Just recently, we could demonstrate that beside other factors like dispersal and fragmentation, habitat suitability is one of the key parameters in determining the occurrence of fishes in river networks (Radinger and Wolter, in press, Disentangling the effects of habitat suitability, dispersal and fragmentation on the distribution of river fishes, Ecological Applications). Most of the studies focussing on habitat quality and modeling habitat suitability only typically use occurrence and or abundance data of species and/or life-traits to obtain a statistical link to the physical habitat. For stream fishes, very often stream velocity, water depth and bottom substrate (sand, gravel, macrophytes etc.) are used as primary predictors for habitat suitability. However, very often measurements of physical habitat-species occurrence relationship are unknown from a pure traditional numerical/statistical point of view. This might be caused by the fact that species are very rare, endangered, already extinct or protected to obtain field data about their habitat requirements. In addition, field surveys might be very costly which also prevents obtaining such field data. So for a classical modeling approach we lack the most important factor, the model itself which describes the species-habitat link.
However, for some fish species expert can provide expertise where these species were typically found in other river systems or in the past. So, often there is expert knowledge available to loosely define the habitat relationships for single species. This might simply be the information that species A is considered to prefer deep fast flowing water whereas it avoids shallow low flowing habitats. Such information can be used to predict the suitability of a habitat for entire river reaches using the so-called fuzzy logic:
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. Compared to traditional binary sets (where variables may take on true or false values), fuzzy logic variables may have a truth value that ranges in degree between 0 and 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific functions. Irrationality can be described in terms of what is known as the fuzzjective.
The term “fuzzy logic” was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. Fuzzy logics had, however, been studied since the 1920s, as infinite-valued logics – notably by Łukasiewicz and Tarski
In GRASS GIS, the tool r.fuzzy system, a general implementation of Zadeh’s (1965) and Mamdani and Assilian’s (1975) fuzzy inference system within a geographical infomation system for large datasets is provided. The tool r.fuzzy.system is entirely based on open source software, highly flexible and can accommodate any combination of custom input raster maps like imports from other software. The inputs required by r.fuzzy.system are (i) the raster maps with the predictor parameters, (ii) a MAP file that defines the fuzzy membership classes for the input (e.g. flow velocity and water depth) and output parameters (e.g. habitat suitability) and (iii) a RULE file that describes the relationship of all possible parameter combinations and the resulting species- and/or life stage-specific habitat suitability.
Here we provide the species-habitat relationships (considering flow velocity and water depth) for juvenile and adult Rutilus rutilus an ubiquitary species in European lowland rivers. The modeling procedure has been conducted in GRASS GIS and executable example script are provided via github: https://github.com/jradinger/fuzzy_habitat_modelling
The modeling data involve the (i) GRASS python script, (ii) a MAP file for defining the linguistic fuzzy sets of flow velocity and water depths and a (iii) RULE file which defines the relationship between the linguistic habitat variables (e.g. high velocity, low depth) and the linguistic habitat suitability (e.g. very suitable, suitable). In addition, we calculated the suitability for a virtual parameter space (combinations of flow velocity and depth) to illustrate the suitability for juvenile and adult Rutilus rutilus. The so modelled habitat requirements were plotted with a 3D wireframe plot using the software R (script also available via github) and converted to an animated GIF using ImageMagick. This work can be cited as: Radinger, Johannes (2014): fuzzy_habitat_modelling. figshare. http://dx.doi.org/10.6084/m9.figshare.1221677