#### 2.1. Dynamically Dimensioned Search Land-Use Optimization Planning Tool (DDSLOP Tool)

DDS is designed for the efficient search of a good global solution for optimization problems, which simultaneously deal with multiple control variables and their resultant massive solution spaces [

16,

19,

20]. DDS searches the solution globally by adjusting most of the control variables at the outset of the model, then becomes progressively more localized by gradually decreasing the number of control variables as the iteration number approaches the maximum number of pre-defined iterations [

16]. This mechanism implies that the DDS algorithm has the ability to escape from the local optima and, consequently, enhances the quality of the global solution through the incorporation of both diversification and intensification processes [

17].

Based on this key feature of DDS, the DDSLOP model stochastically modifies most of the cells within the target landscape from the original land-use types (control variables) to other land-use types at the beginning of the optimization process (

Figure 1). As the iteration count increases, however, the DDSLOP model only modifies those cells, which contribute to relatively lower evaluated suitability of habitat (criteria) for the species in question. In this way, a general reformation of the landscape ensues, resulting in a good habitat structure for the target species. Furthermore, a user-friendly interface compatible with the ArcGIS platform is provided for planners and researchers (see Supplementary 1).

Due to the complexity of spatial optimization problems, the proposed DDSLOP model has a double loop iteration process, which optimizes not only the composition of different land-use types (first loop), but also the spatial configuration of land-use types (second loop), throughout a given landscape. A series of outer optimization processes progressively modify the overall ratios of different land-use types (composition of the landscape) while iterative inner optimizations then modify the spatial configuration of the landscape based on the habitat suitability of selected cells, the new overall ratios of land-use types, as well as the ratio of land-use types of selected cells if restrictions on final land-use type ratios are predefined (

Figure 2). In other words, each of the resultant outer iteration land-use type ratios then undergoes a certain number of inner iterations, which modified the spatial pattern of land-use types. Since the objective is to modify the overall landscape in such a way as to maximize the suitability of habitat for the specific target species in question based on modifications to landscape structure, the fitness function is given as:

where

f_{inner} represents the inner fitness evaluated based on the resultant average habitat suitability index;

HSI_{mean}.

${\stackrel{\rightharpoonup}{M}}_{i}$
represents the spatial configuration of land-use types at count

i of inner iterations. While,

f_{outer} denotes the outer fitness and

${\stackrel{\rightharpoonup}{p}}_{t}$
represents the ratios of land-use types at outer iteration count

t.

**Figure 1.**
Dynamically dimensioned search process: The number of selected control variables decreases gradually while the number of iterations increases in the optimization process. These cells are stochastically selected from a target landscape for modification; therefore, the DDSLOP can dynamically scale down the search to find a good global solution throughout consecutive iterations.

**Figure 1.**
Dynamically dimensioned search process: The number of selected control variables decreases gradually while the number of iterations increases in the optimization process. These cells are stochastically selected from a target landscape for modification; therefore, the DDSLOP can dynamically scale down the search to find a good global solution throughout consecutive iterations.

In order to evaluate the inner fitness based on habitat suitability of the target species, we used logistic regression to construct habitat suitability models for each species [

3,

4,

6]. The habitat suitability models were used for estimating the probability of target species occurrence under updated DDSLOP outputs. The model is:

where,

$hsi\left({M}_{x,y}\right)\in \left[0,1\right]$
represents the index of habitat suitability at location (

x,

y) in a candidate landscape

M_{x,y}.

Cells represents the total number of cell grids in the landscape.

β_{0} is the intercept of the habitat suitability model.

β_{k} is the coefficient of each driving factor

df_{k}(

x,

y) at location (

x,

y) in the landscape.

**Figure 2.**
Inner optimization process of the DDSLOP model (Step 5): To promote efficiency of the optimization process, cells with lower habitat suitability are given higher priority for both selection and subsequent exchange, which means that places with higher suitability for the target species have overall lower probabilities of being modified. Based on the updated overall ratios of land-use types selected during the given outer iteration, DDSLOP allocates randomly ranked land-use types to habitat suitability ranked cells during each inner iteration. In the example below, the lawn-green land-use type is stochastically chosen to carry the highest rank in the first inner iteration, and is therefore chosen to replace cells with lowest suitability.

**Figure 2.**
Inner optimization process of the DDSLOP model (Step 5): To promote efficiency of the optimization process, cells with lower habitat suitability are given higher priority for both selection and subsequent exchange, which means that places with higher suitability for the target species have overall lower probabilities of being modified. Based on the updated overall ratios of land-use types selected during the given outer iteration, DDSLOP allocates randomly ranked land-use types to habitat suitability ranked cells during each inner iteration. In the example below, the lawn-green land-use type is stochastically chosen to carry the highest rank in the first inner iteration, and is therefore chosen to replace cells with lowest suitability.

In order to evaluate the effects of spatial patterns on specific species, four types of landscape metrics were considered, including: class area (

ca_{l}), largest patch index (

lpi), sum of edge lengths between two land-use types (

es_{l,k}), and patch cohesion (

coh_{l}) of specific land-use types (see Supplementary 2). The habitat suitability model used each of these metrics as factors contributing to habitability at a territorial scale for each species [

3,

6], based on presence data correlated with current landscape metrics. A moving window analysis, based on a radius that correlates to the territorial range of the target species [

3,

6] about each cell, was used to evaluate the landscape metrics and corresponding habitat suitability indexes of each cell. The steps of the DDSLOP model are as follows (modified from [

16]) (see Supplementary 3 for the flowchart of the steps):

Step 1. Define DDS inputs:

Define maximum iteration count t_{max} for outer fitness function evaluations.

Define maximum iteration count i_{max} for inner fitness function evaluations.

Define initial solution of outer control variable (composition)
${\stackrel{\rightharpoonup}{p}}_{0}=\left[{p}_{1},\mathrm{\dots},{p}_{D}\right]$
and inner control variable (configuration)
${\stackrel{\rightharpoonup}{M}}_{0}=\left[{M}_{1,1},{M}_{1,2},\mathrm{\dots},{M}_{m,n}\right]$
, which denotes the spatial composition and configuration, respectively, of the original-unmodified landscape. Where M_{m,n} represents the land-use type at location (m, n).

Step 2. Set the counter of outer iteration

t = 1, and evaluate fitness (mean habitat suitability) at initial solution

${f}_{outer}\left({\stackrel{\rightharpoonup}{p}}_{0}\right)$
with respect to the original landscape:

Current best fitness
${f}_{outer}^{best}={f}_{outer}({\stackrel{\rightharpoonup}{p}}_{0})={f}_{inner}({\stackrel{\rightharpoonup}{M}}_{0})$.

Current best solution
${\stackrel{\rightharpoonup}{p}}^{best}={\stackrel{\rightharpoonup}{p}}_{0}$
and
${\stackrel{\rightharpoonup}{M}}^{best}={\stackrel{\rightharpoonup}{M}}_{0}$
for outer and inner optimization, respectively.

Step 3. Stochastically place

j variables (land-use type ratios) from

${\stackrel{\rightharpoonup}{p}}^{best}$
(current optimal composition) into the {

N} set, which will undergo modifications in step 4:

Calculate the proportion of land-use type ratios, which will be selected for modification, based on a function of current iteration count:
${S}_{t}^{outer}=1-\text{ln}\left(t\right)/\text{ln}({t}_{\mathrm{max}})$.

For d = 1, …, D, move p_{d} from
${\stackrel{\rightharpoonup}{p}}^{best}$
to {N} until j control variables have been selected, (j ˂ D) based on the
${S}_{t}^{outer}$.

If {N} is empty, randomly place one element from
${\stackrel{\rightharpoonup}{p}}^{best}$
into it.

Step 4. In order to get new candidate

${\stackrel{\rightharpoonup}{p}}_{t}^{new}$
, perturb the selected control variables (land-use ratios), (

p_{d},

d = 1, …,

j) in {

N}. The perturbation of each variable (land-use ratio) corresponds in intensity proportional to a random sample taken from a standard normal distribution n(0,1), reflecting at bounds of control variables if necessary:

Step 5. Set the counter of inner iteration to

i = 1 and perturb the spatial configuration of the landscape

${\stackrel{\rightharpoonup}{M}}_{i}={\stackrel{\rightharpoonup}{M}}^{best}$
given the new proportions of the exchangeable land-use types

${\stackrel{\rightharpoonup}{p}}_{t}^{new}$.

Step 6. Evaluate outer fitness and update current best solution if necessary:

Step 7. Update iteration count t = t + 1 and check stop criterion. The maximum inner iteration count t_{max} was equal to 1000 for each case in this study. Therefore, for each case, the DDSLOP model conducted 200,000 evaluations of fitness.

#### 2.3. Study Site and Data Description

The National Taiwan University Highland Experimental Farm (NTU-HEF) (24°05′N, 121°10′E, altitude 2100 m.a.s.l., size 42.68 ha) was established for academic and educational purposes in horticulture and agriculture. In order to find optimal land-use patterns for bird conservation at a cellular scale, we included: land coverage, the distribution of birds, and geographic data (distance variables) at a 10 × 10 m (

Figure 4) resolution. This data was provided by earlier field surveys using a territory mapping method [

6,

21] from 2005 to 2007 (see Supplementary 4). Additionally, to take species’ territorial ranges into consideration, the study area was extended 50 m outward from the boundary of NTU-HEF [

6]. In the total 61.61 ha area, about 36.13% was covered by pristine forest. Other land-use types include: buildings, orchards, croplands, conifer plantations, broadleaf plantations, and manmade water bodies. From this description, we can see that the landscape has been markedly influence by human activities.

**Figure 3.**
Crossover and mutation operator in the GA-based LUPOlib model (modified from [

3,

4,

6]): Spatial pattern of a landscape is coded as a vector of the spatial pattern (

i.e., a GA genome) based on the patch topology. The crossover operator leads an exchange of selected elements for corresponding elements in another genome. The mutation operator leads to modifications of selected elements to randomly generated land-use types. In the example, land-use type 1 (for red patches) is not exchangeable. On the other hand, land-use types 2, 3, and 4 (for yellow, lawngreen, and purple patches) are exchangeable.

**Figure 3.**
Crossover and mutation operator in the GA-based LUPOlib model (modified from [

3,

4,

6]): Spatial pattern of a landscape is coded as a vector of the spatial pattern (

i.e., a GA genome) based on the patch topology. The crossover operator leads an exchange of selected elements for corresponding elements in another genome. The mutation operator leads to modifications of selected elements to randomly generated land-use types. In the example, land-use type 1 (for red patches) is not exchangeable. On the other hand, land-use types 2, 3, and 4 (for yellow, lawngreen, and purple patches) are exchangeable.

**Figure 4.**
The spatial pattern of NTU-HEF and distributions of each target species (modified from [

6]).

**Figure 4.**
The spatial pattern of NTU-HEF and distributions of each target species (modified from [

6]).

We chose three species, the Green-backed Tit (

Parus monticolus insperatus) (endemic subspecies), Taiwan Yuhina (

Yuhina brunneiceps) (endemic species) and Vinous-throated Parrotbill (

Paradoxornis webbianus bulomachus) (endemic species) for conservation scenarios. The presence data included 138 occurrence points of the Green-backed Tit, 1614 occurrence points of the Taiwan Yuhina and 210 occurrence points of the Vinous-throated Parrotbill (

Figure 4).

We applied the two optimization models to each species (case 1 = the Green-backed Tit, case 2 = the Taiwan Yuhina, and case 3 = the Vinous-throated Parrotbill) not only to evaluate the proposed model, but also in order to explore the advantages of landscape optimization at both cellular and patch levels. Due to existing land-use policies, which take both species conservation and economic self-sustainability into consideration, certain constraints were placed on the models. For NTU-HEF, land-use types including orchard, cropland, conifer plantation and broadleaf plantation were replaceable; however, the added restraint that 72.5% of the total area of both orchards and croplands need to be maintained for financial purposes was imposed upon the models [

6]. Accordingly, 117 patches consisted of 2085 cells were exchangeable in the spatial optimization processes.