# Slope of extinction simulation

### Description

Fits a hyperbolic function to the extinction simulation of `second.extinct`

.

### Usage

1 |

### Arguments

`object` |
An object of class “bipartite”, usually generated by |

`plot.it` |
Logical; want to see the graph? |

`...` |
Graphical parameters passed on to the |

### Details

Function scales extinction sequences to values between 0 and 1 for each participant. The x-axis of the graph features the proportion of exterminated participants, while the y-axis depicts the proportion of secondary extinctions. Since these curves usually follow a hyperbolic function (see examples in Memmott et al. 2004), this is fitted to the data.

At present, only a function of type *y \sim 1 - x^a* is fitted (using `nls`

), i.e. without offset. While usually this
function provides very good fits, do check the graph and judge for yourself. Fitting this simple function makes its
parameter ‘a’ a measure of extinction vulnerability. The more gradual the secondary extinctions, the lower the absolute value of ‘a’. Or, phrased differently, large absolute values of ‘a’ indicate a very abrupt die-off, indicative of high initial redundancy in the network.

### Value

Returns one number, the exponent of the fitted hyperbolic model.

### Note

This function is not as vigorously tested as it should probably be. It worked fine for large networks, but small ones it may behave strangely, I fathom.

### Author(s)

Carsten F. Dormann

### References

Memmott, J., Waser, N. M. and Price, M. V. (2004) Tolerance of pollination networks to species extinctions. *Proceedings of the Royal Society B* **271**, 2605–2611

### See Also

`second.extinct`

for generating the required input object.

### Examples

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