Modeling Landscape changes using Logit Models
Fig. 1. Landscape changes at the Liukuei ecosystem area.
For each land cover patch, or polygon, its land cover type, area, and perimeter were recorded. The two maps were then overlaid together using a geographic information system to identify land cover changes during the time interval.
The purpose of this study is to develop a set of probabilistic models for predicting landscape changes spatially. Binomial and multinomial models were used to examine the factors contributing to landscape changes. Supposing the observed landscape changes were related to some exogenous factors x's, then, in multinomial logit models, the probability that a land cover type would become land cover type i , or Pn(i), can be written as:
where
b'x
in is the vector of x's and their coefficients,
b'x
jn is the corresponding vector of every land cover type. When there are only two possible land cover types, the multinomial logit model is reduced to binomial logit model:
Factors examined in this
study can be classified into three categories:
locational factors, environmental factors, and
patch characteristics. Locational factors include
distance to roads (TOROAD), distance to streams
(TOSTREAM), distance to natural breadleaf forests
(TONATURE). Environmental factors elevations
(ELEVATION), slopes (SLOPE), and aspects (ASPECT).
Patch characteristics include patch size (SIZE),
perimeter (PERI), patch shape index (SHAPE) and
soil type (SOIL). In order to estimate logit
models, sample points were randomly selected from
the land cover maps. For each sample point,
landscape change from 1988 and 1996, its
associated environmental factors, and
characteristics of its associated patch were
recorded. Parameters in equation [1] and equation
[2] were estimated using maximum likelihood
method. To obtain the final models, backward
selection was used to eliminate the least
correlated variables step by step until the
t-statistics of all parameters were statistically
significant at
a
=0.05.
Statistical significance of a logit model can be tested using likelihood ratio test statistics, which follow Chi-square distribution with k degrees of freedom (k = number of parameters been estimated). Alternatively, the likelihood ratio index, orp
2 can be used to examine the goodness of fit of a model. The likelihood ratio index is similar to the determinant coefficient (R
2) of a regression model. p
2 = 1 when the model fits the observed data perfectly, and when p
2 = 0, it means that the included variables do not explain the observation at all.
3. Results and Disscusions
This study focused on landscape changes under natural conditions (without human interference), therefore, man-made modification such as cutting tract reforestation, forest roads, buildings and nurseries were not included in the analysis. Observed landscape changes from 1988 to 1996 included the following: (1) from coniferous plantations to coniferous plantations, natural forests, or bare lands, (2) from hardwood plantations to hardwood plantations or natural forests, (3) from natural forests to natural forests or bare lands, (4) from mixed forests to mixed forests, natural forests, or bare lands, (5) from bare lands to bare lands or natural forests. Among them, coniferous plantations and mixed forests included more than two possible ways of landscape changes, and therefore multinomial logit models were applied. For other land cover types including hardwood plantations, natural forests, and bare lands, binary logit models were used because they had exactly two possible ways of landscape changes.
The results of model fitting were shown in Table 1. Among the explanatory variables, the effects of locational factors and some of the environmental factors such as elevations and slopes were more significant. On the other hand, patch characteristics and aspects were not significant. Table 1 showed that for all the logit models, nether likelihood ratio test statistics, nor likelihood ratio indices (p
2) were statistically significant. This is mainly because the landscape changes only consisted of a fairly small portion of the landscape. As a result, the models tend to underestimate the probabilities of a land cover type converting to other land cover types. Therefore, it would be difficult to judge which land cover type would a place convert according to equation [1] and equation [2]. However, comparisons show that for places where landscape changes did occur, their associated probabilities of land cover changes is significantly higher than other places. That is, despite that the models tends to underestimate the probabilities of landscape changes, the relative magnitudes of probabilities can be used to identify areas where landscape changes are more likely to occur.
The effects of explanatory variables on landscape changes can be inferred from the signs and magnitudes of coefficients shown in Table 1. The results showed that changes from coniferous plantation to natural forests or mixed forests were related to distances to natural forests and elevations. The closer the distance to natural forests, and the lower the elevation, the likelier a coniferous plantation would turn into natural forests or mixed forests. On the other hand, the occurrences of bare lands were related to elevations and slopes. Bare lands were more likely to occur on coniferous plantations at high elevations and with steep slopes. For mixed forests, the closer they were to natural forests, the likelier they would turn into natural forests, and the higher the elevation, the likelier they would remain as mixed forests. Similar to coniferous plantations, bare lands were also more likely to occur on mixed forests at high elevations and with steep slopes. For hardwood plantations, the conversions to natural forests were related to distances to natural forests, elevations, as well as distances to streams. Low elevation hardwood plantations near natural forests were more likely to become natural forests, but if they were near to the streams, the trends became less obvious. As to natural forests, bare lands were more likely to occur on forests near the roads and with steep slopes. In contrast, low elevation bare lands farther away from roads, and near natural forests were more likely to be reclaimed by natural forests.
