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Park S, Gordon CT, Swager TM. Resistivity detection of perfluoroalkyl substances with fluorous polyaniline in an electrical lateral flow sensor. Proc Natl Acad Sci U S A 2024; 121:e2317300121. [PMID: 38470924 PMCID: PMC10963003 DOI: 10.1073/pnas.2317300121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Accepted: 02/06/2024] [Indexed: 03/14/2024] Open
Abstract
Perfluoroalkyl substances (PFAS), known as "forever chemicals," are a growing concern in the sphere of human and environmental health. In response, rapid, reproducible, and inexpensive methods for PFAS detection in the environment and home water supplies are needed. We have developed a simple and inexpensive perfluoroalkyl acid detection method based on an electrically read lateral flow assay (e-LFA). Our method employs a fluorous surfactant formulation with undoped polyaniline (F-PANI) fabricated to create test lines for the lateral flow assay. In perfluoroalkyl acid sensing studies, an increase in conductivity of the F-PANI film is caused by acidification and doping of PANI. A conductivity enhancement by 104-fold can be produced by this method, and we demonstrate a limit of detection for perfluorooctanoic acid (PFOA) of 400 ppt and perfluorobutanoic acid of 200 ppt. This method for PFOA detection can be expanded for wide-scale environmental and at-home water testing.
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Affiliation(s)
- Sohyun Park
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Collette T. Gordon
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Timothy M. Swager
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA02139
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Pizurica M, Larmuseau M, Van der Eecken K, de Schaetzen van Brienen L, Carrillo-Perez F, Isphording S, Lumen N, Van Dorpe J, Ost P, Verbeke S, Gevaert O, Marchal K. Whole Slide Imaging-Based Prediction of TP53 Mutations Identifies an Aggressive Disease Phenotype in Prostate Cancer. Cancer Res 2023; 83:2970-2984. [PMID: 37352385 PMCID: PMC10538366 DOI: 10.1158/0008-5472.can-22-3113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 03/08/2023] [Accepted: 06/20/2023] [Indexed: 06/25/2023]
Abstract
In prostate cancer, there is an urgent need for objective prognostic biomarkers that identify the metastatic potential of a tumor at an early stage. While recent analyses indicated TP53 mutations as candidate biomarkers, molecular profiling in a clinical setting is complicated by tumor heterogeneity. Deep learning models that predict the spatial presence of TP53 mutations in whole slide images (WSI) offer the potential to mitigate this issue. To assess the potential of WSIs as proxies for spatially resolved profiling and as biomarkers for aggressive disease, we developed TiDo, a deep learning model that achieves state-of-the-art performance in predicting TP53 mutations from WSIs of primary prostate tumors. In an independent multifocal cohort, the model showed successful generalization at both the patient and lesion level. Analysis of model predictions revealed that false positive (FP) predictions could at least partially be explained by TP53 deletions, suggesting that some FP carry an alteration that leads to the same histological phenotype as TP53 mutations. Comparative expression and histologic cell type analyses identified a TP53-like cellular phenotype triggered by expression of pathways affecting stromal composition. Together, these findings indicate that WSI-based models might not be able to perfectly predict the spatial presence of individual TP53 mutations but they have the potential to elucidate the prognosis of a tumor by depicting a downstream phenotype associated with aggressive disease biomarkers. SIGNIFICANCE Deep learning models predicting TP53 mutations from whole slide images of prostate cancer capture histologic phenotypes associated with stromal composition, lymph node metastasis, and biochemical recurrence, indicating their potential as in silico prognostic biomarkers. See related commentary by Bordeleau, p. 2809.
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Affiliation(s)
- Marija Pizurica
- Internet Technology and Data Science Lab (IDLab/IMEC), Ghent University, Gent, Belgium
- Department of Plant biotechnology and Bioinformatics, Ghent University, Gent, Belgium
- Department of Biomedical Data Science, Stanford University, School of Medicine, Stanford, California
| | - Maarten Larmuseau
- Internet Technology and Data Science Lab (IDLab/IMEC), Ghent University, Gent, Belgium
- Department of Plant biotechnology and Bioinformatics, Ghent University, Gent, Belgium
| | | | - Louise de Schaetzen van Brienen
- Internet Technology and Data Science Lab (IDLab/IMEC), Ghent University, Gent, Belgium
- Department of Plant biotechnology and Bioinformatics, Ghent University, Gent, Belgium
| | - Francisco Carrillo-Perez
- Department of Architecture and Computer Technology (ATC), University of Granada, Granada, Spain
- Stanford Center for Biomedical Informatics Research (BMIR), Stanford University, School of Medicine, Stanford, California
| | - Simon Isphording
- Internet Technology and Data Science Lab (IDLab/IMEC), Ghent University, Gent, Belgium
- Department of Plant biotechnology and Bioinformatics, Ghent University, Gent, Belgium
| | - Nicolaas Lumen
- Department of Urology, Ghent University Hospital, Ghent, Belgium
| | - Jo Van Dorpe
- Department of Urology, Ghent University Hospital, Ghent, Belgium
| | - Piet Ost
- Department of Radiotherapy, Ghent University Hospital, Ghent, Belgium
| | - Sofie Verbeke
- Department of Urology, Ghent University Hospital, Ghent, Belgium
| | - Olivier Gevaert
- Department of Biomedical Data Science, Stanford University, School of Medicine, Stanford, California
- Stanford Center for Biomedical Informatics Research (BMIR), Stanford University, School of Medicine, Stanford, California
| | - Kathleen Marchal
- Internet Technology and Data Science Lab (IDLab/IMEC), Ghent University, Gent, Belgium
- Department of Plant biotechnology and Bioinformatics, Ghent University, Gent, Belgium
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Bittleston LS, Wolock CJ, Maeda J, Infante V, Ané JM, Pierce NE, Pringle A. Carnivorous Nepenthes Pitchers with Less Acidic Fluid House Nitrogen-Fixing Bacteria. Appl Environ Microbiol 2023; 89:e0081223. [PMID: 37338413 PMCID: PMC10370301 DOI: 10.1128/aem.00812-23] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Accepted: 05/24/2023] [Indexed: 06/21/2023] Open
Abstract
Carnivorous pitcher plants are uniquely adapted to nitrogen limitation, using pitfall traps to acquire nutrients from insect prey. Pitcher plants in the genus Sarracenia may also use nitrogen fixed by bacteria inhabiting the aquatic microcosms of their pitchers. Here, we investigated whether species of a convergently evolved pitcher plant genus, Nepenthes, might also use bacterial nitrogen fixation as an alternative strategy for nitrogen capture. First, we constructed predicted metagenomes of pitcher organisms from three species of Singaporean Nepenthes using 16S rRNA sequence data and correlated predicted nifH abundances with metadata. Second, we used gene-specific primers to amplify and quantify the presence or absence of nifH directly from 102 environmental samples and identified potential diazotrophs with significant differential abundance in samples that also had positive nifH PCR tests. Third, we analyzed nifH in eight shotgun metagenomes from four additional Bornean Nepenthes species. Finally, we conducted an acetylene reduction assay using greenhouse-grown Nepenthes pitcher fluids to confirm nitrogen fixation is indeed possible within the pitcher habitat. Results show active acetylene reduction can occur in Nepenthes pitcher fluid. Variation in nifH from wild samples correlates with Nepenthes host species identity and pitcher fluid acidity. Nitrogen-fixing bacteria are associated with more neutral fluid pH, while endogenous Nepenthes digestive enzymes are most active at low fluid pH. We hypothesize Nepenthes species experience a trade-off in nitrogen acquisition; when fluids are acidic, nitrogen is primarily acquired via plant enzymatic degradation of insects, but when fluids are neutral, Nepenthes plants take up more nitrogen via bacterial nitrogen fixation. IMPORTANCE Plants use different strategies to obtain the nutrients that they need to grow. Some plants access their nitrogen directly from the soil, while others rely on microbes to access the nitrogen for them. Carnivorous pitcher plants generally trap and digest insect prey, using plant-derived enzymes to break down insect proteins and generate a large portion of the nitrogen that they subsequently absorb. In this study, we present results suggesting that bacteria living in the fluids formed by Nepenthes pitcher plants can fix nitrogen directly from the atmosphere, providing an alternative pathway for plants to access nitrogen. These nitrogen-fixing bacteria are only likely to be present when pitcher plant fluids are not strongly acidic. Interestingly, the plant's enzymes are known to be more active under strongly acidic conditions. We propose a potential trade-off where pitcher plants sometimes access nitrogen using their own enzymes to digest prey and at other times take advantage of bacterial nitrogen fixation.
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Affiliation(s)
- Leonora S. Bittleston
- Department of Biological Sciences, Boise State University, Boise, Idaho, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, USA
| | - Charles J. Wolock
- Department of Biostatistics, University of Washington, Seattle, Washington, USA
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, USA
| | - Junko Maeda
- Department of Bacteriology, University of Wisconsin—Madison, Madison, Wisconsin, USA
| | - Valentina Infante
- Department of Bacteriology, University of Wisconsin—Madison, Madison, Wisconsin, USA
| | - Jean-Michel Ané
- Department of Bacteriology, University of Wisconsin—Madison, Madison, Wisconsin, USA
- Department of Agronomy, University of Wisconsin—Madison, Madison, Wisconsin, USA
| | - Naomi E. Pierce
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, USA
- Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts, USA
| | - Anne Pringle
- Department of Bacteriology, University of Wisconsin—Madison, Madison, Wisconsin, USA
- Department of Botany, University of Wisconsin—Madison, Madison, Wisconsin, USA
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Abisado-Duque RG, Townsend KA, Mckee BM, Woods K, Koirala P, Holder AJ, Craddock VD, Cabeen M, Chandler JR. An Amino Acid Substitution in Elongation Factor EF-G1A Alters the Antibiotic Susceptibility of Pseudomonas aeruginosa LasR-Null Mutants. J Bacteriol 2023; 205:e0011423. [PMID: 37191503 PMCID: PMC10294626 DOI: 10.1128/jb.00114-23] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Accepted: 04/22/2023] [Indexed: 05/17/2023] Open
Abstract
The opportunistic bacterium Pseudomonas aeruginosa uses the LasR-I quorum-sensing system to increase resistance to the aminoglycoside antibiotic tobramycin. Paradoxically, lasR-null mutants are commonly isolated from chronic human infections treated with tobramycin, suggesting there may be a mechanism that permits the emergence of lasR-null mutants under tobramycin selection. We hypothesized that some other genetic mutations that emerge in these isolates might modulate the effects of lasR-null mutations on antibiotic resistance. To test this hypothesis, we inactivated lasR in several highly tobramycin-resistant isolates from long-term evolution experiments. In some of these isolates, inactivating lasR further increased resistance, compared with decreasing resistance of the wild-type ancestor. These strain-dependent effects were due to a G61A nucleotide polymorphism in the fusA1 gene encoding amino acid substitution A21T in the translation elongation factor EF-G1A. The EF-G1A mutational effects required the MexXY efflux pump and the MexXY regulator ArmZ. The fusA1 mutation also modulated ΔlasR mutant resistance to two other antibiotics, ciprofloxacin and ceftazidime. Our results identify a gene mutation that can reverse the direction of the antibiotic selection of lasR mutants, a phenomenon known as sign epistasis, and provide a possible explanation for the emergence of lasR-null mutants in clinical isolates. IMPORTANCE One of the most common mutations in Pseudomonas aeruginosa clinical isolates is in the quorum sensing lasR gene. In laboratory strains, lasR disruption decreases resistance to the clinical antibiotic tobramycin. To understand how lasR mutations emerge in tobramycin-treated patients, we mutated lasR in highly tobramycin-resistant laboratory strains and determined the effects on resistance. Disrupting lasR enhanced the resistance of some strains. These strains had a single amino acid substitution in the translation factor EF-G1A. The EF-G1A mutation reversed the selective effects of tobramycin on lasR mutants. These results illustrate how adaptive mutations can lead to the emergence of new traits in a population and are relevant to understanding how genetic diversity contributes to the progression of disease during chronic infections.
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Affiliation(s)
| | - Kade A. Townsend
- Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas, USA
| | - Brielle M. Mckee
- Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas, USA
| | - Kathryn Woods
- Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas, USA
| | - Pratik Koirala
- Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas, USA
| | - Alexandra J. Holder
- Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas, USA
| | - Vaughn D. Craddock
- Department of Molecular Biosciences, University of Kansas, Lawrence, Kansas, USA
| | - Matthew Cabeen
- Department of Microbiology and Molecular Genetics, Oklahoma State University, Stillwater, Oklahoma, USA
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Berryhill BA, Gil-Gil T, Manuel JA, Smith AP, Margollis E, Baquero F, Levin BR. What's the Matter with MICs: Bacterial Nutrition, Limiting Resources, and Antibiotic Pharmacodynamics. Microbiol Spectr 2023; 11:e0409122. [PMID: 37130356 PMCID: PMC10269441 DOI: 10.1128/spectrum.04091-22] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 03/21/2023] [Indexed: 05/04/2023] Open
Abstract
The MIC of an antibiotic required to prevent replication is used both as a measure of the susceptibility/resistance of bacteria to that drug and as the single pharmacodynamic parameter for the rational design of antibiotic treatment regimes. MICs are experimentally estimated in vitro under conditions optimal for the action of the antibiotic. However, bacteria rarely grow in these optimal conditions. Using a mathematical model of the pharmacodynamics of antibiotics, we make predictions about the nutrient dependency of bacterial growth in the presence of antibiotics. We test these predictions with experiments in broth and a glucose-limited minimal media with Escherichia coli and eight different antibiotics. Our experiments question the sufficiency of using MICs and simple pharmacodynamic functions as measures of the pharmacodynamics of antibiotics under the nutritional conditions of infected tissues. To an extent that varies among drugs: (i) the estimated MICs obtained in rich media are greater than those estimated in minimal media; (ii) exposure to these drugs increases the time before logarithmic growth starts, their lag; and (iii) the stationary-phase density of E. coli populations declines with greater sub-MIC antibiotic concentrations. We postulate a mechanism to account for the relationship between sub-MICs of antibiotics and these growth parameters. This study is limited to a single bacterial strain and two types of culture media with different nutritive content. These limitations aside, the results of our study clearly question the use of MIC as the unique pharmacodynamic parameter to develop therapeutically oriented protocols. IMPORTANCE For studies of antibiotics and how they work, the most-often used measurement of drug efficacy is the MIC. The MIC is the concentration of an antibiotic needed to inhibit bacterial growth. This parameter is critical to the design and implementation of antibiotic therapy. We provide evidence that the use of MIC as the sole measurement for antibiotic efficacy ignores important aspects of bacterial growth dynamics. Before now, there has not been a nexus between bacteria, the conditions in which they grow, and the MIC. Most importantly, few studies have considered sub-MICs of antibiotics, despite their clinical importance. Here, we explore these concentrations in-depth, and we demonstrate MIC to be an incomplete measure of how an infection will interact with a specific antibiotic. Understanding the critiques of MIC is the first of many steps needed to improve infectious disease treatment.
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Affiliation(s)
- Brandon A. Berryhill
- Department of Biology, Emory University, Atlanta, Georgia, USA
- Program in Microbiology and Molecular Genetics, Graduate Division of Biological and Biomedical Sciences, Laney Graduate School, Emory University, Atlanta, Georgia, USA
| | - Teresa Gil-Gil
- Department of Biology, Emory University, Atlanta, Georgia, USA
- Centro Nacional de Biotecnología, Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain
- Programa de Doctorado en Biociencias Moleculares, Universidad Autónoma de Madrid, Madrid, Spain
| | | | - Andrew P. Smith
- Department of Biology, Emory University, Atlanta, Georgia, USA
| | - Ellie Margollis
- Department of Infectious Diseases, St. Jude Children's Research Hospital, Memphis, Tennessee, USA
| | - Fernando Baquero
- Hospital Universitario Ramón y Cajal, Instituto Ramón y Cajal de Investigación Sanitaria, and Centro de Investigación Médica en Red, Epidemiología y Salud Pública (CIBERESP), Madrid, Spain
| | - Bruce R. Levin
- Department of Biology, Emory University, Atlanta, Georgia, USA
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Blatti C, de la Fuente J, Gao H, Marín-Goñi I, Chen Z, Zhao SD, Tan W, Weinshilboum R, Kalari KR, Wang L, Hernaez M. Bayesian Machine Learning Enables Identification of Transcriptional Network Disruptions Associated with Drug-Resistant Prostate Cancer. Cancer Res 2023; 83:1361-1380. [PMID: 36779846 PMCID: PMC10102853 DOI: 10.1158/0008-5472.can-22-1910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Revised: 07/29/2022] [Accepted: 02/08/2023] [Indexed: 02/14/2023]
Abstract
Survival rates of patients with metastatic castration-resistant prostate cancer (mCRPC) are low due to lack of response or acquired resistance to available therapies, such as abiraterone (Abi). A better understanding of the underlying molecular mechanisms is needed to identify effective targets to overcome resistance. Given the complexity of the transcriptional dynamics in cells, differential gene expression analysis of bulk transcriptomics data cannot provide sufficient detailed insights into resistance mechanisms. Incorporating network structures could overcome this limitation to provide a global and functional perspective of Abi resistance in mCRPC. Here, we developed TraRe, a computational method using sparse Bayesian models to examine phenotypically driven transcriptional mechanistic differences at three distinct levels: transcriptional networks, specific regulons, and individual transcription factors (TF). TraRe was applied to transcriptomic data from 46 patients with mCRPC with Abi-response clinical data and uncovered abrogated immune response transcriptional modules that showed strong differential regulation in Abi-responsive compared with Abi-resistant patients. These modules were replicated in an independent mCRPC study. Furthermore, key rewiring predictions and their associated TFs were experimentally validated in two prostate cancer cell lines with different Abi-resistance features. Among them, ELK3, MXD1, and MYB played a differential role in cell survival in Abi-sensitive and Abi-resistant cells. Moreover, ELK3 regulated cell migration capacity, which could have a direct impact on mCRPC. Collectively, these findings shed light on the underlying transcriptional mechanisms driving Abi response, demonstrating that TraRe is a promising tool for generating novel hypotheses based on identified transcriptional network disruptions. SIGNIFICANCE The computational method TraRe built on Bayesian machine learning models for investigating transcriptional network structures shows that disruption of ELK3, MXD1, and MYB signaling cascades impacts abiraterone resistance in prostate cancer.
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Affiliation(s)
- Charles Blatti
- NCSA, University of Illinois at Urbana-Champaign, Champaign, Illinois
| | | | - Huanyao Gao
- Department of Molecular Pharmacology and Experimental Therapeutics, Mayo Clinic, Rochester, Minnesota
| | - Irene Marín-Goñi
- Computational Biology Program, CIMA University of Navarra, Navarra, Spain
| | - Zikun Chen
- Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, Illinois
| | - Sihai D. Zhao
- Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, Illinois
- Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Champaign, Illinois
| | - Winston Tan
- Department of Internal Medicine, Mayo Clinic, Rochester, Minnesota
| | - Richard Weinshilboum
- Department of Molecular Pharmacology and Experimental Therapeutics, Mayo Clinic, Rochester, Minnesota
| | - Krishna R. Kalari
- Department of Quantitative Health Sciences, Mayo Clinic, Rochester, Minnesota
| | - Liewei Wang
- Department of Molecular Pharmacology and Experimental Therapeutics, Mayo Clinic, Rochester, Minnesota
| | - Mikel Hernaez
- Computational Biology Program, CIMA University of Navarra, Navarra, Spain
- Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Champaign, Illinois
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Oro D, Alsedà L, Hastings A, Genovart M, Sardanyés J. Social copying drives a tipping point for nonlinear population collapse. Proc Natl Acad Sci U S A 2023; 120:e2214055120. [PMID: 36877850 PMCID: PMC10089190 DOI: 10.1073/pnas.2214055120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2022] [Accepted: 01/21/2023] [Indexed: 03/08/2023] Open
Abstract
Sudden changes in populations are ubiquitous in ecological systems, especially under perturbations. The agents of global change may increase the frequency and severity of anthropogenic perturbations, but complex populations' responses hamper our understanding of their dynamics and resilience. Furthermore, the long-term environmental and demographic data required to study those sudden changes are rare. Fitting dynamical models with an artificial intelligence algorithm to population fluctuations over 40 y in a social bird reveals that feedback in dispersal after a cumulative perturbation drives a population collapse. The collapse is well described by a nonlinear function mimicking social copying, whereby dispersal made by a few individuals induces others to leave the patch in a behavioral cascade for decision-making to disperse. Once a threshold for deterioration of the quality of the patch is crossed, there is a tipping point for a social response of runaway dispersal corresponding to social copying feedback. Finally, dispersal decreases at low population densities, which is likely due to the unwillingness of the more philopatric individuals to disperse. In providing the evidence of copying for the emergence of feedback in dispersal in a social organism, our results suggest a broader impact of self-organized collective dispersal in complex population dynamics. This has implications for the theoretical study of population and metapopulation nonlinear dynamics, including population extinction, and managing of endangered and harvested populations of social animals subjected to behavioral feedback loops.
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Affiliation(s)
- Daniel Oro
- Theoretical and Computational Ecology Laboratory, Centre d’Estudis Avançats de Blanes, Consejo Superior de Investigaciones Científicas,17300Girona, Spain
- Department of Environmental Science and Policy, University of California, Davis, CA95616
| | - Lluís Alsedà
- Departament de Matemàtiques, Universitat Autònoma de Barcelona,08193Bellaterra, Spain
- Centre de Recerca Matemàtica,08193Bellaterra, Spain
| | - Alan Hastings
- Department of Environmental Science and Policy, University of California, Davis, CA95616
- Santa Fe Institute, Santa Fe, NM87501
| | - Meritxell Genovart
- Theoretical and Computational Ecology Laboratory, Centre d’Estudis Avançats de Blanes, Consejo Superior de Investigaciones Científicas,17300Girona, Spain
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