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A biodiversity simulation frameworkWe 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.Conservation planning within a reinforcement learning frameworkIn 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 πX, 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 πY. 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 πY.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 death–replacement–dispersal 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.Policy definition and optimization algorithmWe 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 πY. 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 πX, 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 πY, 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)  More

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This is the first study analyzing mandible shape in both mink species and, together with a previous study on their cranial shape38, it has revealed how small morphological differences in highly similar species can lead to substantial biomechanical differences (see breakdown below). As with cranial shape, mandible shape in minks is influenced by the complex interaction of size and sexual dimorphism both at the inter- and intraspecific levels. However, while in cranial shape both species had divergent shape allometries and parallel interspecific sexual allometries, the opposite was true for mandible shape.Differences in mandible shape between European and American mink were summarized by PC1 (Fig. 2, Fig. S1) and can be mainly related to muscle size and jaw biomechanics (i.e., in-levers and out-levers). The relatively taller and slightly wider coronoid process of European minks suggests a relatively larger temporalis muscle, while the anteriorly expanded masseteric fossa of American mink is indicative of a relatively larger masseter complex17,22,25. The relatively enlarged angular process of European mink provides a larger attachment area for the superficial masseter, with both mink species having a distinctive fossa on the lateral side of the angular process where this muscle attaches. This angular fossa is not present in European polecats (Gálvez-López, pers. obs.), part of the sister clade to European mink41.Regarding jaw biomechanics, the particular morphology of the American mink illustrates the compromise between maximizing both bite force efficiency and increased gape. The MAs for all masticatory muscles were higher in European mink due to their relatively longer in-levers (and also shorter out-levers if measured on PC1 configurations), with the exception of the MA of the deep masseter which was considerably higher in American mink (Table S2; Fig. 1D). These findings indicate that American mink exhibit features that allow them to produce larger forces at wide gape, which is particularly useful for holding and killing terrestrial vertebrates22,42. In agreement with this, a short moment arm of the superficial masseter (as observed in American mink) has been associated with increased gape in other mammals43. It is also worth noting that low MAs for the posterior temporalis and superficial masseter have also been associated with fish capture, as they indicate a relatively longer mandible relative to the muscle in-levers, which in turn allows the mouth to close faster when trying to catch elusive prey underwater21. In contrast, the characteristic features of European mink are indicative of stronger bites at the carnassials, which would allow them to cut through relatively tougher tissues and also to crush harder objects (e.g. shells of aquatic prey). Favoring carnassial over anterior bites could also be advantageous to feeding on fish. Mink catch fish underwater by grabbing them by the fins or back with their anterior teeth, and then dragging them to the surface where they are processed using cheek (carnassial) bites (Gálvez-López, pers. obs.).In our previous study on cranial shape in mink38, morphological differences between both species indicated relatively larger muscle volumes overall in the American mink (temporalis: more developed sagittal and nuchal crests, narrower braincase; masseter: longer and more curved zygomatic arches, larger infratemporal fossa), which suggested that bite forces both at the anterior dentition and at the carnassials were larger in this species. However, when combined with the MA results from this study on mandible shape, the relationship between muscle volume and force production becomes less straightforward. In the case of the European mink, the relatively smaller temporalis has a larger attachment site on the mandible (i.e., a broader and taller coronoid) and becomes more efficient (i.e., has higher MAs) due to the relatively longer in-lever. Similarly, in the American mink the effective length of the superficial masseter is increased by the marked curvature of the zygomatic arches, which mitigates the dorsal displacement of the angular process. However, the efficiency of the relatively larger temporalis is diminished by a smaller coronoid (i.e., reduced attachment area and shorter in-levers). The remaining differences in cranial morphology align with differences in mandible shape. Namely, the relatively broader zygomatic arches of the European mink support a strong superficial masseter, while the larger infratemporal fossae of American mink account for their enlarged deep masseter. On a final note, another finding common to both cranial and mandible shape was the relatively larger crushing dentition of American mink.Thus, after combining the results of cranial and mandible shape, it appears that, while the characteristic features of European mink indeed allow stronger carnassial bites, American mink present morphological indicators of both strong killing bites at wide gapes and powerful carnassial bites with a marked crushing component.The allometric effect on mandible size common to both species was represented by PC2 (Fig. 2, Fig. S3), which complements the common allometric trend recovered for both mink species in cranial shape38. The relative expansion of the masseteric fossa and the angular process with increasing size suggests that larger mink present a larger masseter complex. However, most of the allometric shape changes are related to muscle in-levers and out-levers. With increasing size, the length of both the out-lever at the anterior teeth and the in-levers of its related muscles (anterior temporalis, deep masseter) increases (Table S2), but the in-levers scale faster than the out-lever (Table S2). Thus, the mechanical advantages of both muscles at the anterior teeth also increase with size (Table S2), indicating that larger mink have markedly stronger and more efficient killing bites (particularly true for the deep masseter, which also becomes larger with size). This, together with their relatively larger anterior dentition (both in the mandible and the cranium) and taller anterior corpus, can be related to feeding on larger prey as size increases (i.e., stronger bites to perforate tougher skulls and hold onto stronger struggling prey, which would also require more robust teeth and corpora to resist the stresses placed on them). Similar features have been described for felids18, which also kill prey in this way22,32.Note, however, that one of the shape changes along PC2 does not accurately reflect the common allometric pattern: the lever arm of the superficial masseter, which slightly decreases along PC2 (Fig. 2; Table S2) and results in a decrease of the mechanical advantage of the superficial masseter and hence bite force at the carnassials along this axis (Table S2). In contrast, this lever arm significantly increases with size in the original specimens (Table S2), in agreement with the common allometric trend in cranial shape suggesting stronger bites at all teeth with increasing size38. A likely explanation for this phenomenon is that the common allometric trend is being confounded with interspecific shape differences, as American mink have significantly shorter superficial masseter in-levers than European mink (Fig. 1F; Table S2) yet their males are significantly larger than all other specimens (Fig. 1A). As mentioned above, the relative decrease in MA might reflect the trade-off between producing strong bite forces at the anterior teeth and having a wider gape to capture larger prey43, both of which are heavily supported by other morphological features in this common allometric trend.Sexual dimorphism in mandible shape was significant both within each species, and when grouping sexes from both species together. In her study of Palearctic mustelids, Romaniuk28 also found evidence for interspecific sexual dimorphism in mandible shape, but within species it was only significant for the Siberian weasel (Mustela sibirica). The different results for the European mink in that study might be related to its smaller sample. Note, however, that Hernández-Romero et al.40 did not find evidence for sexual dimorphism in mandible shape within Neotropical otters (Lontra longicaudis) even though their sample sizes were equivalent to those in the present study.Overall, the results of the present study reveal that mandible shape differences between males and females are the consequence of a complex interaction between sex and size at both inter- and intraspecific levels. For instance, each sex in each species has a mandible shape significantly different from each other (Table 1), but allometric shape changes within each of them are similar (except maybe female American mink; Fig. S5A). Additionally, while trajectory analysis indicates that the degree of sexual dimorphism in mandible shape is similar within each species, the specific differences between sexes are different in each species (i.e., same magnitude, different orientation; Table 2, Fig. S5B). While at the interspecific level, male and female mandible shapes change differently with increasing size even though the change per unit size is similar in both sexes (Tables 1, 2; Fig. S5C,D), and some of the allometric changes are common to both species and sexes (see section above; PC2 in Fig. 2). Finally, another set of shape changes related to sexual dimorphism and common to both species are those related to sexual dimorphism in mandible size, illustrated by PC3 (Figs. 2, Fig. S4).Shape changes related to sexual dimorphism in size are represented along PC3 and can be related to an overall increase in bite force (i.e., at all teeth), as higher scores on this axis correspond to increased muscle attachment areas and longer in-levers (taller and wider coronoid, anteriorly expanded masseteric fossa, ventrally expanded angular process), shorter out-levers (particularly at the anterior teeth), and a more robust corpus (dorsoventrally and mediolaterally expanded). This interpretation of shape changes along PC3 is supported by the results of the ANOVAs on the lever arms and MAs measured on the PC3 configurations (Table S2). These variables were only related to sex and size, with female mink having longer out-levers and male mink presenting longer in-levers and higher MAs, while out-levers decreased with increasing size and in-levers and MAs increased in both sexes (no significant interaction between sex and size indicates parallel allometric trajectories in both sexes). This trend is consistent with the common sexual allometry described for cranial shape, which suggested that larger males have bigger masticatory muscles than smaller females and thus produce higher bite forces38. Additionally, even though the relative length of the toothrow decreases, the size of the canine markedly increases and there is no change in molar size or the relative proportions in its shearing and crushing regions. Although this might be interpreted as reinforcing the canines to cope with killing larger prey while maintaining an otherwise similar dietary regime20, it is worth noting that larger canines have been long described as a feature of sexual size dimorphism in mustelids19,44,45.In terms of interspecific differences in sexual allometry, with increasing size the following shape changes were observed in females but not in males (Fig. S5C): a dorsoventrally more robust corpus, a ventral expansion of the angular process, longer in-levers for all masticatory muscles, larger incisors, and an increase in the shearing portion of m1 relative to the crushing portion. Most of these shape changes are similar to those described for PC3, which suggests that the female interspecific allometry bridges the bite force gap caused by sexual dimorphism in size. The changes to the female dentition suggest a shift in diet from crushing tough food items (e.g. aquatic invertebrates) towards slicing meat, which makes sense since these changes occur simultaneously with the common allometric trend (related to improved capabilities for killing larger vertebrate prey). However, as noted earlier, the increased shearing component is also advantageous for a piscivorous diet. Shape changes in male mandibles not observed in females seem to emphasize the common allometric trend (i.e., stronger killing bite at larger gapes) (Fig. S5D): a wider coronoid process for more muscle attachment, a dorsally displaced angular process to allow wider gapes, and mediolateral expansion of the corpus to increase its strength. Regarding their dentition, the opposite trend to females was observed (i.e., slightly smaller anterior teeth and a longer crushing molar portion), suggesting a larger durophagous component in the diet of larger males.As expected, variation in mandible shape could be linked to potential dietary differences between European and American mink, and also between sexes. In summary, the results of the present study show that:

American mink are better equipped for preying on terrestrial vertebrates, as they can achieve relatively larger gapes and their mandibles are able to produce larger forces during the killing bite (i.e., at the anterior teeth and with an open mouth).

European mink, on the other hand, can produce relatively stronger bites at the carnassials, suggesting that they rely more on tougher prey and/or fish.

Regardless of species and sex, morphological features in larger mink demonstrate increased capabilities for feeding on larger terrestrial prey (stronger killing bites and more robust anterior teeth and corpora to resist the stresses caused by struggling prey).

Due to their larger size, male mink of both species have stronger bites than females at both the anterior teeth and the carnassials. However, with increasing size, females bridge the gap by developing relatively stronger bites overall while shifting their diet from tougher or harder prey (probably aquatic invertebrates) towards less mechanically demanding food items (e.g. terrestrial vertebrates and/or fish). In contrast, increasing size in males leads to even more specialization towards feeding on larger terrestrial prey while tough items become more relevant in their diets (probably crushing bones of small prey).

These findings confirm our original predictions based on previous results on cranial shape differences, but do they agree with observed dietary preferences in minks? Diet studies in American mink are numerous, and provide a wide picture of seasonal and regional variation8,11 as well as intraspecific dietary competition6,7,12. However, studies on European mink diet are scarcer9,14, particularly those comparing the sexes13. Additionally, a few studies have compared diets of sympatric European and American mink10,15. All these studies can be summarized as: A, male American mink favor medium-sized mammals and birds usually heavier than themselves; B, female American mink favor aquatic prey, but are displaced towards small mammals and birds when seasonal changes in prey availability shift the males’ diet towards aquatic prey; C, European mink favor aquatic prey, particularly fish and crayfish; but D, they are displaced towards amphibians and small mammals when sympatric with American mink. From these, our results on mandible shape variation support A and somewhat B and C, but provide no information on the interspecific competition scenario or on potential seasonal or local dietary differences. Additionally, there is no information on size-related dietary changes in either species that could validate our findings on sexual allometry in mandible shape. Thus, while mandible shape is very useful for identifying broad dietary indicators even between highly similar species, its ability to provide accurate information on their potential prey is limited.As a final note on mink diets, our previous study on cranial shape38, suggested a gradient in muscle force (and potential dietary range) from female European mink to male American mink. Based on those results and studies on social interactions between and within species35,46, we hypothesized that competition between both mink species could be displacing female European mink towards narrower and poorer diets, which could affect their survivability and ability to successfully reproduce. Fortunately, the results of the present study not only propose that there might be less overlap in diets between species and sexes than suggested by dietary studies7,10,13,15, but also indicate that dietary competition seems to be higher for small terrestrial vertebrates, not aquatic prey (on which female European mink are particularly well equipped to feed). More

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