Species Distributions, Quantum Theory, and the Enhancement of Biodiversity Measures

Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics

Nonequilibrium and instability features of prey-predator-like systems associated to topological quantum domains emerging from a quantum phase-space description are investigated in the framework of the Weyl-Wigner quantum mechanics. Reporting about the generalized Wigner flow for one-dimensional Hamiltonian systems, H(x,k), constrained by ∂^{2}H/∂x∂k=0, the prey-predator dynamics driven by Lotka-Volterra (LV) equations is mapped onto the Heisenberg-Weyl noncommutative algebra, [x,k]=i, where the canonical variables x and k are related to the two-dimensional LV parameters, y=e^{-x} and z=e^{-k}. From the non-Liouvillian pattern driven by the associated Wigner currents, hyperbolic equilibrium and stability parameters for the prey-predator-like dynamics are then shown to be affected by quantum distortions over the classical background, in correspondence with nonstationarity and non-Liouvillianity properties quantified in terms of Wigner currents and Gaussian ensemble parameters. As an extension, considering the hypothesis of discretizing the time parameter, nonhyperbolic bifurcation regimes are identified and quantified in terms of z-y anisotropy and Gaussian parameters. The bifurcation diagrams exhibit, for quantum regimes, chaotic patterns highly dependent on Gaussian localization. Besides exemplifying a broad range of applications of the generalized Wigner information flow framework, our results extend, from the continuous (hyperbolic regime) to discrete (chaotic regime) domains, the procedure for quantifying the influence of quantum fluctuations over equilibrium and stability scenarios of LV driven systems.

Noncommutative phase-space Lotka-Volterra dynamics: The quantum analog

The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics extended to one-dimensional Hamiltonian systems, H(x,k) constrained by the ∂^{2}H/∂x∂k=0 condition. Supported by the Heisenberg-Weyl noncommutative algebra, where [x,k]=i, the canonical variables x and k are interpreted in terms of the LV variables, y=e^{-x} and z=e^{-k}, eventually associated with the number of individuals in a closed competitive dynamics: the so-called prey-predator system. The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales and for quantifying quantum analog effects. Through the results from the associated Wigner currents, (non-)Liouvillian and stationary properties are described for thermodynamic and Gaussian quantum ensembles in order to account for the corrections due to quantum features over the classical phase-space pattern yielded by the Hamiltonian description of the LV dynamics. In particular, for Gaussian statistical ensembles, the Wigner flow framework provides the exact profile for the quantum modifications over the classical LV phase-space trajectories so that Gaussian quantum ensembles can be interpreted as an adequate Hilbert space state configuration for comparing quantum and classical regimes. The generality of the framework developed here extends the boundaries of the understanding of quantumlike effects on competitive microscopical biosystems.

Factors associated with the differential distribution of cetaceans linked with deep habitats in the Western Mediterranean Sea

Deep-habitat cetaceans are generally difficult to study, leading to a limited knowledge of their population. This paper assesses the differential distribution patterns of three deep-habitat cetaceans (Sperm whale—Physeter macrocephalus, Risso’s dolphin—Grampus griseus & Cuvier’s beaked whale—Ziphius cavirostris). We used data of 842 opportunistic sightings of cetaceans in the western Mediterranean sea. We inferred environmental and spatio-temporal factors that affect their distribution. Binary logistic regression models were generated to compare the presence of deep-habitat cetaceans with the presence of other cetacean species in the dataset. Then, the favourability function was applied, allowing for comparison between all the models. Sperm whale and Risso’s dolphin presence was differentially favoured by the distance to towns in the eastern part of the western Mediterranean sea. The differential distribution of sperm whale was also influenced by the stability of SST, and that of the Risso’s dolphin by lower mean salinity and higher mean Chlorophyll A concentration. When modelling the three deep-habitat cetaceans (including Cuvier’s beaked whale), the variable distance to towns had a negative influence on the presence of any of them more than it did to other cetaceans, being more favourable far from towns, so this issue should be further investigated.

Dark host specificity in two ectoparasite taxa: repeatability, parasite traits, and environmental effects

We applied the concept of dark diversity (species that may potentially inhabit a locality but are absent) to the host spectrum of a parasite and defined it as dark host specificity (DHS). We studied the trait-associated and geographic patterns of dark host specificity in fleas and gamasid mites parasitic on small mammals, asking the following questions: (a) Is dark host specificity repeatable across populations of the same species? (b) Is it associated with morphological and/or ecological species traits? (c) What are the factors associated with geographical variation in the DHS among populations of the same species? The DHS was repeatable within species with a large proportion of variance among samples, accounted for by differences between species. The average DHS of fleas, but not mites, was affected by parasite traits, with the DHS being higher in fleas with larger geographic ranges, higher characteristic abundance levels, and summer reproduction peaks. In the majority of ectoparasites, the regional DHS decreased with an increase in either structural or phylogenetic host specificity. The associations between the DHS and the environmental or host-associated characteristics of a region were revealed in a few species (eight of 22 fleas and three of 12 mites). The DHS decreased with (a) an increase in air temperature in two fleas, (b) a decrease in precipitation in two fleas, and (c) an increase in regional host species richness (in three fleas and three mites). Overall, our results suggest that dark host specificity in arthropod ectoparasites is a species-specific character associated, to a large extent, with the breadth of their host-related niches, while the influences of parasite traits and local environmental conditions are minor.

Metapopulation Patterns of Iberian Butterflies Revealed by Fuzzy Logic

Metapopulation theory considers that the populations of many species are fragmented into patches connected by the migration of individuals through an interterritorial matrix. We applied fuzzy set theory and environmental favorability (F) functions to reveal the metapopulational structure of the 222 butterfly species in the Iberian Peninsula. We used the sets of contiguous grid cells with high favorability (F ≥ 0.8), to identify the favorable patches for each species. We superimposed the known occurrence data to reveal the occupied and empty favorable patches, as unoccupied patches are functional in a metapopulation dynamics analysis. We analyzed the connectivity between patches of each metapopulation by focusing on the territory of intermediate and low favorability for the species (F < 0.8). The friction that each cell opposes to the passage of individuals was computed as 1-F. We used the r.cost function of QGIS to calculate the cost of reaching each cell from a favorable patch. The inverse of the cost was computed as connectivity. Only 126 species can be considered to have a metapopulation structure. These metapopulation structures are part of the dark biodiversity of butterflies because their identification is not evident from the observation of the occurrence data but was revealed using favorability functions.

Population-level diversity-disease relationship (p-DDR) in the human microbiome associated diseases

Diversity-disease relationship (DDR) is a de facto standard analysis in the studies of human microbiome associated diseases (MADs). For example, the species richness or Shannon entropy are routinely compared between the healthy and diseased groups. Nevertheless, the basic scale of the standard diversity analysis is individual subject rather than a cohort or population because the diversity is computed for individual samples, not for the group. Here we aim to expand the current DDR study from individual focus to population level, which can offer important insights for understanding the epidemiology of MADs. We analyzed the diversity-disease relationship at cohort scale based on a collection of 23 datasets covering the major human MADs. Methodologically, we harness the power of a recent extension to the classic species-area relationship (SAR), i.e., the diversity-area relationship (DAR), to achieve the expansion from individual DDR to inter-subject diversity scaling analysis. Specifically, we apply the DAR analysis to estimate and compare the potentially maximal accrual diversities of the healthy and diseases groups, as well as the inter-subject diversity scaling parameters and the individual-to-population diversity ratios. It was shown that, except for the potential diversity (D_max) at the cohort level in approximately 5.4% cases of MADs, DAR parameters displayed no significant differences between healthy and diseased treatments. That is, the DAR parameters are rather resilient against MADs, except for the potential diversity in some diseases. We compared our population-level DDR with the existing individual-level DDR patterns and proposed a hypothesis to interpret their differences.

Fuzzy sets allow gaging the extent and rate of species range shift due to climate change

The recent modification of species distribution ranges in response to a warmer climate has constituted a major and generalized biogeographic change. The main driver of the shift in distribution is the disequilibrium of the species ranges with their climatic favourability. Most species distribution modelling approaches assume equilibrium of the distribution with the environment, which hinders their applicability to the analysis of this change. Using fuzzy set theory we assessed the response to climate change of a historically African species, the Atlas Long-legged Buzzard. With this approach we were able to quantify that the Buzzard's distribution is in a latitudinal disequilibrium of the species distribution with the current climate of 4 km, which is driving the species range northwards at a speed of around 1.3 km/year, i.e., it takes 3 years for the species to occupy new climatically favourable areas. This speed is expected to decelerate to 0.5 km/year in 2060-2080.

Applying fuzzy logic to assess the biogeographical risk of dengue in South America

BACKGROUND

Over the last decade, reports about dengue cases have increase worldwide, which is particularly worrisome in South America due to the historic record of dengue outbreaks from the seventeenth century until the first half of the twentieth century. Dengue is a viral disease that involves insect vectors, namely Aedes aegypti and Ae. albopictus, which implies that, to prevent and combat outbreaks, it is necessary to understand the set of ecological and biogeographical factors affecting both the vector species and the virus.

METHODS

We contribute with a methodology based on fuzzy logic that is helpful to disentangle the main factors that determine favorable environmental conditions for vectors and diseases. Using favorability functions as fuzzy logic modelling technique and the fuzzy intersection, union and inclusion as fuzzy operators, we were able to specify the territories at biogeographical risk of dengue outbreaks in South America.

RESULTS

Our results indicate that the distribution of Ae. aegypti mostly encompasses the biogeographical framework of dengue in South America, which suggests that this species is the principal vector responsible for the geographical extent of dengue cases in the continent. Nevertheless, the intersection between the favorability for dengue cases and the union of the favorability for any of the vector species provided a comprehensive map of the biogeographical risk for dengue.

CONCLUSIONS

Fuzzy logic is an appropriate conceptual and operational tool to tackle the nuances of the vector-illness biogeographical interaction. The application of fuzzy logic may be useful in decision-making by the public health authorities to prevent, control and mitigate vector-borne diseases.

Assessment of the National Park network of mainland Spain by the Insecurity Index of vertebrate species

The evaluation of protected area networks on their capacity to preserve species distributions is a key topic in conservation biology. There are different types of protected areas, with National Parks those with highest level of protection. National Parks can be declared attending to many ecological features that include the presence of certain animal species. Here, we selected 37 vertebrate species that were highlighted as having relevant natural value for at least one of the 10 National Parks of mainland Spain. We modelled species distributions with the favourability function, and applied the Insecurity Index to detect the degree of protection of favourable areas for each species. Two metrics of Insecurity Index were defined for each species: the Insecurity Index in each of the cells, and the Overall Insecurity Index of a species. The former allows the identification of insecure areas for each species that can be used to establish spatial conservation priorities. The latter gives a value of Insecurity for each species, which we used to calculate the Representativeness of favourable areas for the species in the network. As expected, due to the limited extension of the National Park network, all species have high values of Insecurity; i.e., just a narrow proportion of their favourable areas are covered by a National Park. However, the majority of species favourable areas are well represented in the network, i.e., the percentage of favourable areas covered by the National Park network is higher than the percentage of mainland Spain covered by the network (result also supported by a randomization approach). Even if a reserve network only covers a low percentage of a country, the Overall Insecurity Index allows an objective assessment of its capacity to represent species. Beyond the results presented here, the Insecurity Index has the potential to be extrapolated to other areas and to cover a wide range of species.

Changes in potential mammal diversity in national parks and their implications for conservation

Observed species richness (OSR) is a widely used and well-studied biodiversity metric. However, non-observed species in favorable ecosystems are also relevant. Two metrics that include observed and potential species were recently defined: potential biodiversity (hereafter potential species richness—PSR) and geometric mean of favorabilities (GMF). We used these metrics to evaluate the national park network of mainland Spain at two time periods (2002 and 2015), using terrestrial mammals on a UTM 100-km² grid. PSR and GMF are based on the favorability function, a species distribution model that assesses how favorable an area is for the presence of a species, over and above its prevalence in the study area. For each park and for the whole network, we calculated the mean and sum of OSR, PSR, and GMF in each time period, as well as changes between periods. OSR and PSR were higher inside than outside the park network in both time periods. Thus, although the network covers a very small proportion of the country, it performs well for the representation of mammal species and their favorable areas. However, mean PSR was lower in 2015 than in 2002 inside the national park network, whereas the opposite was the case outside the network. Mountainous Parks generally not only concentrated highly favorable areas for mammals, but they also showed less favorable areas in 2015 compared to 2002, although the reduction was moderate to low. This is a result to consider for future analyses because if the tendency increases, it may have consequences for the conservation of mammals and for the adequacy of the national park network.