Habitat vulnerability in conservation planning—when it matters and how much

Habitat vulnerability in conservation planning—when it matters and how much Introduction Conservation actions must be scheduled when resources are limited, because it is not possible to simultaneously protect all features of conservation interest ( Possingham 2009 ). Conservation priority setting therefore occurs over two dimensions: space and time ( Pressey & Taffs 2001 ). Many approaches to scheduling are possible but two iterative heuristics define its extremes: minimizing biodiversity loss (hereafter MinLoss) and maximizing biodiversity gain (hereafter MaxGain) ( Wilson 2006 ). MinLoss focuses on vulnerable areas by attempting to minimize the expected short‐term biodiversity loss from the entire planning region. It assumes that low‐vulnerability areas constitute de facto short‐term reserves. MaxGain assumes that habitat loss is equally distributed in the planning region and targets the areas with the highest biodiversity value. Prior studies have found that MinLoss outperforms MaxGain in retaining biodiversity features when ongoing habitat loss is considered, except when there is low‐spatial variability in habitat vulnerability ( Costello & Polasky 2004 ; Wilson 2006 ). In these circumstances, the approaches converge to the same solution. They also converge when loss rates are much higher than reservation rates—circumstances that partially validate MaxGain's underlying assumption that everything will eventually be lost ( Wilson 2006 ). MaxGain outperforms MinLoss with uncertain funding or implementation opportunities, when areas with high biodiversity values and low short‐term vulnerability cannot be scheduled for later protection (as assumed by MinLoss). Examples include abrupt funding cessation ( McBride 2007 ) or uncertain availability of areas for conservation ( Meir 2004 ). Each of these analyses, however, assumes that MinLoss uses accurate vulnerability estimates—but these are not always available. As Wilson . (2005) state, “If vulnerability is overestimated, scarce resources could be allocated to areas that do not, in fact, need protection. Conversely, if vulnerability is underestimated, areas that are, in fact, threatened could be overlooked and have their conservation values reduced or eliminated.” Using a badly informed MinLoss might therefore be worse than ignoring vulnerability altogether. Intuitively, such negative consequences would be worse if biodiversity value was positively correlated with vulnerability, because areas of high biodiversity value would be consistently under prioritized. The impacts of such correlations remain unexplored. Furthermore, the prediction of future habitat loss is typically based on two alternative assumptions. Either a constant number of areas are lost each time step regardless of reservation (“threat displacement,” e.g., Pressey 2004 ; Spring 2007 ), or the number of areas lost diminishes through time as reservation proceeds (“threat inhibition,” e.g., Costello & Polasky 2004 ; Wilson 2006 ). With displacement, destructive activities locally prevented by reservation are displaced elsewhere within the region because the drivers of habitat loss are unaffected by the diminishing supply of land resulting from ongoing loss and reservation ( Armsworth 2006 ). Alternatively, inhibition would occur if the drivers of habitat loss require particular, nonsubstitutable areas, when new reserves are buffered by development restrictions or reduced supply increases land prices and reduces demand ( Armsworth 2006 ). Table 1 summarizes the main factors known or expected to influence the relative performance of MinLoss and MaxGain. These factors are likely to determine the most effective allocation of limited conservation resources, yet some are unexplored while the effects of others are understood from only one or a few studies. 1 Factors known or expected to affect the relative performance of MaxGain and MinLoss Factor Effects References Spatial variance in vulnerability Increasing values favor MinLoss ( Wilson 2006 ) Vulnerability uncertainty Increasing values could disfavor MinLoss Correlation between vulnerability and biodiversity value Positive values might amplify the effects of vulnerability uncertainty. Wider difference between MinLoss and MaxGain with negative correlation. Moilanen & Cabeza (2007) Inhibition or displacement effects of reservation on habitat loss Unknown Uncertainty about future conservation opportunities Increasing values disfavor MinLoss ( Wilson 2006 ; McBride 2007 ) Correlation between cost and vulnerability Positive values disfavor MinLoss ( Newburn 2006 ; Spring 2007 ; Visconti 2010 ) Spatial autocorrelation of habitat loss Increasing values disfavor MinLoss for species sensitive to habitat fragmentation ( Visconti 2010 ) Rates of habitat loss and reservation Increasing values amplify the differences determined by other factors ( Pressey 2004 ; Moilanen & Cabeza 2007 ; Visconti 2010 ); Conservation targets Larger targets amplify the differences determined by other factors ( Pressey 2004 ) Length of planning period Increasing values amplify the differences determined by other factors ( Pressey 2004 ; Moilanen & Cabeza 2007 ; Visconti 2010 ) Here, we assess the relative performance of MinLoss and MaxGain in a suite of scenarios that reflect the range of ecological and socioeconomic conditions encountered by conservation planners. To construct these scenarios, we vary the following factors from Table 1 in combination: 1 Spatial correlation between biodiversity value and vulnerability 2 Displacement or inhibition of biodiversity loss by new reserves 3 Spatial variance of vulnerability 4 Uncertainty in vulnerability estimates We limited the factors to focus on those not already investigated plus vulnerability variance, which interacts directly with the remaining factors. We measured the influence of these factors on the relative performance of MinLoss and MaxGain in terms of retention, that is, the proportion of biodiversity value in our hypothetical study region still extant after 10 years of simulated, interacting habitat loss, and reservation. We interpreted our results by providing rules of thumb for conservation practitioners to apply in deciding whether to: (1) take conservation actions based on the available information on vulnerability; (2) improve information on vulnerability; or (3) discard information on vulnerability and prioritize solely on biodiversity benefit. Methods Study design Our study design ( Figure 1 ) involved simulated landscapes made of environmentally homogeneous habitat patches, which we considered as potential conservation areas. We chose a simulation study because this allowed us complete control over the range of variation in key factors. We expect actual conservation regions to be located within this parameter space. Each landscape was characterized by a level of vulnerability variance among areas and populated by biodiversity features with specific levels of correlation between their abundances and the vulnerability values of areas. For the MinLoss approach, we tested different levels of uncertainty in the vulnerability estimate (MaxGain does not consider vulnerability). Finally, for each combination of uncertainty and variance in vulnerability, we simulated two effects of reservation on habitat loss: displacement and inhibition. 1 Study design. We varied four factors simultaneously: 1. Spatial variance in vulnerability across the landscape (21 levels); 2. Uncertainty in vulnerability estimates provided to managers for applying the MinLoss approach (11 levels); 3. Type of interaction between habitat loss and reservation (two levels); and 4. Correlation between abundance of biodiversity features and vulnerability (five levels). All five levels of correlation (the five features) were subject simultaneously to the variation of the other factors because the five features coexisted in the same landscape. We simulated each of the 462 combinations of the first three factors 100 times to account for the variation in performance of individual simulations related to their independent sequences of reservation and stochastic loss events. Simulations Model definition The system consisted of a set of N = 1,000 areas for conservation assessment. Each area n contained five biodiversity features. The correlation between each feature's abundance and vulnerability varied independently, between −0.8 and +0.8 in intervals of 0.4. Total abundance and the variation in local abundance among areas were constant for each feature. Each area immediately lost all features if it was developed. If reserved, all features were preserved in perpetuity. Reserve selection Managers made decisions about the locations of new reserves using either MinLoss or MaxGain approaches. The objective functions and constraints applied to these heuristics are in Appendix S1. Managers could reserve a maximum of 20 areas per year. Habitat loss models The annual probability that an area would be lost P n0 was equal to its vulnerability, multiplied by the habitat loss rate LR (the proportion of habitat lost per year), reflecting the development pressure in the region. Areas with high‐inherent vulnerability have characteristics that make them amenable to development (e.g., high soil fertility) but even these would not be developed in the absence of a driving force such as human population growth. We applied an annual loss rate LR of 5% of the areas to all simulations. Such high habitat loss rates can amplify the differences between good and poor approaches to scheduling conservation action ( Pressey 2004 ; Visconti 2010 ). They can also alter conclusions about best‐performing algorithms for scheduling ( Moilanen 2009 ). Therefore, we also tested a lower loss rate (2%) to assess the sensitivity of our rules of thumb to this parameter. We implemented the displacement model using a weighted random sample without replacement ( Efraimidis & Spirakis 2006 ), with the sample equal to the (constant) number of areas lost annually: N*LR . The vulnerability of an area determined its relative probability of being part of the sample. We implemented the inhibition model as follows: 1 Compare the probability of loss of each area against a random number U∼[0,1]. 2 Destroy areas with probability of loss higher than this number. The expected proportion of areas lost in the first year with the inhibition model was LR /2 (mathematical explanation in Appendix S2). To ensure the same expected loss (in the first year only) as with the displacement model, we doubled the P values for the inhibition simulations. Subsequently, the proportion decreased because higher vulnerability areas were lost faster than lower vulnerability areas, reducing the mean vulnerability of extant areas. Reserving areas with high vulnerability values had the same effect, hence the inhibition. Spatial variance in vulnerability Across the 1,000 areas, we generated 21 different spatial distributions of vulnerability (details in Appendix S3). All distributions were symmetric beta distributions, with a mean of 0.5, and with variances ranging from 0.004 (very little variation around the mean) to 0.083 (vulnerability values distributed uniformly between 0 and 1). Vulnerability uncertainty To simulate managers’ uncertainty about vulnerability, we chose a random subset of the values from the “real” vulnerability distribution Vr , used in the habitat loss model, and permuted them randomly. The result is a distribution of “estimated” vulnerability Ve, representing the knowledge of managers, used to set priorities with MinLoss. The size of the subset reflected the degree of uncertainty (e.g., 10% of the values were permuted for 10% uncertainty). This method ensured that Ve and Vr had the same variance. To test the sensitivity of our results to the different effects of uncertainty, we tested an alternative method to derive Ve from Vr . For x % uncertainty, we let Ve vary uniformly between [max (0, Vr − x /100), min (1, Vr + x /100)](details in Appendix S4). Evaluation The total number of scenarios was 462 (combinations of 21 levels of vulnerability variance, 11 levels of vulnerability uncertainty, and two habitat loss models). To account for the stochastic variation in loss events, we replicated each scenario 100 times. We recorded the retention of each feature for each replicate and for both MaxGain and MinLoss approaches. We calculated the relative improvement of one approach over the other as the difference in retention of feature f between the approaches: RPB f = RetML f − RetMG f . We also measured relative performance in terms of the minimum retention (the worst‐case outcome of reduced abundance) across all five features: RPminret = min (RetML 1 ...RetML f ) − min (RetMG 1 ...RetMG f ) . We evaluated each scenario, across its 100 replicates, with mean RPB and RPminret . To analyze the influence of each factor on the relative performance of MaxGain and MinLoss, we performed a four‐way ANOVA with RPB f as the response variable and, as independent variables, the four factors investigated plus their second‐order interactions. We also performed a three‐way ANOVA with RPminret as the response variable and, as independent variables, all factors except the correlation between the features’ abundance and vulnerability. We derived regression coefficients from a linear regression and the effect size (η squared) from the ANOVAs, representing respectively the direction and strength of each effect. Results Minimum retention Measured by minimum retention across all features, MinLoss outperformed MaxGain for most of our parameter space ( Figure 2 ). MinLoss performed better under threat inhibition than displacement. With both the habitat loss models, the difference in performance decreased with increasing uncertainty in Ve . The difference increased with increasing variance but only for low uncertainty values. Applying a random deviation from real vulnerability, rather than a permutation, shifted the level of uncertainty at which MaxGain performed best to almost 100% (Figure S4,1). A loss rate of 2% produced identical gradients in relative performance but decreased the magnitude of the differences by ∼50% for both methods of generating uncertainty (Figures S4,2 and S4,3). 2 Difference in minimum retention across five biodiversity features between MinLoss and MaxGain and implications for managers. For (a) and (b), retention was measured as the percentage of initial abundance still extant at the end of the planning period. We calculated percentage difference as MinLoss retention (%)–MaxGain retention (%), so positive values indicate higher retention for MinLoss and negative values (green) indicate higher retention for MaxGain. Each contour line represents an increment of 0.8%. The thicker contour line represents zero difference. x‐ axes show vulnerability uncertainty (difference between real vulnerability and estimated vulnerability provided to the MinLoss manager). y‐ axes show vulnerability variance (spatial variation in vulnerability values in the simulated landscape). Parts (c) and (d) represent the decision space for scheduling conservation actions based on the results in panels (a) and (b). White indicates that the manager should take a MinLoss approach with existing vulnerability data. Grey indicates that the manager should improve the vulnerability estimate before taking a MinLoss approach. Black indicates that the manager should take a MaxGain approach. Note that these rules of thumb are conservative for the application of MinLoss. The alternative model for uncertainty (details in Appendix S4) reduces the black area toward the right‐hand side of the graphs. The differences in Figure 2 manifest underlying patterns in the performance ( RPminret ) of MinLoss and MaxGain individually. MinLoss performed worse with higher variance combined with higher uncertainty in vulnerability ( Figure 3 ). With higher variance, vulnerability is important in predicting biodiversity loss, so higher uncertainty can direct MinLoss toward lower priority areas. With lower variance, higher uncertainty has a smaller detrimental effect because there is reduced scope for mistakes. For MinLoss, inhibition produced best results with high variance and low uncertainty, and worst results with high variance and high uncertainty ( Figure 3 ). Displacement produced a different interaction. MinLoss performed best with low variance and low uncertainty and worst with high variance and high uncertainty ( Figure 3 ). For displacement and low uncertainty, MinLoss improved over MaxGain with increasing vulnerability variance ( Figure 2b ), despite the absolute performance of MinLoss remaining the same along this gradient ( Figure 3 ). This is because MaxGain performed more poorly across the same parameter space ( Figure 3 ). MaxGain ignored vulnerability, so was better when vulnerability was less variable and made less difference to conservation outcomes ( Figure 3 ). For the same reason, vulnerability uncertainty did not affect MaxGain. 3 Distribution of values of minimum retention across five biodiversity features for MinLoss and MaxGain with inhibition and displacement effects. Values are the minimum percentages of initial abundances of features still extant at the end of the planning period. x‐ axes show vulnerability uncertainty (difference between real vulnerability and estimated vulnerability provided to the MinLoss manager). y‐ axes show vulnerability variance (spatial variation in vulnerability values in the simulated landscape). Features with different spatial correlation with vulnerability MaxGain better protected features that were negatively correlated with vulnerability, whereas MinLoss better protected positively correlated features ( Figure 4 ). 4 Differences in retention between MinLoss and MaxGain across five biodiversity features. Retention was measured for each feature as the percentage of initial abundance still extant at the end of the planning period. We calculated percentage difference as MinLoss retention (%)–MaxGain retention (%). The thicker contour line represents zero difference. Positive values indicate higher retention for MinLoss and negative values (green) indicate higher retention for MaxGain. x‐ axes show vulnerability uncertainty (difference between real vulnerability and estimated vulnerability provided to the MinLoss manager). y‐ axes show vulnerability variance (spatial variation in vulnerability values in the simulated landscape). The correlation coefficient between each feature's abundance and the vulnerability of areas is above each graph. With inhibition, the relative performance of MinLoss decreased as uncertainty increased but, as we hypothesized, uncertainty had most effect on features that were positively correlated with vulnerability ( Figure 4a ). With displacement, uncertainty improved the relative performance of MinLoss for negatively correlated features, worsened it for positively correlated features, and was neutral for the feature with no correlation ( Figure 4b ). Like the results for minimum retention, vulnerability variance was influential only when uncertainty was low, especially with the displacement model. Overall effects and interactions Of all the factors tested, uncertainty in vulnerability had the greatest influence on RPminret , explaining about 38% of its variation ( Table 2 ). The interaction term between vulnerability variance and uncertainty also had a moderate effect size. Overall, the three factors and their interactions explained about 48% of the variation in RPminret . For RPB f values, the correlation between feature abundances and vulnerability was the strongest factor influencing variation, both in isolation and when interacting with vulnerability uncertainty ( Table 3 ). In summary, vulnerability variance and the correlation between features’ abundances and vulnerability had positive effects on MinLoss, while vulnerability uncertainty had negative effects. Threat inhibition favored MinLoss more than threat displacement. 2 ANOVA results with the response variable being the difference between MinLoss and MaxGain in minimum retention across all five features. The multi‐linear regression coefficients (β) between minimum retention and each numerical factor are in the final column (no regression possible with the categorical variable loss model and its interactions terms). All coefficients are highly significant. The r 2 of the multiple linear regression is 0.407. η 2 is the effect size and represents the percentage variance in the response variable explained by each factor. η 2 values equal to 2, 6, and 14% represent respectively small, medium, and strong effects of the factor on the response variable. Source Sum sq. η 2 (%) df Mean sq. F P value β Variance (1) 0.48 2.28 20 0.02 99.34 0 0.2903 Uncertainty (2) 8.00 37.86 10 0.80 3.30 × 10 4 0 −0.0025 Loss model (3) 0.30 1.40 1 0.30 1.22 × 10 4 0 – 1 × 2 1.01 4.77 200 5.00 × 10 −3 20.80 0 −0.4475 1 × 3 0.01 0.07 20 7.66 × 10 −4 3.16 0 – 2 × 3 0.18 0.85 10 0.02 73.94 0 – 1 × 2 × 3 0.06 0.31 200 3.26 × 10 −4 1.34 < 0.001 – Error 11.09 52.46 45,938 2.42 × 10 −4 Total 21.15 100 46,199 3 ANOVA results with the response variable being the difference between MinLoss and MaxGain in retention for each of the five features individually. The multi‐linear regression coefficients (β) between feature retention and each numerical factor are in the final column (no regression possible with the categorical variable loss model and its interactions terms). All coefficients are highly significant. The r 2 of the multiple linear regression is 0.420. η 2 is the effect size and represents the percentage variance in the response variable explained by each factor. η 2 values equal to 2, 6, and 14% represent respectively small, medium, and strong effects of the factor on the response variable Source Sum sq. η 2 (%) df Mean sq. F P value β Variance (1) 0.380 0.14 20 0.02 31.23 0 0.5689 Uncertainty (2) 12.39 4.57 10 1.23 2.03 × 10 3 0 0.0043 Loss model (3) 18.62 6.88 1 18.62 3.05 × 10 4 0 – Abundance‐vulnerability correlation (4) 39.65 14.65 4 9.91 1.62 × 10 4 0 0.0792 1 × 2 1.90 0.70 200 9.50 × 10 −3 15.56 0 0.1137 1 × 3 1.39 0.51 20 0.07 114.03 < 0.01 – 1 × 4 0.42 0.16 80 5.40 × 10 −3 8.81 0 0.0754 2 × 3 6.47 2.39 10 0.65 1.06 × 10 3 0 – 2 × 4 43.72 16.15 40 1.09 1.79 × 10 3 0 0.0718 3 × 4 5.15 1.90 4 1.29 2.11 × 10 3 0 – Error 140.60 51.93 230,610 6.1 × 10 −4 Total 270.70 100 230,999 Discussion Spatial correlation between biodiversity value and vulnerability of areas We found that MinLoss better protected features that were positively correlated with vulnerability, while MaxGain was better for negatively correlated features. In contrast, Moilanen & Cabeza (2007) found that MinLoss was always superior to MaxGain but especially with negatively correlated biodiversity values. This implies a trade‐off between biodiversity representation and retention overlooked by MaxGain, explaining the superiority of MinLoss in their study. The trade‐off applies when the correlation with vulnerability involves the overall biodiversity value of an area. In our study, with different correlations for individual biodiversity features, the trade‐off in protection was among features. The approaches resolved this trade‐off differently. MinLoss favored features with worse retention (positively correlated with vulnerability) and MaxGain favored those with worse representation. Although our results are not surprising, given the focus of MinLoss on vulnerable areas and features with the poorest outlook, it is important to consider their implications for ongoing decline of vulnerable species where opportunistic conservation takes place ( Pressey 1994 ; Pressey 2002 ; Turner 2006 ). In principle, threatened features should have highest priority because delayed protection will likely result in their decline or extinction. Our results indicate that managers should therefore take a MinLoss approach, although the choice depends also on other factors, below. However, given chronic funding shortages for conservation, when reversing the prognosis for critically endangered features is unlikely, a triage approach suggests protecting areas with lower threats, thereby maximizing conservation efficiency and effectiveness ( Bottrill 2008 ). Displacement or inhibition of biodiversity loss by new reserves The nature of threat dynamics determined the magnitude of the difference between approaches but did not qualitatively alter the best approach. When reservation only displaced habitat loss, the improvement of MinLoss over MaxGain in terms of minimum retention was modest and attributable to MinLoss identifying areas with highest contributions to retention. This was subject, of course, to the uncertainty of information on vulnerability (below). With inhibition, the relative performance of MinLoss was stronger. MinLoss quickly removed suitable areas from development by reserving very vulnerable areas. In doing so, it not only influenced which areas would persist, it also reduced the total area lost by reducing the mean vulnerability in the landscape. There are many evidences all over the world of displacement (aka leakage) effects of habitat loss by protected areas ( Ewers & Rodrigues 2008 ). Displacement result in a limited net gain of natural habitat or in some cases even a net loss compared to a baseline of habitat loss. Our findings reinforce this empirical evidence, and suggest that implementing protected areas is not strategically smart if their only effect is to displace habitat conversion into other ecologically valuable areas. In such circumstances, habitat protection needs to be followed by political and economical incentives directly targeting the drivers of habitat loss. Spatial variance in vulnerability This factor had a small but significant effect both in isolation and in interaction with other factors ( Tables 2 and 3 ). With inhibition, variance in vulnerability determined the extent to which MinLoss could decrease the mean vulnerability of remaining habitat. If variance was high, preempting development by reserving vulnerable areas could decrease the mean vulnerability of remaining areas thereby reducing the extent of further loss of features. When variance was low, the mean vulnerability of the landscape was unaltered by reservation so MinLoss and MaxGain performed equally. The stronger reduction in loss rate with higher vulnerability variance did not apply with displacement because the rate of development was fixed. With both inhibition and displacement, increasing vulnerability variance increased the scope for MaxGain to misallocate conservation effort to areas with little contribution to biodiversity retention, thus widening the gap with MinLoss. Vulnerability variances similar to the maximum value tested here have been reported for terrestrial ( Pressey 1996 ) and marine regions ( Halpern 2008 ). Uncertainty in estimates of vulnerability Uncertainty in estimates of vulnerability was the most important factor in this study, accounting for much of the variability in the difference between MinLoss and MaxGain in minimum retention across features. With both loss models and across all levels of vulnerability variance, the best approach switched to MaxGain when approximately 70% of the estimates were incorrect (but at larger values with the random deviation method). Uncertainty also determined the magnitude of the difference between approaches via its interaction with vulnerability variance that explained ∼5% of variation in relative performance between approaches ( Table 2 ). When variance was high, any increase in uncertainty caused an important loss of information about expected biodiversity loss, and therefore reduced the relative performance of MinLoss. When variance was low, increasing uncertainty made little difference because vulnerability itself was less influential. Uncertainty was also involved in a three‐way interaction with the habitat loss model and vulnerability variance. With inhibition effects, strong vulnerability variance benefited MinLoss only with low uncertainty. Only in these circumstances could MinLoss effectively identify and secure the most valuable and vulnerable areas before they were developed, while reducing overall habitat loss. We discuss a second three‐way interaction in Appendix S5. Rules of thumb for conservation decision making To minimize biodiversity loss, we suggest using a MinLoss approach with existing vulnerability estimates (white areas in Figure 2c,d ) if uncertainty is estimated at less than 20%, regardless of vulnerability variance. This remains the best choice up to 70% uncertainty with variance <0.02 (inhibition) and variance <0.03 (displacement). With uncertainty between 20% and 70% and larger variance values, improving the estimate of vulnerability is the best strategy, given that a small reduction in uncertainty under these circumstances gives a large improvement in the relative performance of MinLoss (grey areas). With any other combination of values for both loss models, MaxGain is the best approach (black areas, which reduce to the right if uncertainty is generated with the random deviation method, Appendix S4). To use our rule of thumb, managers need to estimate uncertainty in vulnerability, requiring expert scrutiny of the vulnerability model or a validation dataset of actual land‐use transitions. Validation could involve applying the model to a past landscape and comparing with the present. Improving Ve will often require money and time to collect more data and/or develop better loss models. Although these investments are not necessarily large, the benefit of improving Ve needs to be evaluated against potential lost opportunities for timely protection ( McDonald‐Madden 2008 ; Grantham 2009 ). Methods are still needed to balance these considerations when selecting a prioritization strategy and to develop adaptive approaches that set initial priorities with available vulnerability estimates, and then refine the approach as new data become available. Applying the rule of thumb to real‐world case studies We tested the predictive ability of our rules of thumb with two case studies that applied simulations and measured retention for datasets used in actual planning exercises ( Table 4 ). While these studies are not perfectly comparable because of slight differences in habitat loss models and longer planning periods, the results agree with our findings here, especially regarding the effects of vulnerability variance. 4 Two case studies of retention from simulations that have reported values of some of the factors investigated here, and the observed improvement in biodiversity retention from considering vulnerability (equivalent to the benefit of MinLoss over MaxGain) References Habitat loss model Planning period Loss rate (LR, % landscape p.a.) Reservation rate (RR, % landscape p.a.) Assumed uncertainty Vulnerability variance a Performance difference Features abundance versus vulnerability correlation ( Visconti 2010 ) b Displacement 20 years 0.65 (low) 3.25 (high) 0.15 (low) 0.75 (high) 0 0.051 (59%) c,d 0.32% (low LR and low RR) 0.3653 8.87% (high LR and high RR) ( Pressey 2004 ) Displacement 25 years e 0.17 0.3 0 0.11 (100%) f 5.97% g −0.3305 a The value in parentheses next to the vulnerability variances expresses the proportion of vulnerability distribution tested in the present study that had variance lower than the variance observed in the case study. b This case study tested both variable costs and homogeneous costs; we report here only the results from using homogeneous costs for comparability with the present study. c Across the species tested in this study, we report only the Squirrel glider Petaurus norfolcensis , which, like the virtual species in the present study, did not exhibit responses to habitat fragmentation. d This case study reported the relative difference in performance ([best retention–worst retention]/worst retention) that we have expressed here in absolute differences for comparability with the present study. e A longer planning period was simulated in this case study but 25 years was the available time‐slice closest to the planning period tested in the present study. f The vulnerability distribution in this dataset was strongly right skewed and had a variance outside the scale of values possible with symmetric distributions like the ones tested here. g This study tested retention resulting from many approaches to scheduling. We have selected approaches that were the most similar to those tested in the present study. The value shown is the average gain in minimum retention from incorporating vulnerability into these scheduling approaches. Limitations Our results only apply to MinLoss and MaxGain that we chose because they are widely published and often used for their ability to solve large, complex, and realistic problems involving nonlinearities such as the effects of connectivity. Other approaches include integer linear programing ( Snyder 2004 ) and stochastic dynamic programing ( Costello & Polasky 2004 ; Strange 2006 ; Wilson 2006 ) and its approximations ( Drechsler 2005 ; Moilanen & Cabeza 2007 ). Most of these can only solve simple problems ( Moilanen 2008 ). Future research should expand our analyses to other dynamic reserve selection algorithms. A second limitation is that we assumed homogeneous costs, despite the potential for costs to vary more than biodiversity value ( Naidoo 2006 ; Bode 2008 ). The potential positive correlation of acquisition and opportunity costs with habitat vulnerability can influence the relative performance of MinLoss and MaxGain ( Newburn 2005 ; Visconti 2010 ) but considering costs here would have added another dimension to an already complex study design, so we leave for later work the investigation of interactions between costs with other factors influencing retention. Footnotes 1 Habitat is defined here as the part of the physical and/or biological environment in which an individual organism lives. Acknowledgments The authors would like to thank Robin Naidoo, Atte Moilanen, and an anonymous reviewer for the helpful comments that greatly improved earlier version of this manuscript. Piero Visconti was supported by an IDP Australia student mobility scholarship and a James Cook University postgraduate scholarship. Robert L. Pressey acknowledges the support of the Australian Research Council. Piero Visconti acknowledges James Cook University for providing access to the high‐performance computing facility. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Conservation Letters Wiley

Habitat vulnerability in conservation planning—when it matters and how much

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Abstract

Introduction Conservation actions must be scheduled when resources are limited, because it is not possible to simultaneously protect all features of conservation interest ( Possingham 2009 ). Conservation priority setting therefore occurs over two dimensions: space and time ( Pressey & Taffs 2001 ). Many approaches to scheduling are possible but two iterative heuristics define its extremes: minimizing biodiversity loss (hereafter MinLoss) and maximizing biodiversity gain (hereafter MaxGain) ( Wilson 2006 ). MinLoss focuses on vulnerable areas by attempting to minimize the expected short‐term biodiversity loss from the entire planning region. It assumes that low‐vulnerability areas constitute de facto short‐term reserves. MaxGain assumes that habitat loss is equally distributed in the planning region and targets the areas with the highest biodiversity value. Prior studies have found that MinLoss outperforms MaxGain in retaining biodiversity features when ongoing habitat loss is considered, except when there is low‐spatial variability in habitat vulnerability ( Costello & Polasky 2004 ; Wilson 2006 ). In these circumstances, the approaches converge to the same solution. They also converge when loss rates are much higher than reservation rates—circumstances that partially validate MaxGain's underlying assumption that everything will eventually be lost ( Wilson 2006 ). MaxGain outperforms MinLoss with uncertain funding or implementation opportunities, when areas with high biodiversity values and low short‐term vulnerability cannot be scheduled for later protection (as assumed by MinLoss). Examples include abrupt funding cessation ( McBride 2007 ) or uncertain availability of areas for conservation ( Meir 2004 ). Each of these analyses, however, assumes that MinLoss uses accurate vulnerability estimates—but these are not always available. As Wilson . (2005) state, “If vulnerability is overestimated, scarce resources could be allocated to areas that do not, in fact, need protection. Conversely, if vulnerability is underestimated, areas that are, in fact, threatened could be overlooked and have their conservation values reduced or eliminated.” Using a badly informed MinLoss might therefore be worse than ignoring vulnerability altogether. Intuitively, such negative consequences would be worse if biodiversity value was positively correlated with vulnerability, because areas of high biodiversity value would be consistently under prioritized. The impacts of such correlations remain unexplored. Furthermore, the prediction of future habitat loss is typically based on two alternative assumptions. Either a constant number of areas are lost each time step regardless of reservation (“threat displacement,” e.g., Pressey 2004 ; Spring 2007 ), or the number of areas lost diminishes through time as reservation proceeds (“threat inhibition,” e.g., Costello & Polasky 2004 ; Wilson 2006 ). With displacement, destructive activities locally prevented by reservation are displaced elsewhere within the region because the drivers of habitat loss are unaffected by the diminishing supply of land resulting from ongoing loss and reservation ( Armsworth 2006 ). Alternatively, inhibition would occur if the drivers of habitat loss require particular, nonsubstitutable areas, when new reserves are buffered by development restrictions or reduced supply increases land prices and reduces demand ( Armsworth 2006 ). Table 1 summarizes the main factors known or expected to influence the relative performance of MinLoss and MaxGain. These factors are likely to determine the most effective allocation of limited conservation resources, yet some are unexplored while the effects of others are understood from only one or a few studies. 1 Factors known or expected to affect the relative performance of MaxGain and MinLoss Factor Effects References Spatial variance in vulnerability Increasing values favor MinLoss ( Wilson 2006 ) Vulnerability uncertainty Increasing values could disfavor MinLoss Correlation between vulnerability and biodiversity value Positive values might amplify the effects of vulnerability uncertainty. Wider difference between MinLoss and MaxGain with negative correlation. Moilanen & Cabeza (2007) Inhibition or displacement effects of reservation on habitat loss Unknown Uncertainty about future conservation opportunities Increasing values disfavor MinLoss ( Wilson 2006 ; McBride 2007 ) Correlation between cost and vulnerability Positive values disfavor MinLoss ( Newburn 2006 ; Spring 2007 ; Visconti 2010 ) Spatial autocorrelation of habitat loss Increasing values disfavor MinLoss for species sensitive to habitat fragmentation ( Visconti 2010 ) Rates of habitat loss and reservation Increasing values amplify the differences determined by other factors ( Pressey 2004 ; Moilanen & Cabeza 2007 ; Visconti 2010 ); Conservation targets Larger targets amplify the differences determined by other factors ( Pressey 2004 ) Length of planning period Increasing values amplify the differences determined by other factors ( Pressey 2004 ; Moilanen & Cabeza 2007 ; Visconti 2010 ) Here, we assess the relative performance of MinLoss and MaxGain in a suite of scenarios that reflect the range of ecological and socioeconomic conditions encountered by conservation planners. To construct these scenarios, we vary the following factors from Table 1 in combination: 1 Spatial correlation between biodiversity value and vulnerability 2 Displacement or inhibition of biodiversity loss by new reserves 3 Spatial variance of vulnerability 4 Uncertainty in vulnerability estimates We limited the factors to focus on those not already investigated plus vulnerability variance, which interacts directly with the remaining factors. We measured the influence of these factors on the relative performance of MinLoss and MaxGain in terms of retention, that is, the proportion of biodiversity value in our hypothetical study region still extant after 10 years of simulated, interacting habitat loss, and reservation. We interpreted our results by providing rules of thumb for conservation practitioners to apply in deciding whether to: (1) take conservation actions based on the available information on vulnerability; (2) improve information on vulnerability; or (3) discard information on vulnerability and prioritize solely on biodiversity benefit. Methods Study design Our study design ( Figure 1 ) involved simulated landscapes made of environmentally homogeneous habitat patches, which we considered as potential conservation areas. We chose a simulation study because this allowed us complete control over the range of variation in key factors. We expect actual conservation regions to be located within this parameter space. Each landscape was characterized by a level of vulnerability variance among areas and populated by biodiversity features with specific levels of correlation between their abundances and the vulnerability values of areas. For the MinLoss approach, we tested different levels of uncertainty in the vulnerability estimate (MaxGain does not consider vulnerability). Finally, for each combination of uncertainty and variance in vulnerability, we simulated two effects of reservation on habitat loss: displacement and inhibition. 1 Study design. We varied four factors simultaneously: 1. Spatial variance in vulnerability across the landscape (21 levels); 2. Uncertainty in vulnerability estimates provided to managers for applying the MinLoss approach (11 levels); 3. Type of interaction between habitat loss and reservation (two levels); and 4. Correlation between abundance of biodiversity features and vulnerability (five levels). All five levels of correlation (the five features) were subject simultaneously to the variation of the other factors because the five features coexisted in the same landscape. We simulated each of the 462 combinations of the first three factors 100 times to account for the variation in performance of individual simulations related to their independent sequences of reservation and stochastic loss events. Simulations Model definition The system consisted of a set of N = 1,000 areas for conservation assessment. Each area n contained five biodiversity features. The correlation between each feature's abundance and vulnerability varied independently, between −0.8 and +0.8 in intervals of 0.4. Total abundance and the variation in local abundance among areas were constant for each feature. Each area immediately lost all features if it was developed. If reserved, all features were preserved in perpetuity. Reserve selection Managers made decisions about the locations of new reserves using either MinLoss or MaxGain approaches. The objective functions and constraints applied to these heuristics are in Appendix S1. Managers could reserve a maximum of 20 areas per year. Habitat loss models The annual probability that an area would be lost P n0 was equal to its vulnerability, multiplied by the habitat loss rate LR (the proportion of habitat lost per year), reflecting the development pressure in the region. Areas with high‐inherent vulnerability have characteristics that make them amenable to development (e.g., high soil fertility) but even these would not be developed in the absence of a driving force such as human population growth. We applied an annual loss rate LR of 5% of the areas to all simulations. Such high habitat loss rates can amplify the differences between good and poor approaches to scheduling conservation action ( Pressey 2004 ; Visconti 2010 ). They can also alter conclusions about best‐performing algorithms for scheduling ( Moilanen 2009 ). Therefore, we also tested a lower loss rate (2%) to assess the sensitivity of our rules of thumb to this parameter. We implemented the displacement model using a weighted random sample without replacement ( Efraimidis & Spirakis 2006 ), with the sample equal to the (constant) number of areas lost annually: N*LR . The vulnerability of an area determined its relative probability of being part of the sample. We implemented the inhibition model as follows: 1 Compare the probability of loss of each area against a random number U∼[0,1]. 2 Destroy areas with probability of loss higher than this number. The expected proportion of areas lost in the first year with the inhibition model was LR /2 (mathematical explanation in Appendix S2). To ensure the same expected loss (in the first year only) as with the displacement model, we doubled the P values for the inhibition simulations. Subsequently, the proportion decreased because higher vulnerability areas were lost faster than lower vulnerability areas, reducing the mean vulnerability of extant areas. Reserving areas with high vulnerability values had the same effect, hence the inhibition. Spatial variance in vulnerability Across the 1,000 areas, we generated 21 different spatial distributions of vulnerability (details in Appendix S3). All distributions were symmetric beta distributions, with a mean of 0.5, and with variances ranging from 0.004 (very little variation around the mean) to 0.083 (vulnerability values distributed uniformly between 0 and 1). Vulnerability uncertainty To simulate managers’ uncertainty about vulnerability, we chose a random subset of the values from the “real” vulnerability distribution Vr , used in the habitat loss model, and permuted them randomly. The result is a distribution of “estimated” vulnerability Ve, representing the knowledge of managers, used to set priorities with MinLoss. The size of the subset reflected the degree of uncertainty (e.g., 10% of the values were permuted for 10% uncertainty). This method ensured that Ve and Vr had the same variance. To test the sensitivity of our results to the different effects of uncertainty, we tested an alternative method to derive Ve from Vr . For x % uncertainty, we let Ve vary uniformly between [max (0, Vr − x /100), min (1, Vr + x /100)](details in Appendix S4). Evaluation The total number of scenarios was 462 (combinations of 21 levels of vulnerability variance, 11 levels of vulnerability uncertainty, and two habitat loss models). To account for the stochastic variation in loss events, we replicated each scenario 100 times. We recorded the retention of each feature for each replicate and for both MaxGain and MinLoss approaches. We calculated the relative improvement of one approach over the other as the difference in retention of feature f between the approaches: RPB f = RetML f − RetMG f . We also measured relative performance in terms of the minimum retention (the worst‐case outcome of reduced abundance) across all five features: RPminret = min (RetML 1 ...RetML f ) − min (RetMG 1 ...RetMG f ) . We evaluated each scenario, across its 100 replicates, with mean RPB and RPminret . To analyze the influence of each factor on the relative performance of MaxGain and MinLoss, we performed a four‐way ANOVA with RPB f as the response variable and, as independent variables, the four factors investigated plus their second‐order interactions. We also performed a three‐way ANOVA with RPminret as the response variable and, as independent variables, all factors except the correlation between the features’ abundance and vulnerability. We derived regression coefficients from a linear regression and the effect size (η squared) from the ANOVAs, representing respectively the direction and strength of each effect. Results Minimum retention Measured by minimum retention across all features, MinLoss outperformed MaxGain for most of our parameter space ( Figure 2 ). MinLoss performed better under threat inhibition than displacement. With both the habitat loss models, the difference in performance decreased with increasing uncertainty in Ve . The difference increased with increasing variance but only for low uncertainty values. Applying a random deviation from real vulnerability, rather than a permutation, shifted the level of uncertainty at which MaxGain performed best to almost 100% (Figure S4,1). A loss rate of 2% produced identical gradients in relative performance but decreased the magnitude of the differences by ∼50% for both methods of generating uncertainty (Figures S4,2 and S4,3). 2 Difference in minimum retention across five biodiversity features between MinLoss and MaxGain and implications for managers. For (a) and (b), retention was measured as the percentage of initial abundance still extant at the end of the planning period. We calculated percentage difference as MinLoss retention (%)–MaxGain retention (%), so positive values indicate higher retention for MinLoss and negative values (green) indicate higher retention for MaxGain. Each contour line represents an increment of 0.8%. The thicker contour line represents zero difference. x‐ axes show vulnerability uncertainty (difference between real vulnerability and estimated vulnerability provided to the MinLoss manager). y‐ axes show vulnerability variance (spatial variation in vulnerability values in the simulated landscape). Parts (c) and (d) represent the decision space for scheduling conservation actions based on the results in panels (a) and (b). White indicates that the manager should take a MinLoss approach with existing vulnerability data. Grey indicates that the manager should improve the vulnerability estimate before taking a MinLoss approach. Black indicates that the manager should take a MaxGain approach. Note that these rules of thumb are conservative for the application of MinLoss. The alternative model for uncertainty (details in Appendix S4) reduces the black area toward the right‐hand side of the graphs. The differences in Figure 2 manifest underlying patterns in the performance ( RPminret ) of MinLoss and MaxGain individually. MinLoss performed worse with higher variance combined with higher uncertainty in vulnerability ( Figure 3 ). With higher variance, vulnerability is important in predicting biodiversity loss, so higher uncertainty can direct MinLoss toward lower priority areas. With lower variance, higher uncertainty has a smaller detrimental effect because there is reduced scope for mistakes. For MinLoss, inhibition produced best results with high variance and low uncertainty, and worst results with high variance and high uncertainty ( Figure 3 ). Displacement produced a different interaction. MinLoss performed best with low variance and low uncertainty and worst with high variance and high uncertainty ( Figure 3 ). For displacement and low uncertainty, MinLoss improved over MaxGain with increasing vulnerability variance ( Figure 2b ), despite the absolute performance of MinLoss remaining the same along this gradient ( Figure 3 ). This is because MaxGain performed more poorly across the same parameter space ( Figure 3 ). MaxGain ignored vulnerability, so was better when vulnerability was less variable and made less difference to conservation outcomes ( Figure 3 ). For the same reason, vulnerability uncertainty did not affect MaxGain. 3 Distribution of values of minimum retention across five biodiversity features for MinLoss and MaxGain with inhibition and displacement effects. Values are the minimum percentages of initial abundances of features still extant at the end of the planning period. x‐ axes show vulnerability uncertainty (difference between real vulnerability and estimated vulnerability provided to the MinLoss manager). y‐ axes show vulnerability variance (spatial variation in vulnerability values in the simulated landscape). Features with different spatial correlation with vulnerability MaxGain better protected features that were negatively correlated with vulnerability, whereas MinLoss better protected positively correlated features ( Figure 4 ). 4 Differences in retention between MinLoss and MaxGain across five biodiversity features. Retention was measured for each feature as the percentage of initial abundance still extant at the end of the planning period. We calculated percentage difference as MinLoss retention (%)–MaxGain retention (%). The thicker contour line represents zero difference. Positive values indicate higher retention for MinLoss and negative values (green) indicate higher retention for MaxGain. x‐ axes show vulnerability uncertainty (difference between real vulnerability and estimated vulnerability provided to the MinLoss manager). y‐ axes show vulnerability variance (spatial variation in vulnerability values in the simulated landscape). The correlation coefficient between each feature's abundance and the vulnerability of areas is above each graph. With inhibition, the relative performance of MinLoss decreased as uncertainty increased but, as we hypothesized, uncertainty had most effect on features that were positively correlated with vulnerability ( Figure 4a ). With displacement, uncertainty improved the relative performance of MinLoss for negatively correlated features, worsened it for positively correlated features, and was neutral for the feature with no correlation ( Figure 4b ). Like the results for minimum retention, vulnerability variance was influential only when uncertainty was low, especially with the displacement model. Overall effects and interactions Of all the factors tested, uncertainty in vulnerability had the greatest influence on RPminret , explaining about 38% of its variation ( Table 2 ). The interaction term between vulnerability variance and uncertainty also had a moderate effect size. Overall, the three factors and their interactions explained about 48% of the variation in RPminret . For RPB f values, the correlation between feature abundances and vulnerability was the strongest factor influencing variation, both in isolation and when interacting with vulnerability uncertainty ( Table 3 ). In summary, vulnerability variance and the correlation between features’ abundances and vulnerability had positive effects on MinLoss, while vulnerability uncertainty had negative effects. Threat inhibition favored MinLoss more than threat displacement. 2 ANOVA results with the response variable being the difference between MinLoss and MaxGain in minimum retention across all five features. The multi‐linear regression coefficients (β) between minimum retention and each numerical factor are in the final column (no regression possible with the categorical variable loss model and its interactions terms). All coefficients are highly significant. The r 2 of the multiple linear regression is 0.407. η 2 is the effect size and represents the percentage variance in the response variable explained by each factor. η 2 values equal to 2, 6, and 14% represent respectively small, medium, and strong effects of the factor on the response variable. Source Sum sq. η 2 (%) df Mean sq. F P value β Variance (1) 0.48 2.28 20 0.02 99.34 0 0.2903 Uncertainty (2) 8.00 37.86 10 0.80 3.30 × 10 4 0 −0.0025 Loss model (3) 0.30 1.40 1 0.30 1.22 × 10 4 0 – 1 × 2 1.01 4.77 200 5.00 × 10 −3 20.80 0 −0.4475 1 × 3 0.01 0.07 20 7.66 × 10 −4 3.16 0 – 2 × 3 0.18 0.85 10 0.02 73.94 0 – 1 × 2 × 3 0.06 0.31 200 3.26 × 10 −4 1.34 < 0.001 – Error 11.09 52.46 45,938 2.42 × 10 −4 Total 21.15 100 46,199 3 ANOVA results with the response variable being the difference between MinLoss and MaxGain in retention for each of the five features individually. The multi‐linear regression coefficients (β) between feature retention and each numerical factor are in the final column (no regression possible with the categorical variable loss model and its interactions terms). All coefficients are highly significant. The r 2 of the multiple linear regression is 0.420. η 2 is the effect size and represents the percentage variance in the response variable explained by each factor. η 2 values equal to 2, 6, and 14% represent respectively small, medium, and strong effects of the factor on the response variable Source Sum sq. η 2 (%) df Mean sq. F P value β Variance (1) 0.380 0.14 20 0.02 31.23 0 0.5689 Uncertainty (2) 12.39 4.57 10 1.23 2.03 × 10 3 0 0.0043 Loss model (3) 18.62 6.88 1 18.62 3.05 × 10 4 0 – Abundance‐vulnerability correlation (4) 39.65 14.65 4 9.91 1.62 × 10 4 0 0.0792 1 × 2 1.90 0.70 200 9.50 × 10 −3 15.56 0 0.1137 1 × 3 1.39 0.51 20 0.07 114.03 < 0.01 – 1 × 4 0.42 0.16 80 5.40 × 10 −3 8.81 0 0.0754 2 × 3 6.47 2.39 10 0.65 1.06 × 10 3 0 – 2 × 4 43.72 16.15 40 1.09 1.79 × 10 3 0 0.0718 3 × 4 5.15 1.90 4 1.29 2.11 × 10 3 0 – Error 140.60 51.93 230,610 6.1 × 10 −4 Total 270.70 100 230,999 Discussion Spatial correlation between biodiversity value and vulnerability of areas We found that MinLoss better protected features that were positively correlated with vulnerability, while MaxGain was better for negatively correlated features. In contrast, Moilanen & Cabeza (2007) found that MinLoss was always superior to MaxGain but especially with negatively correlated biodiversity values. This implies a trade‐off between biodiversity representation and retention overlooked by MaxGain, explaining the superiority of MinLoss in their study. The trade‐off applies when the correlation with vulnerability involves the overall biodiversity value of an area. In our study, with different correlations for individual biodiversity features, the trade‐off in protection was among features. The approaches resolved this trade‐off differently. MinLoss favored features with worse retention (positively correlated with vulnerability) and MaxGain favored those with worse representation. Although our results are not surprising, given the focus of MinLoss on vulnerable areas and features with the poorest outlook, it is important to consider their implications for ongoing decline of vulnerable species where opportunistic conservation takes place ( Pressey 1994 ; Pressey 2002 ; Turner 2006 ). In principle, threatened features should have highest priority because delayed protection will likely result in their decline or extinction. Our results indicate that managers should therefore take a MinLoss approach, although the choice depends also on other factors, below. However, given chronic funding shortages for conservation, when reversing the prognosis for critically endangered features is unlikely, a triage approach suggests protecting areas with lower threats, thereby maximizing conservation efficiency and effectiveness ( Bottrill 2008 ). Displacement or inhibition of biodiversity loss by new reserves The nature of threat dynamics determined the magnitude of the difference between approaches but did not qualitatively alter the best approach. When reservation only displaced habitat loss, the improvement of MinLoss over MaxGain in terms of minimum retention was modest and attributable to MinLoss identifying areas with highest contributions to retention. This was subject, of course, to the uncertainty of information on vulnerability (below). With inhibition, the relative performance of MinLoss was stronger. MinLoss quickly removed suitable areas from development by reserving very vulnerable areas. In doing so, it not only influenced which areas would persist, it also reduced the total area lost by reducing the mean vulnerability in the landscape. There are many evidences all over the world of displacement (aka leakage) effects of habitat loss by protected areas ( Ewers & Rodrigues 2008 ). Displacement result in a limited net gain of natural habitat or in some cases even a net loss compared to a baseline of habitat loss. Our findings reinforce this empirical evidence, and suggest that implementing protected areas is not strategically smart if their only effect is to displace habitat conversion into other ecologically valuable areas. In such circumstances, habitat protection needs to be followed by political and economical incentives directly targeting the drivers of habitat loss. Spatial variance in vulnerability This factor had a small but significant effect both in isolation and in interaction with other factors ( Tables 2 and 3 ). With inhibition, variance in vulnerability determined the extent to which MinLoss could decrease the mean vulnerability of remaining habitat. If variance was high, preempting development by reserving vulnerable areas could decrease the mean vulnerability of remaining areas thereby reducing the extent of further loss of features. When variance was low, the mean vulnerability of the landscape was unaltered by reservation so MinLoss and MaxGain performed equally. The stronger reduction in loss rate with higher vulnerability variance did not apply with displacement because the rate of development was fixed. With both inhibition and displacement, increasing vulnerability variance increased the scope for MaxGain to misallocate conservation effort to areas with little contribution to biodiversity retention, thus widening the gap with MinLoss. Vulnerability variances similar to the maximum value tested here have been reported for terrestrial ( Pressey 1996 ) and marine regions ( Halpern 2008 ). Uncertainty in estimates of vulnerability Uncertainty in estimates of vulnerability was the most important factor in this study, accounting for much of the variability in the difference between MinLoss and MaxGain in minimum retention across features. With both loss models and across all levels of vulnerability variance, the best approach switched to MaxGain when approximately 70% of the estimates were incorrect (but at larger values with the random deviation method). Uncertainty also determined the magnitude of the difference between approaches via its interaction with vulnerability variance that explained ∼5% of variation in relative performance between approaches ( Table 2 ). When variance was high, any increase in uncertainty caused an important loss of information about expected biodiversity loss, and therefore reduced the relative performance of MinLoss. When variance was low, increasing uncertainty made little difference because vulnerability itself was less influential. Uncertainty was also involved in a three‐way interaction with the habitat loss model and vulnerability variance. With inhibition effects, strong vulnerability variance benefited MinLoss only with low uncertainty. Only in these circumstances could MinLoss effectively identify and secure the most valuable and vulnerable areas before they were developed, while reducing overall habitat loss. We discuss a second three‐way interaction in Appendix S5. Rules of thumb for conservation decision making To minimize biodiversity loss, we suggest using a MinLoss approach with existing vulnerability estimates (white areas in Figure 2c,d ) if uncertainty is estimated at less than 20%, regardless of vulnerability variance. This remains the best choice up to 70% uncertainty with variance <0.02 (inhibition) and variance <0.03 (displacement). With uncertainty between 20% and 70% and larger variance values, improving the estimate of vulnerability is the best strategy, given that a small reduction in uncertainty under these circumstances gives a large improvement in the relative performance of MinLoss (grey areas). With any other combination of values for both loss models, MaxGain is the best approach (black areas, which reduce to the right if uncertainty is generated with the random deviation method, Appendix S4). To use our rule of thumb, managers need to estimate uncertainty in vulnerability, requiring expert scrutiny of the vulnerability model or a validation dataset of actual land‐use transitions. Validation could involve applying the model to a past landscape and comparing with the present. Improving Ve will often require money and time to collect more data and/or develop better loss models. Although these investments are not necessarily large, the benefit of improving Ve needs to be evaluated against potential lost opportunities for timely protection ( McDonald‐Madden 2008 ; Grantham 2009 ). Methods are still needed to balance these considerations when selecting a prioritization strategy and to develop adaptive approaches that set initial priorities with available vulnerability estimates, and then refine the approach as new data become available. Applying the rule of thumb to real‐world case studies We tested the predictive ability of our rules of thumb with two case studies that applied simulations and measured retention for datasets used in actual planning exercises ( Table 4 ). While these studies are not perfectly comparable because of slight differences in habitat loss models and longer planning periods, the results agree with our findings here, especially regarding the effects of vulnerability variance. 4 Two case studies of retention from simulations that have reported values of some of the factors investigated here, and the observed improvement in biodiversity retention from considering vulnerability (equivalent to the benefit of MinLoss over MaxGain) References Habitat loss model Planning period Loss rate (LR, % landscape p.a.) Reservation rate (RR, % landscape p.a.) Assumed uncertainty Vulnerability variance a Performance difference Features abundance versus vulnerability correlation ( Visconti 2010 ) b Displacement 20 years 0.65 (low) 3.25 (high) 0.15 (low) 0.75 (high) 0 0.051 (59%) c,d 0.32% (low LR and low RR) 0.3653 8.87% (high LR and high RR) ( Pressey 2004 ) Displacement 25 years e 0.17 0.3 0 0.11 (100%) f 5.97% g −0.3305 a The value in parentheses next to the vulnerability variances expresses the proportion of vulnerability distribution tested in the present study that had variance lower than the variance observed in the case study. b This case study tested both variable costs and homogeneous costs; we report here only the results from using homogeneous costs for comparability with the present study. c Across the species tested in this study, we report only the Squirrel glider Petaurus norfolcensis , which, like the virtual species in the present study, did not exhibit responses to habitat fragmentation. d This case study reported the relative difference in performance ([best retention–worst retention]/worst retention) that we have expressed here in absolute differences for comparability with the present study. e A longer planning period was simulated in this case study but 25 years was the available time‐slice closest to the planning period tested in the present study. f The vulnerability distribution in this dataset was strongly right skewed and had a variance outside the scale of values possible with symmetric distributions like the ones tested here. g This study tested retention resulting from many approaches to scheduling. We have selected approaches that were the most similar to those tested in the present study. The value shown is the average gain in minimum retention from incorporating vulnerability into these scheduling approaches. Limitations Our results only apply to MinLoss and MaxGain that we chose because they are widely published and often used for their ability to solve large, complex, and realistic problems involving nonlinearities such as the effects of connectivity. Other approaches include integer linear programing ( Snyder 2004 ) and stochastic dynamic programing ( Costello & Polasky 2004 ; Strange 2006 ; Wilson 2006 ) and its approximations ( Drechsler 2005 ; Moilanen & Cabeza 2007 ). Most of these can only solve simple problems ( Moilanen 2008 ). Future research should expand our analyses to other dynamic reserve selection algorithms. A second limitation is that we assumed homogeneous costs, despite the potential for costs to vary more than biodiversity value ( Naidoo 2006 ; Bode 2008 ). The potential positive correlation of acquisition and opportunity costs with habitat vulnerability can influence the relative performance of MinLoss and MaxGain ( Newburn 2005 ; Visconti 2010 ) but considering costs here would have added another dimension to an already complex study design, so we leave for later work the investigation of interactions between costs with other factors influencing retention. Footnotes 1 Habitat is defined here as the part of the physical and/or biological environment in which an individual organism lives. Acknowledgments The authors would like to thank Robin Naidoo, Atte Moilanen, and an anonymous reviewer for the helpful comments that greatly improved earlier version of this manuscript. Piero Visconti was supported by an IDP Australia student mobility scholarship and a James Cook University postgraduate scholarship. Robert L. Pressey acknowledges the support of the Australian Research Council. Piero Visconti acknowledges James Cook University for providing access to the high‐performance computing facility.

Journal

Conservation LettersWiley

Published: Dec 1, 2010

Keywords: ; ; ; ; ; ; ; ;

References

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