04.1_model_expansion.lyx

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\begin_layout Section
Model Expansion
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\begin_layout Standard
Our previous model is based on the assumption that species are subject to
 random distribution.
 Under this assumption, we ignore the differences in the environment.
 However, in the real world, the environment of a region cannot be the same
 everywhere.
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\begin_layout Standard
In order to get closer to the realistic situation of species distribution,
 we use Maxent (Maximum entropy)
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 to model the species geographic distributions.
 The Maxent software is implemented in Java and available at the website
 
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LatexCommand cite
key "L-Maxent"
literal "false"

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.
 In maximum entropy density estimation, we input the species distribution
 samples' data (species name, longitude, latitude)
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LatexCommand cite
key "Z-Sheep,Z-Cattle"
literal "false"

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 of sheep, cattle and climate data 
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key "L-worldclim"
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 in Australia, and then the true distribution of a species is simulated
 as a probability distribution 
\begin_inset Formula $π$
\end_inset

 over the set 
\begin_inset Formula $X$
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 of sites in the study area.
 Thus, 
\begin_inset Formula $π$
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 assigns a non‐negative value to every site 
\begin_inset Formula $x$
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 and the values 
\begin_inset Formula $π(x)$
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 sum to one.
 The weather constraints are expressed in terms of simple functions of the
 environmental variables, called features.
 The mean of each feature is required to be close (within some error bounds)
 to the empirical average over the union of the presence sites.
 As a result, the species distribution map for survival appropriation in
 Australia is shown in the Fig.
 
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.
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Sheep distribution model
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Cattle distribution model
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Maxent species distribution modeling result for sheep and cattle in Australia
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name "L-maxent"

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\emph on
Warmer colors indicates areas with high probability of suitable conditions
 for the species,
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\emph on
while white dots show the presence of locations utilized for training.
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\begin_layout Standard
It can be reasonably assumed that the more suitable the species to survive,
 the greater the distribution density of the species.
 So we use the species distribution map for survival appropriation to represent
 the distribution density of the species.
 Replacing the random distribution with this distribution density will make
 our model more realistic.
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