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MODELING DEFORESTATION AT THE LANDSCAPE LEVEL FROM ANALYSIS AT THE PROPERTY-FARM LEVEL:FINDINGS AND FORECAST FROM THE ALTAMIRA CASEBruce Boucek, Stephen McCracken, and Eduardo BrondizioIndiana University / ACT, USAContact Information:Bruce [email protected]
Stephen McCracken [email protected]
Eduardo [email protected]: Analysis of landscape change is often carried out at the aggregate level. In the particular context of frontier settlement it is useful to think about the landscape as a mosaic of farms initiated during different periods and farm formation and development as a long process taking place over a couple of generations. A demographic approach to understanding land-use patterns in agricultural frontier areas is sensitive to the importance of period, cohort, and age effects as successive waves of colonists migrate to, occupy, and transform their forest plots into family farms. In previous analyses we conceptually and empirically examined these interrelated effects associated with farm development in the region. In general, cohort differences in land-use trajectories are quite small while period effects are more noticeable. These are primarily associated with in-migration, credit policies and boom-bust cycle of cocoa. Perhaps, the strongest, underlying patterns of land-use are those associated with age as individual families slowly develop their farm property. In the present poster presentation we focus on the overall pattern of deforestation at the farm level associated with time, or age of the farm.
Questions: What is the pattern of mean annual rates of deforestation associated with age on a typical frontier farm property? What are the spatial patterns of observed and expected levels of deforestation among these frontier farms? Is there a spatial pattern to their differences (a residual map)? What amount of forest can we expect in this area in the years 2010 and 2020?Methods: The map of observed pace of deforestation was constructed by multiple overlay of classified remotely sensed images (1970, 1973, 1975 & 76, 1978 & 1979, 1985, 1991, and 1996) for the study area. A property grid containing 3,913 farm lots was used as an overlay for extracting information on farm area, and the area deforested between the date of each remotely sensed image. This information was used to calculate mean annual rates of deforestation for each property for each period of observation. We also used this information to identify the period of initial occupation of farm properties in our study area. We used a 5 hectare area of deforestation as the signal of settlement and these cohorts of farm settlement are presented spatially in figure 3. The data extracted for each farm property, for each period between remotely sensed data, was reorganized by time (years) since initial occupation to begin our analysis of pattern of deforestation associated with age of farm.Figure 1: The Observed Pace of Deforestation among Frontier Farms along the TransAmazon Highway, Km 20-140, 1970-96Figure 2: Property Grid OverlayFigure 3Figure 4Figure 5Results & Discussion: Scatter plots of the mean annual rate of deforestation by time since occupation on the farm property are presented for each cohort of occupation in Figure 4. Note the great variation in rates. In Table 1 we present results from ordinary least-squared regression of our estimates of mean annual rates of deforestation on age, age-squared, age-cubed, and age-quadrupled to provide a predicted pattern of deforestation. This fitted regression line is presented in Figure 5. Again we note the great variation in observed rates above the estimated pattern. In general the age pattern of deforestation is large during the initial years (approximating 6 % per year). By the end of the 5th year average rates of deforestation are close to 3% per year and by the 10th year have fallen to less than 2 percent and level off at approximately 1.6%. The implication of this pattern of rates is represented for the AVERAGE FARM of 100 hectares in Figure 6. After 25 years we can expect the average farm to have slightly more than half of their farm in forest.
Taking these regression results we calculated predicted levels of deforestation in 1996 for each property based on initial period of occupation to compare our results with observed levels of deforestation. In Figures 7 and 8 we present these results The map of residuals illustrates some interesting spatial patterns. Areas with dark blue shading represent farms with smaller-than-expected deforestation given the length of settlement while dark red shading represent area with greater levels of deforestation. Visual inspection suggest that patterns of deforestation are also related to issues of distance, topography, and agglomeration of farms into cattle ranches. Note the higher-than-expected levels of deforestation near the sugar cane refinery near Medicilandia, and the lower than expected deforestation in the distant, more remote, farms in the western section of the study area. Similarly we note lower levels of deforestation a few areas at the extreme southern fringe of the study area that have rugged terrain. In subsequent analysis we will examine how distance, topography, and particular types of land-cover following deforestation affect the trajectory of deforestation over time. In Figure 9 we present landscape level estimates from our projections, at the farm level, to the years 2010 and 2020. These results indicate a slowing of deforestation in this 30-year old agricultural frontier.Figure 6Figure 7Figure 8Figure 9
PredDefRate
1005.7832654
94.21673464.9785548
89.52610283724.314271
85.6637041453.7719028
82.43255248983.334247
79.68404758142.9854084
77.30515333142.7107998
75.20956538952.497142
73.33147574422.3324638
71.62104561842.206102
70.04101229862.1087014
68.56405649172.0322148
67.17068758821.969903
65.84749019831.9163348
64.58563182871.867387
63.37956813611.8202444
62.22590509631.7733998
61.12239101981.726654
60.06701881031.6811158
59.05722266651.639202
58.08915549141.6046374
57.15703517711.5824548
56.25255093041.578995
55.36432596381.6019068
54.47744106141.660147
&A
Page &P
Forest
DefRate
Time (Years) Since Farm Occupation
Forest Remaining (Hectares)
Predicted Annual Rate of Deforestation
Predicted Deforestation Over Time (Farm Level)
TrendsMod
1005.7612537
94.21673464.931506
89.52610283724.2549469
85.6637041453.71022
82.43255248983.2775505
79.68404758142.9387452
77.30515333142.6771925
75.20956538952.4778624
73.33147574422.3273065
71.62104561842.213658
70.04101229862.1266317
68.56405649172.057524
67.17068758821.9992129
65.84749019831.946158
64.58563182871.8944005
63.37956813611.8415632
62.22590509631.7868505
61.12239101981.7310484
60.06701881031.6765245
59.05722266651.627228
58.08915549141.5886897
57.15703517711.568022
56.25255093041.5739189
55.36432596381.616656
54.47744106141.62
52.71586689061.62
51.87241302041.62
&A
Page &P
Forest
DefRate
Time (Years) Since Farm Occupation
Forest Remaining (Hectares)
Predicted Annual Rate of Deforestation
Predicted Deforestation Over Time (Farm Level)
Rates
CONSERVATIVE MEASURE of DEFORESTATION (ie Incl. SS3)ESTIMATEDLife TableSET UP FOR GRAPH
Constantyryrs-sqyrs-cuyrs-qdRATE
6.748222-1.0520130.0906321-0.00363020.0000545HectaresForest
DefRateYears100100ForestDefRatePercentPercent
16.748222-1.0520130.0906321-0.00363020.00005455.7815.7894.220100.005.7833ForestDeforest
26.748222-2.1040260.3625284-0.02904160.0008724.9824.6989.53194.224.978601000
36.748222-3.1560390.8156889-0.09801540.00441454.3133.8685.66289.534.31432.587.594903491112.4050965089
46.748222-4.2080521.4501136-0.23233280.0139523.7743.2382.43385.663.77198.572.476260681327.5237393187
56.748222-5.2600652.2658025-0.4537750.03406253.3352.7579.68482.433.334214.563.982599982436.0174000176
66.748222-6.3120783.2627556-0.78412320.0706322.9962.3877.31579.682.985417.560.594704915139.4052950849
76.748222-7.3640914.4409729-1.24515860.13085452.7172.1075.21677.312.710820.557.623095334342.3769046657
86.748222-8.4161045.8004544-1.85866240.2232322.5081.8873.33775.212.497123.554.920883512645.0791164874
96.748222-9.4681177.3412001-2.64641580.35757452.3391.7171.62873.332.332525.552.294139955547.7058600445
106.748222-10.520139.06321-3.63020.5452.21101.5870.04971.622.2061
116.748222-11.57214310.9664841-4.83179620.79793452.11111.4868.561070.042.1087
126.748222-12.62415613.0510224-6.27298561.1301122.03121.3967.171168.562.0322
136.748222-13.67616915.3168249-7.97554941.55657451.97131.3265.851267.171.9699
146.748222-14.72818217.7638916-9.96126882.0936721.92141.2664.591365.851.9163
156.748222-15.78019520.3922225-12.2519252.75906251.87151.2163.381464.591.8674
166.748222-16.83220823.2018176-14.86929923.5717121.82161.1562.231563.381.8202
176.748222-17.88422126.1926769-17.83517264.55189451.77171.1061.121662.231.7734
186.748222-18.93623429.3648004-21.17132645.7211921.73181.0660.071761.121.7267
196.748222-19.98824732.7181881-24.89954187.10249451.68191.0159.061860.071.6811
206.748222-21.0402636.25284-29.04168.721.64200.9758.091959.061.6392
216.748222-22.09227339.9687561-33.619282210.59921451.60210.9357.162058.091.6046
226.748222-23.14428643.8659364-38.654369612.7669521.58220.9056.252157.161.5825
236.748222-24.19629947.9443809-44.168643415.25133451.58230.8955.362256.251.5790
246.748222-25.24831252.2040896-50.183884818.0817921.60240.8954.482355.361.5790
256.748222-26.30032556.6450625-56.72187521.28906251.66250.9053.572454.481.5790
1.6260.8652.722552.721.5790
1.6270.8451.872651.871.5790
MODERATE MEASURE of DEFORESTATION (ieESTIMATEDLife TableSET UP FOR GRAPH
Constantyryrs-sqyrs-cuyrs-qdRATE
6.767128-1.1019790.1002572-0.00421840.0000659HectaresForest
DefRateYears100100ForestDefRatePercentPercent
16.767128-1.1019790.1002572-0.00421840.00006595.7615.7694.240100.005.76ForestDeforest
26.767128-2.2039580.4010288-0.03374720.00105444.9324.6589.59194.224.9301000
36.767128-3.3059370.9023148-0.11389680.00533794.2533.8185.78289.534.252.587.594903491112.4050965089
46.767128-4.4079161.6041152-0.26997760.01687043.7143.1882.60385.663.718.572.476260681327.5237393187
56.767128-5.5098952.50643-0.52730.04118753.2852.7179.89482.433.2814.563.982599982436.0174000176
66.767128-6.6118743.6092592-0.91117440.08540642.9462.3577.54579.682.9417.560.594704915139.4052950849
76.767128-7.7138534.9126028-1.44691120.15822592.6872.0875.47677.312.6820.557.623095334342.3769046657
86.767128-8.8158326.4164608-2.15982080.26992642.4881.8773.60775.212.4823.554.920883512645.0791164874
96.767128-9.9178118.1208332-3.07521360.43236992.3391.7171.88873.332.3325.552.294139955547.7058600445
106.767128-11.0197910.02572-4.21840.6592.21101.5970.29971.622.21
116.767128-12.12176912.1311212-5.61469040.96484192.13111.4968.801070.042.13
126.767128-13.22374814.4370368-7.28939521.36650242.06121.4267.381168.562.06
136.767128-14.32572716.9434668-9.26782481.88216992.00131.3566.031267.172.00
146.767128-15.42770619.6504112-11.57528962.53161441.95141.2964.751365.851.95
156.767128-16.52968522.55787-14.23713.33618751.89151.2363.521464.591.89
166.767128-17.63166425.6658432-17.27856644.31882241.84161.1762.351563.381.84
176.767128-18.73364328.9743308-20.72499925.50403391.79171.1161.241662.231.79
186.767128-19.83562232.4833328-24.60170886.91791841.73181.0660.181761.121.73
196.767128-20.93760136.1928492-28.93400568.58815391.68191.0159.171860.071.68
206.767128-22.0395840.10288-33.747210.5441.63200.9658.211959.061.63
216.767128-23.14155944.2134252-39.066602412.81629791.59210.9257.282058.091.59
226.767128-24.24353848.5244848-44.917523215.43747041.57220.9056.382157.161.57
236.767128-25.34551753.0360588-51.325272818.44152191.57230.8955.502256.251.57
246.767128-26.44749657.7481472-58.315161621.86403841.62240.9054.602355.361.62
256.767128-27.54947562.66075-65.912525.74218751.62250.8853.712454.481.62
1.62260.8752.842552.721.62
1.62270.8651.992651.871.62
Sheet2
Sheet3
PredDefRate
1005.7832654
94.21673464.9785548
89.52610283724.314271
85.6637041453.7719028
82.43255248983.334247
79.68404758142.9854084
77.30515333142.7107998
75.20956538952.497142
73.33147574422.3324638
71.62104561842.206102
70.04101229862.1087014
68.56405649172.0322148
67.17068758821.969903
65.84749019831.9163348
64.58563182871.867387
63.37956813611.8202444
62.22590509631.7733998
61.12239101981.726654
60.06701881031.6811158
59.05722266651.639202
58.08915549141.6046374
57.15703517711.5824548
56.25255093041.578995
55.36432596381.6019068
54.47744106141.660147
&A
Page &P
Forest
DefRate
Time (Years) Since Farm Occupation
Forest Remaining (Hectares)
Predicted Annual Rate of Deforestation
Predicted Deforestation Over Time (Farm Level)
TrendsMod
1005.7612537
94.21673464.931506
89.52610283724.2549469
85.6637041453.71022
82.43255248983.2775505
79.68404758142.9387452
77.30515333142.6771925
75.20956538952.4778624
73.33147574422.3273065
71.62104561842.213658
70.04101229862.1266317
68.56405649172.057524
67.17068758821.9992129
65.84749019831.946158
64.58563182871.8944005
63.37956813611.8415632
62.22590509631.7868505
61.12239101981.7310484
60.06701881031.6765245
59.05722266651.627228
58.08915549141.5886897
57.15703517711.568022
56.25255093041.5739189
55.36432596381.616656
54.47744106141.62
52.71586689061.62
51.87241302041.62
&A
Page &P
Forest
DefRate
Time (Years) Since Farm Occupation
Forest Remaining (Hectares)
Predicted Annual Rate of Deforestation
Predicted Deforestation Over Time (Farm Level)
Forest ARea
383.0883299.7396432154
375.6783297.8103994415
357.9803293.2026050675
314.1353281.7872618464
284.0873273.9640611826
252.9833265.8659237542
213.7963255.6633224358
195.6040250.9268337032
166.6445243.3870313994
&A
Page &P
Forest Area
% Forest
Year
Hectares (Thousands)
Percent
Forest in Study Area - Observed, 1970-96& Predicted for 2010 & 2020Based on Farm Level Projection
Rates
CONSERVATIVE MEASURE of DEFORESTATION (ie Incl. SS3)ESTIMATEDLife TableSET UP FOR GRAPH
Constantyryrs-sqyrs-cuyrs-qdRATE
6.748222-1.0520130.0906321-0.00363020.0000545HectaresForest
DefRateYears100100ForestDefRatePercentPercent
16.748222-1.0520130.0906321-0.00363020.00005455.7815.7894.220100.005.7833ForestDeforest
26.748222-2.1040260.3625284-0.02904160.0008724.9824.6989.53194.224.978601000
36.748222-3.1560390.8156889-0.09801540.00441454.3133.8685.66289.534.31432.587.594903491112.4050965089
46.748222-4.2080521.4501136-0.23233280.0139523.7743.2382.43385.663.77198.572.476260681327.5237393187
56.748222-5.2600652.2658025-0.4537750.03406253.3352.7579.68482.433.334214.563.982599982436.0174000176
66.748222-6.3120783.2627556-0.78412320.0706322.9962.3877.31579.682.985417.560.594704915139.4052950849
76.748222-7.3640914.4409729-1.24515860.13085452.7172.1075.21677.312.710820.557.623095334342.3769046657
86.748222-8.4161045.8004544-1.85866240.2232322.5081.8873.33775.212.497123.554.920883512645.0791164874
96.748222-9.4681177.3412001-2.64641580.35757452.3391.7171.62873.332.332525.552.294139955547.7058600445
106.748222-10.520139.06321-3.63020.5452.21101.5870.04971.622.2061
116.748222-11.57214310.9664841-4.83179620.79793452.11111.4868.561070.042.1087
126.748222-12.62415613.0510224-6.27298561.1301122.03121.3967.171168.562.0322
136.748222-13.67616915.3168249-7.97554941.55657451.97131.3265.851267.171.9699
146.748222-14.72818217.7638916-9.96126882.0936721.92141.2664.591365.851.9163
156.748222-15.78019520.3922225-12.2519252.75906251.87151.2163.381464.591.8674
166.748222-16.83220823.2018176-14.86929923.5717121.82161.1562.231563.381.8202
176.748222-17.88422126.1926769-17.83517264.55189451.77171.1061.121662.231.7734
186.748222-18.93623429.3648004-21.17132645.7211921.73181.0660.071761.121.7267
196.748222-19.98824732.7181881-24.89954187.10249451.68191.0159.061860.071.6811
206.748222-21.0402636.25284-29.04168.721.64200.9758.091959.061.6392
216.748222-22.09227339.9687561-33.619282210.59921451.60210.9357.162058.091.6046
226.748222-23.14428643.8659364-38.654369612.7669521.58220.9056.252157.161.5825
236.748222-24.19629947.9443809-44.168643415.25133451.58230.8955.362256.251.5790
246.748222-25.24831252.2040896-50.183884818.0817921.60240.8954.482355.361.5790
256.748222-26.30032556.6450625-56.72187521.28906251.66250.9053.572454.481.5790
1.6260.8652.722552.721.5790
1.6270.8451.872651.871.5790
MODERATE MEASURE of DEFORESTATION (ieESTIMATEDLife TableSET UP FOR GRAPH
Constantyryrs-sqyrs-cuyrs-qdRATE
6.767128-1.1019790.1002572-0.00421840.0000659HectaresForest
DefRateYears100100ForestDefRatePercentPercent
16.767128-1.1019790.1002572-0.00421840.00006595.7615.7694.240100.005.76ForestDeforest
26.767128-2.2039580.4010288-0.03374720.00105444.9324.6589.59194.224.9301000
36.767128-3.3059370.9023148-0.11389680.00533794.2533.8185.78289.534.252.587.594903491112.4050965089
46.767128-4.4079161.6041152-0.26997760.01687043.7143.1882.60385.663.718.572.476260681327.5237393187
56.767128-5.5098952.50643-0.52730.04118753.2852.7179.89482.433.2814.563.982599982436.0174000176
66.767128-6.6118743.6092592-0.91117440.08540642.9462.3577.54579.682.9417.560.594704915139.4052950849
76.767128-7.7138534.9126028-1.44691120.15822592.6872.0875.47677.312.6820.557.623095334342.3769046657
86.767128-8.8158326.4164608-2.15982080.26992642.4881.8773.60775.212.4823.554.920883512645.0791164874
96.767128-9.9178118.1208332-3.07521360.43236992.3391.7171.88873.332.3325.552.294139955547.7058600445
106.767128-11.0197910.02572-4.21840.6592.21101.5970.29971.622.21
116.767128-12.12176912.1311212-5.61469040.96484192.13111.4968.801070.042.13
126.767128-13.22374814.4370368-7.28939521.36650242.06121.4267.381168.562.06
136.767128-14.32572716.9434668-9.26782481.88216992.00131.3566.031267.172.00
146.767128-15.42770619.6504112-11.57528962.53161441.95141.2964.751365.851.95
156.767128-16.52968522.55787-14.23713.33618751.89151.2363.521464.591.89
166.767128-17.63166425.6658432-17.27856644.31882241.84161.1762.351563.381.84
176.767128-18.73364328.9743308-20.72499925.50403391.79171.1161.241662.231.79
186.767128-19.83562232.4833328-24.60170886.91791841.73181.0660.181761.121.73
196.767128-20.93760136.1928492-28.93400568.58815391.68191.0159.171860.071.68
206.767128-22.0395840.10288-33.747210.5441.63200.9658.211959.061.63
216.767128-23.14155944.2134252-39.066602412.81629791.59210.9257.282058.091.59
226.767128-24.24353848.5244848-44.917523215.43747041.57220.9056.382157.161.57
236.767128-25.34551753.0360588-51.325272818.44152191.57230.8955.502256.251.57
246.767128-26.44749657.7481472-58.315161621.86403841.62240.9054.602355.361.62
256.767128-27.54947562.66075-65.912525.74218751.62250.8853.712454.481.62
1.62260.8752.842552.721.62
1.62270.8651.992651.871.62
HectaresForestDefForested
DefRateYears100100
5.7615.7694.245.76
4.9324.6589.5910.41
4.2533.8185.7814.22
3.7143.1882.6017.40
3.2852.7179.8920.11
2.9462.3577.5422.46
2.6872.0875.4724.53
2.4881.8773.6026.40
2.3391.7171.8828.12
2.21101.5970.2929.71
2.13111.4968.8031.20
2.06121.4267.3832.62
2.00131.3566.0333.97
1.95141.2964.7535.251435.25
1.89151.2363.5236.48
1.84161.1762.3537.6516.538.20
1.79171.1161.2438.76
1.73181.0660.1839.82
1.68191.0159.1740.83
1.63200.9658.2141.79
1.59210.9257.2842.72
1.57220.9056.3843.6222.544.06
1.57230.8955.5044.50
1.57240.8754.6245.382445.38
1.57250.8653.7646.24
1.57260.8552.9247.0826.547.50
1.57270.8352.0847.92
1.57280.8251.2648.7428.549.14
1.57290.8150.4649.54
1.57300.7949.6650.34
1.57310.7848.8851.1231.551.50
1.57320.7748.1151.8932.552.27
1.57330.7647.3652.64
1.57340.7546.6153.3934.553.76
1.57350.7345.8854.12
1.57360.7245.1554.85
1.57370.7144.4455.5637.555.91
1.57380.7043.7456.2638.556.60
1.57390.6943.0656.9439.557.28
1.57400.6842.3857.62
1.57410.6741.7158.2941.558.62
1.57420.6641.0558.95
1.57430.6540.4159.59
1.57440.6439.7760.2344.560.54
1.57450.6339.1560.85
1.57460.6238.5361.47
1.57470.6137.9262.0847.562.37
1.57480.6037.3362.67
1.57490.5936.7463.2649.563.55
1.57500.5836.1663.84
YrsLotYrsLot
Cohort20102020
81435.252445.38
716.538.2026.547.50
622.544.0632.552.27
528.549.1438.556.60
431.551.5041.558.62
334.553.7644.560.54
237.555.9147.562.37
139.557.2849.563.55
Forest Area% Forest% DefTotal Area
1970383.0883299.73964321540.26035678461000384088.323840883200.00
1973375.6783297.81039944152.18960055858410384088.323840883200.00
1976357.9803293.20260506756.797394932526108384088.323840883200.00
1979314.1353281.787261846418.212738153669953384088.323840883200.00
1985284.0873273.964061182626.0359388174100001384088.323840883200.00
1991252.9833265.865923754234.1340762458131105384088.323840883200.00
1996213.7963255.663322435844.3366775642170292384088.323840883200.00
2010195.6040250.926833703249.0731662968188484.3384088.323840883200.00
2020166.6445243.387031399456.6129686006217443.8384088.323840883200.00
Sheet2
Sheet3
Table 1: OLS Estimate of Deforestation
(Moderate Measure of Deforestation, Forest Filtered for SS3)
Mean Annual
Rate of Deforestation
Coef.
t
P>|t|
[95% Conf. Interval]
Years on Lot
-1.102
-12.632
0.000
-1.272
-0.931
Years-Squared
0.100
6.963
0.000
0.072
0.128
Years-Cubed
-0.004
-4.815
0.000
-0.006
-0.003
Years-Quadrupled
0.000
3.742
0.000
0.000
0.000
Constant
6.767
45.719
0.000
6.477
7.057
Number of obs = 13528F( 4, 13523) = 595.33R-squared = 0.1497
Root MSE = 3.1324 Prob > F = 0.0000 Adj R-squared = 0.1495