2-species, multi-season parameter definition.

[Sunday]

I was hoping to get a little clarification on the definitions of parameters used in the second parametrization of the 2 species, multi-season model. I could not find where the gamma and epsilon parameters are defined for this type of analysis. Here is how I am interpreting the gammas and epsilons (using gamma as an example).


gamAB Probability species A colonizes given species B is present
gamAb Probability species A colonizes given species b is absent
gamBAA Probability species B colonizes given species A is present in the current season and present in the previous year
gamBAa Probability species B colonizes given species A is present in the current season and absent in the previous year
gamBaA Probability species B colonizes given species A is absent in the current season and present in the previous year
gamBaa Probability species B colonizes given species A is absent in the current season and absent in the previous year

Just wanted to check I was interpreting these right. If I've missed where these have been defined, I'd appreciate it if someone could point me to the reference. All the other parameters have been described elsewhere so I'm good on them.

Cheers,
Trevor

[darryl]

Hi Trevor,
Good guessing. From memory that's the correct interpretation. I'm sure Jim Hines will jump in if that's not right.
Cheers
Darryl

[Sunday]

Thanks Darryl! Much appreciated.

Trevor

[Seth]

Hi,

I had this exact same question! I really appreciate you all helping to explain the parameters. Given the above, I was thinking of testing some hypotheses as follows, but I am relatively new to this and I would very much appreciate any guidance.

I was thinking of trying the following parameterizations;

1) All gammas set equal = Colonization of A and B are independent
2) All gammas estimated separately = Colonization of A depends on B, colonization of B depends on presence of A in current and previous year
3) Set gamAB = gamAb, while estimating all others. I assumed this would indicate Colonization of A does not depend on B, but Colonization of B depends on presence of A in current and previous year.
4) Estimate gamAB and gamAb, but set gamBAA = gamBAa, and gamBaA = gamBaa. I am thinking this would mean that Colonization of A depends on B, while Colonization of B depends on presence of Species A in current season but NOT in the previous season.
5) Set gamAB = gamAb, and set gamBAA = gamBAa, and gamBaA = gamBaa. I am thinking this would mean that Colonization of A is independent of B, while Colonization of B depends on presence of Species A in current season but NOT in the previous season.

Does this seem reasonable to you? Am I missing something? Is there something else I should test?

I really appreciate any help anyone can provide!

-Seth

[jhines]

Seth,

1. All gamma's equal doesn't mean that colonization is independent between species, it means that colonization is the same for both species, and doesn't depend on occupancy state of either species in the preceding survey or whether the other species is colonizing in the same interval. If colonization were independent, then gamB would be different from gamA, gamAb=gamAB, and gamBAA=gamBAa=gamBaA=gamBaa (ie., you would only estimate gamA and gamB).

2. Colonization of A depends on occupancy of B in the previous survey. Colonization of B depends on occupancy of A in the previous survey and whether A is colonizing in the same interval.

3. Colonization of A does not depend on occupancy of B in the previous survey. Colonization of B depends on occupancy of A in the previous survey and whether A is colonizing in the same interval.

4. To be more clear, estimating separate gamAB,gamAb means colonization of A for the interval between surveys t and t+1 depends on occupancy of B in survey t. (gamAB is colonization for A when B was present and gamAb is colonization for A when B was not present.) gamBAA = gamBAa means colonization for B in the interval, t to t+1 when A was present in t is the same, regardless of the colonization for A in the interval t,t+1. The gamB is split into 4 cases: gamBAA(colonization for B when A was present in t and A colonized in the interval, t,t+1), gamBAa(colonization for B when A was present in t and A did not colonize in the interval, t,t+1), gamBaA(colonization for B when A was not present in t and A did colonize in the interval, t,t+1), gamBaa(colonization for B when A was not present in t and A did not colonize in the interval, t,t+1). So, when you refer to gamA, you can distinguish it by the presence (or not) of species B in the preceding survey. When you refer to gamB, you can distinguish it by presence of species A in the preceding survey and whether species A is colonizing (or not) in the same interval. In summary, "Estimate gamAB and gamAb, but set gamBAA = gamBAa, and gamBaA = gamBaa" means colonization of A depends on occupancy of B, and colonization of B depends on occupancy of A, but not colonization of A (in the same interval).

5. Colonization of A is independent of B and colonization of B depends on occupancy of A, but not colonization of A.

This design of the colonization parameters allows you to build models where colonization depends on occupancy of the other species, or whether the other species is colonizing in the same interval, or both. With the most general case (all gam's different), model fit might improve, but you then have the problem of trying to explain why colonization depends on both occupancy of the other species and whether the other species is colonizing. I'm sure I could come up with something after a few pints of Guinness

[Seth]

Thank you so so much!