may be fine if you simply want to increase the amount of habitat available, but multiple narrower corridors that reduce the potential for resident individuals to setup territories within the corridor itself may maximise the potential for individuals to travel and increase migration between habitat patches.

It appears there then becomes a trade-off between maximising habitat and population size potential and maximising flow of individuals between habitat patches.

Conclusion
In conclusion, my findings so far suggest that not all landscape structures/corridor designs are the same and that the critical feature for maximising happiness/fitness of a population is to increase the amount of preferred habitat, no matter where this habitat is (with certain constraints on size of patches to be expected here). However, the key difference between corridor designs and in fact landscape structure per se, is the ability to promote and facilitate migration of individuals from one habitat patch to another. This is enhanced with a design of physically connected corridors that are more numerous and narrower in design (again given certain limits due to edge effects/territory size of the species in question etc).