 # Some questions about the calculation principle of Habitat Quality

In the userguide, the total threat level in grid cell x with LULC or habitat type j is given by Dxj,

Dxj=∑ (r=1;R) ∑ (y=1;Yr) (wr/∑ （Rr=1）wr) ry irxy βx Sjr

But we don’t define the parameter ry , it seems meaningless in the formula.

One more question, could the parameter irxy be minus? Theoretically, when dxy > drmax, it could be.

And I may have found another mistake.

Here it says, when parameter k is equal to the D value, k=0.5.

While z=2.5, apparently it’s wrong. If z=2, that could be right.

That’s all my questions, what 's your opinion?

@dcdenu4 is probably the best person to address this, but we might have to be patient before he has time to respond. I’ll try to address some things if I can.

I believe r is a threat raster and r_y is the pixel value on the raster. Since the threat raster values should represent intensity between 0 and 1, I think this makes sense for the equation.

Theoretically it seems you’re right. But I would expect the model does not apply this equation for pairs of pixels that are separated by a distance > d_rmax because those are pixels where the threat should have no influence.

Well I don’t fully understand this component of the model, but the equation is balanced for z=2.5 in the example given:

5^{2.5} / (5^{2.5} + 5^{2.5}) = 0.5

Hope this helps,

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Regarding the first question, I have a different view. Like you said, it represents intensity between 0 and 1.

Well actually I don’t think so. The parameter that represents intensity should be i_rxy, not r_y.

This also explains that it cannot be negative.So for the second question, I totally agree with your point of view.

When d_xy>d_rmax，it should be equal to 0 which means the intensity of the threat r is 0.

Here is the equation:

I personally think that in this formula, r_y may be used to emphasize the threat.To be clear, it should always be equal to 1, rather than floating between 0 and 1.

Sorry, for the third question, I made a mistake before, thank you very much for your answer.

Forgive me for asking two more questions.

1.Why is the z value set to 2.5?

2.According to the formula, D_xj represents the total threat level of all rasters of all threats to x raster. That being the case, is it possible in theory to exceed 1?

Hi @leige ,

Well actually I don’t think so. The parameter that represents intensity should be i_rxy, not r_y.

`i_rxy` represents the relative impact of each threat. Search for “The impact of threats on habitat in a grid cell is mediated by four factors.” in the User’s Guide to find a run down.

I personally think that in this formula, r_y may be used to emphasize the threat.To be clear, it should always be equal to 1, rather than floating between 0 and 1.

Threat values from threat rasters can be values of presence, absence (0,1) or on a scale of intensity using floating point values from 0 to 1. From the User’s Guide:

Each threat source needs to be mapped on a raster grid. A grid cell value on a threat’s map can either indicate intensity of the threat within the cell (e.g., road length in a grid cell or cultivated area in a gird cell) or simply a 1 if the grid cell contains the threat in a road or crop field cover and 0 otherwise. …
All mapped threats should be measured in the same scale and metric. For example, if one threat is measured in density per grid cell then all degradation sources should be measured in density per grid cell where density is measured with the same metric unit (e.g., km and km2). Or if one threat is measured with presence/absence (1/0) on its map then all threats should be mapped with the presence/absence scale.

The right side of the equation `r_y * i_rxy * beta_x * S_jr` is the threat raster pixel value `r_y` adjusted by the impact score for the threat, the beta score for accessibility (protected), and the sensitivity of the habitat to the threat.

Why is the z value set to 2.5?

Good question, I bet this has been addressed on the forums before. I’ll try and search for it.

According to the formula, D _xj represents the total threat level of all rasters of all threats to x raster. That being the case, is it possible in theory to exceed 1?

From the Users’s Guide:

Also note that threat weights are normalized so that the sum across all threats weights equals 1.

Cheers,

Doug

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