
\section{Conclusion}\label{conc}

The autologistic model provides a tool to further 
explore and describe spatial patterns of plant diseases
beyond methods currently adopted, allowing to better 
understand mechanisms of the spread of the disease, 
not only detecting spatial patterns but also quantifying
effects of presence of disease in different neighbourhood
structures through the associated coefficients.
An important feature of the autologistic model applied to individual trees
is the objectivity
when analysis original data, without the need of some sort 
discretizations, as for instance needed by methods based in  \qs{}. 

The results found here for \MSC{} points to the presence of spatial patterns in the disease
for which evidence becomes clearly as the incidence rises.
In general evidence of aggregation for levels of 
incidences higher than 20\%.
From the third data collection time onwards there was a noticeable 
increase of the probability of a plant become diseased in the presence of
neighbours with the disease. Model fit for $m2$ shows evidence of
infective pressure. 
Notice however the detection can be influenced by the time interval between 
observations.
Overall the within row effect is stronger, reflecting the spacing adopted in the field
and supporting the conjecture of spatial pattern, i.e. the closer the plants the 
higher the infective pressure.

Our conclusion at this stage is that the autologistic model has a potential do
be widely adopted to investigate spatial patterns.
It requires a extra computational burden compared with usual generalised linear models which we have overcomed with our computational implementation.
Further attempts to explore more flexible and general descriptions of the spatial patterns, ways to combine a sequence of time observations are steps to be followed in our investigation. Also the methodology suggests a way to objectively 
combine data from different fields, allowing for investigation of effects of 
choices of spacing between trees, age, type of citrus and tree combinations and other 
properties which can vary between different fields.

