What is the best way to do a prediction of the distribution of plant species and to map them according to their natural existence and climatic data? For example for Atriplex nummularia of prickly pear.
You can use soil map, climate data, elevation map, slop and slop direction map, for example, for zoning of the plant! First, you should reclassify all the layers according to their potential and characteristics, then use a simple way, such as weighted overlay in GIS.
Second way is machine learning algorithm such as support vector machine (SVM) and Random Forest (RF). The aforementioned layers is the input of algorithm (i.e. SVM or RF), and for the training of the model, use the existing plant distribution which you collected through field surveying!!!
Hi. You may test a logistic regression model, if you want to achieve a spatial probabiliy distribution for your species. In this case, you need the presences and absences of the species and a set of numerical predictors, including ecological factors influencing the species distribution.
On the other hand, you can try a principal components aproach, such as the one integrated in Biomapper software.
As an addition to the previous answers, I would like to express my concerns about the expression "best way" used in your question. There are several sources of uncertainty and several decisions that the researcher has to make that affects which way/method is best suited to the given task.
Some methods can deal with changing multicollinearity structure of the input data, and therefore, are able to extrapolate to other regions/time periods (e.g. future climate change), some methods are considered 'black box' which are hard to interpret. Some methods, such as the traditional Climate Envelope Modeling approach, are far easy to interpret but seems to strongly simplify the ecology of the species , other ones are prone to overfit. Some of them can deal with presence+pseudoabsence data (presence-only methods, such as MaxEnt), others (e.g. BRT) need observed absences which is hard to obtain but presence-absence models might be more reliable.
The list can be continued... There is no best way and best modeling method.