236
M. Gevrey . S. Lek' T.Oberdorff
mean annual air temperature and the mean annual rainfall to estimate average
values of terrestrial primary productivity).
The prediction method
ANNs were employed to prediet the endemie species richness using a set of
explanatory variables at the input, whieh were the total species riehness, the
surfaee of the drainage basin and the net primary produetivity. Beeause the
endemie species riehness depends normally only on total species riehness
(Oberdorff et al. 1999), ANNs were also employed to prediet the total species
riehness and investigate the contribution of the drainage basin surfaee area and the
net primary produetivity. There is a range of different types of ANNs but the most
widely used is the multi-Iayered pereeptron whieh is trained using the algorithm of
baekpropagation of errors (Rumelhart et al. 1986). It is based on a supervised
learning of a known data matrix, a correction of the connection weights is done in
order to obtain a minimal error, that is the method of gradient deseent based on the
differenee between the observed and the expeeted outgoing signals. The final
model obtained ean be used to earry out predietions.
For the predietion of ESR, a three layer feed-forward (3-5-1) neural network
was used: i.e. 3 input neurones eorresponding to each quantitative variable (TSR,
SAD, NPP), one hidden layer with 5 neurones determined as the optimal
eonfiguration (best eompromise between bias and varianee, Geman et al. 1992;
Kohavi 1995) and one output neurone for the endemie speeies riehness. The
activation funetion used is the log sigmoi'd function. To test and validate the
model, a leave-one-out proeedure was investigated (Efron 1983; Jain et al. 1987),
where eaeh observation is tested using a model trained by all the observations. In
reality, eaeh observation (river) is unique and can be added to the training sampie
according to aposteriori validation. In this way, 136 training phases were
performed with 135 observations followed by 136 testing phases with only one
observation.
For the predietion of TSR, the network used had two input neurones: SAD and
NPP, also 5 hidden neurones and one output neurone for TSR. The above test and
validation procedure was used for the model.
The eomputational program was undertaken using Matlab® software release
5.3 on Pe.
12.4
Results
12.4.1
Predictive Power
The results of the ANNs model to predict ESR by the leave-one-out testing
procedure, with 500 iterations and 5 neurons in the hidden layer, are presented in
M. Gevrey . S. Lek' T.Oberdorff
mean annual air temperature and the mean annual rainfall to estimate average
values of terrestrial primary productivity).
The prediction method
ANNs were employed to prediet the endemie species richness using a set of
explanatory variables at the input, whieh were the total species riehness, the
surfaee of the drainage basin and the net primary produetivity. Beeause the
endemie species riehness depends normally only on total species riehness
(Oberdorff et al. 1999), ANNs were also employed to prediet the total species
riehness and investigate the contribution of the drainage basin surfaee area and the
net primary produetivity. There is a range of different types of ANNs but the most
widely used is the multi-Iayered pereeptron whieh is trained using the algorithm of
baekpropagation of errors (Rumelhart et al. 1986). It is based on a supervised
learning of a known data matrix, a correction of the connection weights is done in
order to obtain a minimal error, that is the method of gradient deseent based on the
differenee between the observed and the expeeted outgoing signals. The final
model obtained ean be used to earry out predietions.
For the predietion of ESR, a three layer feed-forward (3-5-1) neural network
was used: i.e. 3 input neurones eorresponding to each quantitative variable (TSR,
SAD, NPP), one hidden layer with 5 neurones determined as the optimal
eonfiguration (best eompromise between bias and varianee, Geman et al. 1992;
Kohavi 1995) and one output neurone for the endemie speeies riehness. The
activation funetion used is the log sigmoi'd function. To test and validate the
model, a leave-one-out proeedure was investigated (Efron 1983; Jain et al. 1987),
where eaeh observation is tested using a model trained by all the observations. In
reality, eaeh observation (river) is unique and can be added to the training sampie
according to aposteriori validation. In this way, 136 training phases were
performed with 135 observations followed by 136 testing phases with only one
observation.
For the predietion of TSR, the network used had two input neurones: SAD and
NPP, also 5 hidden neurones and one output neurone for TSR. The above test and
validation procedure was used for the model.
The eomputational program was undertaken using Matlab® software release
5.3 on Pe.
12.4
Results
12.4.1
Predictive Power
The results of the ANNs model to predict ESR by the leave-one-out testing
procedure, with 500 iterations and 5 neurons in the hidden layer, are presented in