A biodiversity simulation framework
We have developed a simulation framework modelling biodiversity loss to optimize and validate conservation policies (in this context, decisions about data gathering and area protection across a landscape) using an RL algorithm. We implemented a spatially explicit individual-based simulation to assess future biodiversity changes based on natural processes of mortality, replacement and dispersal. Our framework also incorporates anthropogenic processes such as habitat modifications, selective removal of a species, rapid climate change and existing conservation efforts. The simulation can include thousands of species and millions of individuals and track population sizes and species distributions and how they are affected by anthropogenic activity and climate change (for a detailed description of the model and its parameters see Supplementary Methods and Supplementary Table 1).
In our model, anthropogenic disturbance has the effect of altering the natural mortality rates on a species-specific level, which depends on the sensitivity of the species. It also affects the total number of individuals (the carrying capacity) of any species that can inhabit a spatial unit. Because sensitivity to disturbance differs among species, the relative abundance of species in each cell changes after adding disturbance and upon reaching the new equilibrium. The effect of climate change is modelled as locally affecting the mortality of individuals based on species-specific climatic tolerances. As a result, more tolerant or warmer-adapted species will tend to replace sensitive species in a warming environment, thus inducing range shifts, contraction or expansion across species depending on their climatic tolerance and dispersal ability.
We use time-forward simulations of biodiversity in time and space, with increasing anthropogenic disturbance through time, to optimize conservation policies and assess their performance. Along with a representation of the natural and anthropogenic evolution of the system, our framework includes an agent (that is, the policy maker) taking two types of actions: (1) monitoring, which provides information about the current state of biodiversity of the system, and (2) protecting, which uses that information to select areas for protection from anthropogenic disturbance. The monitoring policy defines the level of detail and temporal resolution of biodiversity surveys. At a minimal level, these include species lists for each cell, whereas more detailed surveys provide counts of population size for each species. The protection policy is informed by the results of monitoring and selects protected areas in which further anthropogenic disturbance is maintained at an arbitrarily low value (Fig. 1). Because the total number of areas that can be protected is limited by a finite budget, we use an RL algorithm42 to optimize how to perform the protecting actions based on the information provided by monitoring, such that it minimizes species loss or other criteria depending on the policy.
We provide a full description of the simulation system in the Supplementary Methods. In the sections below we present the optimization algorithm, describe the experiments carried out to validate our framework and demonstrate its use with an empirical dataset.
In our model we use RL to optimize a conservation policy under a predefined policy objective (for example, to minimize the loss of biodiversity or maximize the extent of protected area). The CAPTAIN framework includes a space of actions, namely monitoring and protecting, that are optimized to maximize a reward R. The reward defines the optimality criterion of the simulation and can be quantified as the cumulative value of species that do not go extinct throughout the timeframe evaluated in the simulation. If the value is set equal across all species, the RL algorithm will minimize overall species extinctions. However, different definitions of value can be used to minimize loss based on evolutionary distinctiveness of species (for example, minimizing phylogenetic diversity loss), or their ecosystem or economic value. Alternatively, the reward can be set equal to the amount of protected area, in which case the RL algorithm maximizes the number of cells protected from disturbance, regardless of which species occur there. The amount of area that can be protected through the protecting action is determined by a budget Bt and by the cost of protection ({C}_{t}^{c}), which can vary across cells c and through time t.
The granularity of monitoring and protecting actions is based on spatial units that may include one or more cells and which we define as the protection units. In our system, protection units are adjacent, non-overlapping areas of equal size (Fig. 1) that can be protected at a cost that cumulates the costs of all cells included in the unit.
The monitoring action collects information within each protection unit about the state of the system St, which includes species abundances and geographic distribution:
$${S}_{t}={{{{H}}}_{{{t}}},{{{D}}}_{{{t}}},{{{F}}}_{{{t}}},{{{T}}}_{{{t}}},{{{C}}}_{{{t}}},{{{P}}}_{{{t}}},{B}_{t}}$$
(1)
where Ht is the matrix with the number of individuals across species and cells, Dt and Ft are matrices describing anthropogenic disturbance on the system, Tt is a matrix quantifying climate, Ct is the cost matrix, Pt is the current protection matrix and Bt is the available budget (for more details see Supplementary Methods and Supplementary Table 1). We define as feature extraction the result of a function X(St), which returns for each protection unit a set of features summarizing the state of the system in the unit. The number and selection of features (Supplementary Methods and Supplementary Table 2) depends on the monitoring policy X, which is decided a priori in the simulation. A predefined monitoring policy also determines the temporal frequency of this action throughout the simulation, for example, only at the first time step or repeated at each time step. The features extracted for each unit represent the input upon which a protecting action can take place, if the budget allows for it, following a protection policy Y. These features (listed in Supplementary Table 2) include the number of species that are not already protected in other units, the number of rare species and the cost of the unit relative to the remaining budget. Different subsets of these features are used depending on the monitoring policy and on the optimality criterion of the protection policy Y.
We do not assume species-specific sensitivities to disturbance (parameters ds, fs in Supplementary Table 1 and Supplementary Methods) to be known features, because a precise estimation of these parameters in an empirical case would require targeted experiments, which we consider unfeasible across a large number of species. Instead, species-specific sensitivities can be learned from the system through the observation of changes in the relative abundances of species (x3 in Supplementary Table 2). The features tested across different policies are specified in the subsection Experiments below and in the Supplementary Methods.
The protecting action selects a protection unit and resets the disturbance in the included cells to an arbitrarily low level. A protected unit is also immune from future anthropogenic disturbance increases, but protection does not prevent climate change in the unit. The model can include a buffer area along the perimeter of a protected unit, in which the level of protection is lower than in the centre, to mimic the generally negative edge effects in protected areas (for example, higher vulnerability to extreme weather). Although protecting a disturbed area theoretically allows it to return to its initial biodiversity levels, population growth and species composition of the protected area will still be controlled by the deathreplacementdispersal processes described above, as well as by the state of neighbouring areas. Thus, protecting an area that has already undergone biodiversity loss may not result in the restoration of its original biodiversity levels.
The protecting action has a cost determined by the cumulative cost of all cells in the selected protection unit. The cost of protection can be set equal across all cells and constant through time. Alternatively, it can be defined as a function of the current level of anthropogenic disturbance in the cell. The cost of each protecting action is taken from a predetermined finite budget and a unit can be protected only if the remaining budget allows it.
We frame the optimization problem as a stochastic control problem where the state of the system St evolves through time as described in the section above (see also Supplementary Methods), but it is also influenced by a set of discrete actions determined by the protection policy Y. The protection policy is a probabilistic policy: for a given set of policy parameters and an input state, the policy outputs an array of probabilities associated with all possible protecting actions. While optimizing the model, we extract actions according to the probabilities produced by the policy to make sure that we explore the space of actions. When we run experiments with a fixed policy instead, we choose the action with highest probability. The input state is transformed by the feature extraction function X(St) defined by the monitoring policy, and the features are mapped to a probability through a neural network with the architecture described below.
In our simulations, we fix monitoring policy X, thus predefining the frequency of monitoring (for example, at each time step or only at the first time step) and the amount of information produced by X(St), and we optimize Y, which determines how to best use the available budget to maximize the reward. Each action A has a cost, defined by the function Cost(A, St), which here we set to zero for the monitoring action (X) across all monitoring policies. The cost of the protecting action (Y) is instead set to the cumulative cost of all cells in the selected protection unit. In the simulations presented here, unless otherwise specified, the protection policy can only add one protected unit at each time step, if the budget allows, that is if Cost(Y, St)
The protection policy is parametrized as a feed-forward neural network with a hidden layer using a rectified linear unit (ReLU) activation function (Eq. (3)) and an output layer using a softmax function (Eq. (5)). The input of the neural network is a matrix x of J features extracted through the most recent monitoring across U protection units. The output, of size U, is a vector of probabilities, which provides the basis to select a unit for protection. Given a number of nodes L, the hidden layer h(1) is a matrix UL:
$${h}_{u{l}}^{(1)}=gleft(mathop{sum}limits_{j =1}^{J}{x}_{uj}{W}_{j{l}}^{(1)}right)$$
(2)
where u {1, , U} identifies the protection unit, l {1, , L} indicates the hidden nodes and j {1, , J} the features and where
is the ReLU activation function. We indicate with W(1) the matrix of J L coefficients (shared among all protection units) that we are optimizing. Additional hidden layers can be added to the model between the input and the output layer. The output layer takes h(1) as input and gives an output vector of U variables:
$${h}_{u}^{(2)}=sigma left(mathop{sum}limits_{{l=1}}^{L}{h}_{u{l}}^{(1)}{W}_{{l}}^{(2)}right)$$
(4)
where is a softmax function:
$$sigma(x_i) = frac{exp(x_i)}{sum_u{exp(x_u)}}$$
(5)
We interpret the output vector of U variables as the probability of protecting the unit u.
This architecture implements parameter sharing across all protection units when connecting the input nodes to the hidden layer; this reduces the dimensionality of the problem at the cost of losing some spatial information, which we encode in the feature extraction function. The natural next step would be to use a convolutional layer to discover relevant shape and space features instead of using a feature extraction function. To define a baseline for comparisons in the experiments described below, we also define a random protection policy ({hat{pi }}), which sets a uniform probability to protect units that have not yet been protected. This policy does not include any trainable parameter and relies on feature x6 (an indicator variable for protected units; Supplementary Table 2) to randomly select the proposed unit for protection.
The optimization algorithm implemented in CAPTAIN optimizes the parameters of a neural network such that they maximize the expected reward resulting from the protecting actions. With this aim, we implemented a combination of standard algorithms using a genetic strategies algorithm43 and incorporating aspects of classical policy gradient methods such as an advantage function44. Specifically, our algorithm is an implementation of the Parallelized Evolution Strategies43, in which two phases are repeated across several iterations (hereafter, epochs) until convergence. In the first phase, the policy parameters are randomly perturbed and then evaluated by running one full episode of the environment, that is, a full simulation with the system evolving for a predefined number of steps. In the second phase, the results from different runs are combined and the parameters updated following a stochastic gradient estimate43. We performed several runs in parallel on different workers (for example, processing units) and aggregated the results before updating the parameters. To improve the convergence we followed the standard approach used in policy optimization algorithms44, where the parameter update is linked to an advantage function A as opposed to the return alone (Eq. (6)). Our advantage function measures the improvement of the running reward (weighted average of rewards across different epochs) with respect to the last reward. Thus, our algorithm optimizes a policy without the need to compute gradients and allowing for easy parallelization. Each epoch in our algorithm works as:
for every worker p do
({epsilon }_{p}leftarrow {{{mathcal{N}}}}(0,sigma )), with diagonal covariance and dimension W+M
for t=1,...,T do
RtRt1+rt(+p)
end for
end for
Raverage of RT across workers
ReR+(1)Re1
for every coefficient in W+M do
+A(Re, RT, )
end for
where ({mathcal{N}}) is a normal distribution and W + M is the number of parameters in the model (following the notation in Supplementary Table 1). We indicate with rt the reward at time t, with R the cumulative reward over T time steps. Re is the running average reward calculated as an exponential moving average where = 0.25 represents the degree of weighting decrease and Re1 is the running average reward at the previous epoch. =0.1 is a learning rate and A is an advantage function defined as the average of final reward increments with respect to the running average reward Re on every worker p weighted by the corresponding noise p:
$$A({R}_{e},{R}_{T},epsilon )=frac{1}{P}mathop{sum}limits_{p}({R}_{e}-{R}_{T}^{p}){epsilon }_{p}.$$
(6)
We used our CAPTAIN framework to explore the properties of our model and the effect of different policies through simulations. Specifically, we ran three sets of experiments. The first set aimed at assessing the effectiveness of different policies optimized to minimize species loss based on different monitoring strategies. We ran a second set of simulations to determine how policies optimized to minimize value loss or maximize the amount of protected area may impact species loss. Finally, we compared the performance of the CAPTAIN models against the state-of-the-art method for conservation planning (Marxan25). A detailed description of the settings we used in our experiments is provided in the Supplementary Methods. Additionally, all scripts used to run CAPTAIN and Marxan analyses are provided as Supplementary Information.
We analysed a recently published33 dataset of 1,517 tree species endemic to Madagascar, for which presence/absence data had been approximated through species distribution models across 22,394 units of 55km spanning the entire country (Supplementary Fig. 5a). Their analyses included a spatial quantification of threats affecting the local conservation of species and assumed the cost of each protection unit as proportional to its level of threat (Supplementary Fig. 5b), similarly to how our CAPTAIN framework models protection costs as proportional to anthropogenic disturbance.
We re-analysed these data within a limited budget, allowing for a maximum of 10% of the units with the lowest cost to be protected (that is, 2,239 units). This figure can actually be lower if the optimized solution includes units with higher cost. We did not include temporal dynamics in our analysis, instead choosing to simply monitor the system once to generate the features used by CAPTAIN and Marxan to place the protected units. Because the dataset did not include abundance data, the features only included species presence/absence information in each unit and the cost of the unit.
Because the presence of a species in the input data represents a theoretical expectation based on species distribution modelling, it does not consider the fact that strong anthropogenic pressure on a unit (for example, clearing a forest) might result in the local disappearance of some of the species. We therefore considered the potential effect of disturbance in the monitoring step. Specifically, in the absence of more detailed data about the actual presence or absence of species, we initialized the sensitivity of each species to anthropogenic disturbance as a random draw from a uniform distribution ({d}_{s} sim {{{mathcal{U}}}}(0,1)) and we modelled the presence of a species s in a unit c as a random draw from a binomial distribution with a parameter set equal to ({p}_{s}^{c}=1-{d}_{s}times {D}^{c}), where Dc[0, 1] is the disturbance (or threat sensu Carrasco et al.33) in the unit. Under this approach, most of the species expected to live in a unit are considered to be present if the unit is undisturbed. Conversely, many (especially sensitive) species are assumed to be absent from units with high anthropogenic disturbance. This resampled diversity was used for feature extraction in the monitoring steps (Fig. 1c). While this approach is an approximation of how species might respond to anthropogenic pressure, the use of additional empirical data on species-specific sensitivity to disturbance can provide a more realistic input in the CAPTAIN analysis.
We repeated this random resampling 50 times and analysed the resulting biodiversity data in CAPTAIN using the one-time protection model, trained through simulations in the experiments described in the previous section and in the Supplementary Methods. We note that it is possible, and perhaps desirable, in principle to train a new model specifically for this empirical dataset or at least fine-tune a model pretrained through simulations (a technique known as transfer learning), for instance, using historical time series and future projections of land use and climate change. Yet, our experiment shows that even a model trained solely using simulated datasets can be successfully applied to empirical data. Following Carrasco et al.33, we set as the target of our policy the protection of at least 10% of each species range. To achieve this in CAPTAIN, we modified the monitoring action such that a species is counted as protected only when at least 10% of its range falls within already protected units. We ran the CAPTAIN analysis for a single step, in which all protection units are established.
We analysed the same resampled datasets using Marxan with the initial budget used in the CAPTAIN analyses and under two configurations. First, we used a BLM (BLM=0.1) to penalize the establishment of non-adjacent protected units following the settings used in Carrasco et al.33. After some testing, as suggested in Marxans manual45, we set penalties on exceeding the budget, such that the cost of the optimized results indeed does not exceed the total budget (THRESHPEN1=500, THRESHPEN2=10). For each resampled dataset we ran 100 optimizations (with Marxan settings NUMITNS=1,000,000, STARTTEMP=1 and NUMTEMP=10,000 (ref. 45) and used the best of them as the final result. Second, because the BLM adds a constraint that does not have a direct equivalent in the CAPTAIN model, we also repeated the analyses without it (BLM=0) for comparison.
To assess the performance of CAPTAIN and compare it with that of Marxan, we computed the fraction of replicates in which the target was met for all species, the average number of species for which the target was missed and the number of protected units (Supplementary Table 4). We also calculated the fraction of each species range included in protected units to compare it with the target of 10% (Fig. 6c,d and Supplementary Fig. 6c,d). Finally, we calculated the frequency at which each unit was selected for protection across the 50 resampled datasets as a measure of its relative importance (priority) in the conservation plan.
Further information on research design is available in the Nature Research Reporting Summary linked to this article.
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