First, we modelled the national or province-level proportion of extensively raised chickens
or pigs obtained by data-mining as function of GDP per capita (PPP2010). In order to bound
the predictions between 0 and 1, we used a logistic model where the dependent variable was
modelled as:
Pext ¼ 1=ð1 þ e
ð4:mext:ðlextGDPPPPÞþ2Þ
Þ
where Pext is the proportion of extensively raised chickens, GDPPPP is the log10-scale GDP per
capita of the country (PPP2010), and μext and λext parameters of the model controlling, respectively,
the steepness of the growth and its position. Pint for chicken was simply estimated by
default as 1- Pext. For extensively and intensively raised pigs, we used the following models:
Pext ¼ aext=ð1 þ e
ð4:ðmext =aextÞ:ðlextGDPPPPÞþ2Þ
Þ
Pint ¼ 1 aint=ð1 þ e
ð4:ðmint=aintÞ:ðlintGDPPPPÞþ2Þ
Þ
where all terms are defined as above, except Pint, the proportion of pigs raised under intensive
systems, and Pext and Pint, additional model parameters used to account for the maximum proportion
of Pext and Pint that may, in this case, differ from 1. Psint was simply estimated as 1—
(Pext + Pint). The model coefficients were estimated using non-linear least squares regression.
In order simultaneously to account for the variability in the observed data and for the different
stocking levels in different countries we used a Monte Carlo simulation where we sampled
1,000 times 25 countries out of the observed dataset with replacement, with a probability of
being in the sample estimated as the ratio of the national livestock population of chickens or
pigs to the global total for that species. This effectively weighted the contribution of data points
to the analysis by population, ensuring that countries with high chicken or pig populations
would be more often selected in the sample.
First, we modelled the national or province-level proportion of extensively raised chickensor pigs obtained by data-mining as function of GDP per capita (PPP2010). In order to boundthe predictions between 0 and 1, we used a logistic model where the dependent variable wasmodelled as:Pext ¼ 1=ð1 þ eð4:mext:ðlextGDPPPPÞþ2ÞÞwhere Pext is the proportion of extensively raised chickens, GDPPPP is the log10-scale GDP percapita of the country (PPP2010), and μext and λext parameters of the model controlling, respectively,the steepness of the growth and its position. Pint for chicken was simply estimated bydefault as 1- Pext. For extensively and intensively raised pigs, we used the following models:Pext ¼ aext=ð1 þ eð4:ðmext =aextÞ:ðlextGDPPPPÞþ2ÞÞPint ¼ 1 aint=ð1 þ eð4:ðmint=aintÞ:ðlintGDPPPPÞþ2ÞÞwhere all terms are defined as above, except Pint, the proportion of pigs raised under intensivesystems, and Pext and Pint, additional model parameters used to account for the maximum proportionof Pext and Pint that may, in this case, differ from 1. Psint was simply estimated as 1—(Pext + Pint). The model coefficients were estimated using non-linear least squares regression.In order simultaneously to account for the variability in the observed data and for the differentstocking levels in different countries we used a Monte Carlo simulation where we sampled1,000 times 25 countries out of the observed dataset with replacement, with a probability ofbeing in the sample estimated as the ratio of the national livestock population of chickens orpigs to the global total for that species. This effectively weighted the contribution of data pointsto the analysis by population, ensuring that countries with high chicken or pig populationswould be more often selected in the sample.
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