By default, Advanced Search adds a filter to all searches:
   

[exclude] Occurrence status: "absent" 

This is implemented as a URL element:
   

fq=-occurrence_status%3A"absent"

Advanced Search does not allow this to be set either to unfiltered or to only find records where Occurrence status: "present".
The filter is shown under the category 'Selected filters' to to left of the hitlist but cannot be unchecked!

This could readily be solved by adding a section to Advanced Search. The default would not change.

Occurrence status:   

  x  Include Present         (checked by default)
  x  Include Absent          (unchecked by default)

(If both are unchecked, nothing would be found. But people would understand this.)