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Journal of Chemical Theory and... Feb 2022HF-DFT, the practice of evaluating approximate density functionals on Hartree-Fock densities, has long been used in testing density functional approximations....
HF-DFT, the practice of evaluating approximate density functionals on Hartree-Fock densities, has long been used in testing density functional approximations. Density-corrected DFT (DC-DFT) is a general theoretical framework for identifying failures of density functional approximations by separating errors in a functional from errors in its self-consistent (SC) density. Most modern DFT calculations yield highly accurate densities, but important characteristic classes of calculation have large density-driven errors, including reaction barrier heights, electron affinities, radicals and anions in solution, dissociation of heterodimers, and even some torsional barriers. Here, the HF density (if not spin-contaminated) usually yields more accurate and consistent energies than those of the SC density. We use the term DC(HF)-DFT to indicate DC-DFT using HF densities only in such cases. A recent comprehensive study (. , , 1368-1379) of HF-DFT led to many unfavorable conclusions. A reanalysis using DC-DFT shows that DC(HF)-DFT substantially improves DFT results precisely when SC densities are flawed.
PubMed: 35048707
DOI: 10.1021/acs.jctc.1c01045 -
The Journal of Physical Chemistry... Jan 2021Empirical fitting of parameters in approximate density functionals is common. Such fits conflate errors in the self-consistent density with errors in the energy...
Empirical fitting of parameters in approximate density functionals is common. Such fits conflate errors in the self-consistent density with errors in the energy functional, but density-corrected DFT (DC-DFT) separates these two. We illustrate with catastrophic failures of a toy functional applied to H at varying bond lengths, where the standard fitting procedure misses the exact functional; Grimme's D3 fit to noncovalent interactions, which can be contaminated by large density errors such as in the WATER27 and B30 data sets; and double-hybrids trained on self-consistent densities, which can perform poorly on systems with density-driven errors. In these cases, more accurate results are found at no additional cost by using Hartree-Fock (HF) densities instead of self-consistent densities. For binding energies of small water clusters, errors are greatly reduced. Range-separated hybrids with 100% HF at large distances suffer much less from this effect.
PubMed: 33411542
DOI: 10.1021/acs.jpclett.0c03545 -
The Journal of Physical Chemistry... Aug 2022We report a rigorous formulation of density functional theory for excited states, providing a theoretical foundation for a multistate density functional theory. We prove...
We report a rigorous formulation of density functional theory for excited states, providing a theoretical foundation for a multistate density functional theory. We prove the existence of a Hamiltonian matrix functional of the multistate matrix density () in the subspace spanned by the lowest eigenstates. Here, () is an -dimensional matrix of state densities and transition densities. Then, a variational principle of the multistate subspace energy is established, whose minimization yields both the energies and densities of the individual eigenstates. Furthermore, we prove that the -dimensional matrix density () can be sufficiently represented by nonorthogonal Slater determinants, based on which an interacting active space is introduced for practical calculations. This work establishes that the ground and excited states can be treated on an equal footing in density functional theory.
PubMed: 35969514
DOI: 10.1021/acs.jpclett.2c02088 -
Ecology and Evolution Jul 2022Theoretical modeling predicts that both direct and delayed density-dependence are key factors to generate population cycles. Deciphering density-dependent processes that...
Theoretical modeling predicts that both direct and delayed density-dependence are key factors to generate population cycles. Deciphering density-dependent processes that lead to variable population growth characterizing different phases of the cycles remains challenging. This is particularly the case for the period of prolonged low densities, which is inherently data deficient. However, demographic analyses based on long-term capture-mark-recapture datasets can help resolve this question. We relied on a 16-year (2004-2019) live-trapping program to analyze the summer demography and movements of a cyclic brown lemming population in the Canadian Arctic. More specifically, we examined if inversely density-dependent processes could explain why population growth can remain low during the prolonged low phase. We found that the proportion of females in the population was inversely density-dependent with a strong male-biased sex ratio at low densities but not at high densities. However, survival of adult females was higher than adult males, but both had lower survival at low densities than at high ones. Distances moved by both adult males and females were density-dependent, and proportion of females in reproductive condition was weakly density-dependent as it tended to increase at low density. Individual body condition, measured as monthly change in body mass, was not density-dependent. Overall, the strong male-biased sex ratio at very low densities suggests a loss of reproductive potential due to the rarity of females and appears to be the most susceptible demographic factor that could contribute to the prolonged low phase in cyclic brown lemmings. What leads to this sex-bias in the first place is still unclear, potentially owing to our trapping period limited to the summer, but we suggest that it could be due to high predation rate on breeding females in winter.
PubMed: 35813905
DOI: 10.1002/ece3.9055 -
Nature Communications May 2020Facilitation studies typically compare plants under differential stress levels with and without neighbors, while the density of neighbors has rarely been addressed....
Facilitation studies typically compare plants under differential stress levels with and without neighbors, while the density of neighbors has rarely been addressed. However, recent empirical studies indicate that facilitation may be density-dependent too and peak at intermediate neighbor densities. Here, we propose a conceptual model to incorporate density-dependence into theory about changes of plant-plant interactions under stress. To test our predictions, we combine an individual-based model incorporating both facilitative response and effect, with an experiment using salt stress and Arabidopsis thaliana. Theoretical and experimental results are strikingly consistent: (1) the intensity of facilitation peaks at intermediate density, and this peak shifts to higher densities with increasing stress; (2) this shift further modifies the balance between facilitation and competition such that the stress-gradient hypothesis applies only at high densities. Our model suggests that density-dependence must be considered for predicting plant-plant interactions under environmental change.
Topics: Acclimatization; Arabidopsis; Ecosystem; Models, Biological; Plant Development; Plant Physiological Phenomena; Population Dynamics; Stress, Physiological
PubMed: 32439842
DOI: 10.1038/s41467-020-16286-6 -
Journal of Insect Physiology 2022The density-dependent prophylaxis hypothesis predicts that risk of pathogen transmission increases with increase in population density, and in response to this,...
The density-dependent prophylaxis hypothesis predicts that risk of pathogen transmission increases with increase in population density, and in response to this, organisms mount a prophylactic immune response when exposed to high density. This prophylactic response is expected to help organisms improve their chances of survival when exposed to pathogens. Alternatively, organisms living at high densities can exhibit compromised defense against pathogens due to lack of resources and density associated physiological stress; the crowding stress hypothesis. We housed adult Drosophila melanogaster flies at different densities and measured the effect this has on their post-infection survival and resistance to starvation. We find that flies housed at higher densities show greater mortality after being infected with bacterial pathogens, while also exhibiting increased resistance to starvation. Our results are more in line with the crowding stress hypothesis that postulates a compromised immune system when hosts are subjected to high densities.
Topics: Animals; Bacterial Infections; Drosophila melanogaster; Population Density; Starvation; Stress, Physiological
PubMed: 35753428
DOI: 10.1016/j.jinsphys.2022.104415 -
Ecology Sep 2018Dispersal is a key ecological process that influences the dynamics of spatially and socially structured populations and consists of three stages-emigration, transience,...
Dispersal is a key ecological process that influences the dynamics of spatially and socially structured populations and consists of three stages-emigration, transience, and settlement-and each stage is influenced by different social, individual, and environmental factors. Despite our appreciation of the complexity of the process, we lack a firm empirical understanding of the mechanisms underlying the different stages. Here, using data from 65 GPS-collared dispersing female coalitions of the cooperatively breeding meerkat (Suricata suricatta), we present a comprehensive analysis of the effects of population density, mate availability, dispersing coalition size, and individual factors on each of the three stages of dispersal in a wild population. We expected a positive effect of density on dispersal due to increased kin competition at high densities. We further anticipated positive effects of mate availability, coalition size, and body condition on dispersal success. We observed increasing daily emigration and settlement probabilities at high population densities. In addition, we found that emigration and settlement probabilities also increased at low densities and were lowest at medium densities. Daily emigration and settlement probabilities increased with increasing female coalition size and in the presence of unrelated males. Furthermore, the time individuals spent in the transient stage increased with population density, whereas coalition size and presence of unrelated males decreased dispersal distance. The observed nonlinear relationship between dispersal and population density is likely due to limited benefits of cooperation at low population densities and increased kin competition at high densities. Our study provides empirical validation for the theoretical predictions that population density is an important factor driving the evolution of delayed dispersal and philopatry in cooperative breeders.
Topics: Female; Humans; Male; Population Density; Population Dynamics; Reproduction
PubMed: 29934962
DOI: 10.1002/ecy.2433 -
BMC Ecology and Evolution May 2021Population size and densities are key parameters in both fundamental and applied ecology, as they affect population resilience to density-dependent processes, habitat...
BACKGROUND
Population size and densities are key parameters in both fundamental and applied ecology, as they affect population resilience to density-dependent processes, habitat changes and stochastic events. Efficient management measures or species conservation programs thus require accurate estimates of local population densities across time and space, especially for continuously distributed species. For social species living in groups, population density depends on different components, namely the number of groups and the group size, for which relative variations in space may originate from different environmental factors. Whether resulting spatial variations in density are mostly triggered by one component or the other remains poorly known. Here, we aimed at determining the magnitude of the spatial variation in population densities of a social, group-living species, i.e. the European badger Meles meles, in 13 different sites of around 50 km across France, to decipher whether sett density, group size or proportion of occupied sett variation is the main factor explaining density variation. Besides the intrinsic factors of density variation, we also assessed whether habitat characteristics such as habitat fragmentation, urbanisation, and resource availability, drove both the spatial variation of density components and local population densities.
RESULTS
We proposed a new standardised approach combining use of multiple methods, namely distance sampling for estimating the density of occupied sett clusters, i.e. group density, and camera and hair trapping for genetic identification to determine the mean social group size. The density of adult badgers was on average 3.8 per km (range 1.7-7.9 per km) and was positively correlated with the density of sett clusters. The density of adult badgers per site was less related to the social group size or to the proportion of occupied sett clusters. Landscape fragmentation also explained the spatial variation of adult badger density, with highly fragmented landscapes supporting lower adult densities. Density components were linked differently to environmental variables.
CONCLUSIONS
These results underline the need to break down population density estimates into several components in group-living species to better understand the pattern of temporal and spatial variation in population density, as different components may vary due to different ecological factors.
Topics: Animals; Ecosystem; France; Mustelidae; Population Density
PubMed: 33975536
DOI: 10.1186/s12862-021-01809-6 -
Trends in Ecology & Evolution Aug 1986Explicit density-dependence differs from density-vagueness in the sort of regulation imposed on populations. Explicit density-dependence implies regulation toward a...
Explicit density-dependence differs from density-vagueness in the sort of regulation imposed on populations. Explicit density-dependence implies regulation toward a central equilibrium point, whereas density-vagueness implies population change away from the two extremes of extinction and immense densities. Density-vagueness does not much concern regulation within the broad range of medial densities; it is 'liberal'.
PubMed: 21227777
DOI: 10.1016/0169-5347(86)90071-6 -
PeerJ 2021The conservation of large carnivores often requires precise and accurate estimates of their populations. Being cryptic and occurring at low population densities,...
The conservation of large carnivores often requires precise and accurate estimates of their populations. Being cryptic and occurring at low population densities, obtaining an unbiased population estimate is difficult in large carnivores. To overcome the uncertainties in the conventional capture-recapture (CR) methods used to estimate large carnivore densities, more robust methods such as spatially explicit capture-recapture (SECR) framework are now widely used. We modeled the CR data of tiger () and leopard () in the SECR framework with biotic and abiotic covariates likely believed to influence their densities. An effort of 2,211 trap nights resulted in the capture of 33 and 38 individual tigers and leopards. A total of 95 and 74 detections of tigers and leopards were achieved using 35 pairs of camera traps. Tiger and leopard density were estimated at 4.71 ± 1.20 (3.05-5.11) and 3.03 ± 0.78 (1.85-4.99) per 100 km. Our results show that leopard density increased with high road density, high terrain ruggedness and habitats with high percentage of cropland and natural vegetation. The tiger density was positively influenced by the mosaic of cropland and natural vegetation. This study provides the first robust density estimates of tiger and leopard within the study area. Our results support the notion that large carnivores can attain moderate densities within human-dominated regions around protected areas relying on domestic livestock. Broader management strategies aimed at maintaining wild prey in the human-dominated areas around protected areas are necessary for large and endangered carnivores' sustenance in the buffer zones around protected areas.
PubMed: 33643701
DOI: 10.7717/peerj.10634