Fig 1.
Ownership within the study area.
The study area, composed of Green Diamond timberlands in Humboldt and Del Norte Counties, and a surrounding 0.5-mile buffer that contained State, Federal, Tribal, other Private Commercial timberlands, and Private non-timberlands. The Plan Area comprised a subset of Green Diamond Timberlands.
Fig 2.
Balanced acceptance sampling (BAS).
Illustration of Balanced Acceptance Sample (BAS) within the study area. We sampled “used” points (green dots) and “available” locations (both green and red dots) at an average density of one point per 5 acres. We excluded from the sample of “used” points any location within 20 meters inside the boundary of a patch with indirect evidence of nesting to reduce moving window edge effects (white crosses). We classified all BAS points (inside, outside, and near boundary) as “available”. Dark brown areas with low canopy height are prior clear cuts of varying age.
Fig 3.
Predicted-to-Expected (P/E) ratio curve.
P/E curve from the final HSM model showing the continuous Boyce (raw P/E ratio) curve, smoothed curve [54]; function supsmu in R) and fitted lines from a spline model with kinks at habitat classification breaks.
Fig 4.
Map panels show examples of delineated marbled murrelet habitat patches. Patch boundaries (black) were derived by constructing a five-acre (2-hectare, 80.25 meter) buffer around Low or better suitability pixels (HSI values ≥ 0.19, Fig 3), selecting all tree approximate objects (TAO) ≥ 50 meters in height inside the buffer, and computing a concave hull around these trees. TAOs ≥ 50 meters within 80.25 meters of a pixel contributed to predictions of Low and better habitat areas. Panel (A) illustrates a higher quality patch delineated on Green Diamond property within the Plan Area and panel (B) illustrates an area of old-growth forest in Redwood National and State Park between the Plan Area boundary and the ½ mile outer buffer delineating the boundary of the Study Area.
Fig 5.
AIC plot - Final model selection.
Box and whisker plots of Akaike Information Criteria (AIC) values for the four models with three-variable combinations. The best three-variable model (C) consisted of the point density of tree approximate objects (TAO) ≥ 60m within a 5ac buffer, the sum of heights of TAO ≥ 50m within a 5ac buffer, and the standard deviation of TAO ≥ 50m within a 5ac buffer. Median and dispersion for model C are the lowest suggesting both parsimony and consistency between replicates. Box boundaries are at the 25th and 75th percentiles, the whiskers extend from the 10th to the 25th and the 75th to the 90th percentiles, and the outliers (red dots) are represented beyond the whiskers.
Fig 6.
AIC plot - Regularization multiplier assessment.
Box and whisker plots of Akaike Information Criteria (AIC) values for the best three-variable model (C) with regularization multiplier varied from 1.0 to 5.0 in 0.5 increments. Median and dispersion for the model with RM = 2.0 are the lowest suggesting both parsimony and consistency between replicates. Box boundaries are at the 25th and 75th percentiles, the whiskers extend from the 10th to the 25th and the 75th to the 90th percentiles, and the outliers (red dots) are represented beyond the whiskers.
Table 1.
AIC based regularization multiplier assessment.
The results of nine iterative replicated model runs of the best candidate (3var_C) resulting from varying the Regularization Multiplier (RM) in Maxent from 1 to 5 by steps of 0.5 and listed by Akaike Information Criteria (AIC) values. The RM value of 2.0 exhibited both the lowest AIC value and least AIC dispersion between replicates followed by a non-competitive RM of 1.0 (ΔAIC of 6.8).
Fig 7.
(Top, Middle, and Bottom) Final model covariate response plots. Marginal plots showing response of relative habitat suitability to final model covariates: (Top) Density per acre of TAOs ≥ 60 meters tall within a 5-acre circle, (Middle) Standard deviation in height for TAOs ≥ 50 meters tall within a 5-acre circle, and (Bottom) Sum of heights for TAOs ≥ 50 meters tall within a 5-acre circle. The red line represents the mean value for 10 replicate runs and the blue shade is ± one standard deviation.
Fig 8.
Mean and median HSI values for historic murrelet stands.
Box and whisker plots showing mean and median Habitat Suitability Model (HSM) values of 24 historic forest stands containing observed marbled murrelet nesting behavior. Box boundaries are at the 25th and 75th HSM percentiles, the whiskers extend to the extents of the range, and the yellow line represents the mean HSM value. Vertical dashed lines represent the boundaries of the derived habitat classification; unsuitable (0 - 0.03), marginal (0.03 - 0.19), low (0.19 - 0.34), medium (0.34 - 0.57), and high (≥ 0.57).
Table 2.
Summary of habitat classes by plan and study area.
Areal extant and percentage within each marbled murrelet habitat class (HSM raster), along with relative habitat suitability index (HSI) range, on the Plan and Study area.
Fig 9.
Potential habitat across the study area.
Distribution of potential habitat patches within the Study Area. Patches were identified via a concave hull process applied to all TAO’s within a five-acre buffer (80.25m radius) of areas identified as low suitable or better (HSI ≥ 0.19) by the Maxent model.
Table 3.
Summary of model delineated habitat.
The values represent the model predicted area by suitability classes and occupancy status, rounded to the nearest whole hectare, based on the raw HSM raster. “Used” patches are those with documented occupied behaviors, and within the Study Area include patches on Federal and State parks, Bureau of Land Management reserves, unharvested old growth private managed forests, partially harvested old growth forests, and younger (< 70 years old) second and third growth forests with residual old growth trees. “Available” patches are areas with non-confirmed Occupancy (Occupied behaviors) status. Both “Used” and “Available” are delineated by methods described in the text.
Fig 10.
Receiver Operating Characteristic (ROC) curve.
This ROC curve is an average of 10 replicate runs. The average training Area Under the ROC Curve (AUC) for replicate runs is 0.989, and the average standard deviation is 0.001. The best model in our analysis predicting the environmental niche of marbled murrelets for the study area had an AUC value of 0.989 and exhibited very low deviation from the mean of the ten replicates over the full ROC curve. This value indicates a model with high predictive ability and low probability of false negatives.
Table 4.
Predictive performance measures for the final model of marbled murrelet habitat using training data and HSI threshold of 0.19. Sensitivity is the number of correctly predicted used locations divided by the total number of locations predicted to be “habitat” (i.e., TP / (TP + FN) = 956 / 1,080). Positive predictive value is number of correctly predicted used locations divided by total number of used locations (i.e., TP / (TP + FP) = 956 / (956 + 987). Cohen’s Kappa measures the agreement between known and predicted values and is defined as 2(TP * TN – FN * FP) / (TP + FP) * (FP + TN) + (TP + FN) * (FN + TN)) (i.e., 221,044,368 / 351,924,612).
Table 5.
Contingency table showing the true positives, false positives, false negatives, and true negatives based on the “used” and “available” model input and the predicted model output.
Fig 11.
An example of BAS sample locations used to train the Maxent model, TAOs ≥ 50 meters tall, potential habitat classifications, and 5-acre circular moving window with central target cell. As the 5-acre circular window moves from a core area containing higher densities of TAOs ≥ 50 meters to non-habitat area with low densities or no TAOs ≥ 50 meters outside the occupied stand, the modeled HSI values calculated for the target cell decrease as a result. This heterogenous distribution of TAOs ≥ 50 within occupied stands results in internal pockets and areas adjacent to the occupied stand edges with HSI values below the threshold value of 0.19 leading to perceived errors of omission (black circle/red +).