PeerJ:Mathematical Biologyhttps://peerj.com/articles/index.atom?journal=peerj&subject=1900Mathematical Biology articles published in PeerJThe spindle assembly checkpoint and speciationhttps://peerj.com/articles/90732020-05-112020-05-11Robert C. JacksonHitesh B. Mistry
A mechanism is proposed by which speciation may occur without the need to postulate geographical isolation of the diverging populations. Closely related species that occupy overlapping or adjacent ecological niches often have an almost identical genome but differ by chromosomal rearrangements that result in reproductive isolation. The mitotic spindle assembly checkpoint normally functions to prevent gametes with non-identical karyotypes from forming viable zygotes. Unless gametes from two individuals happen to undergo the same chromosomal rearrangement at the same place and time, a most improbable situation, there has been no satisfactory explanation of how such rearrangements can propagate. Consideration of the dynamics of the spindle assembly checkpoint suggest that chromosomal fission or fusion events may occur that allow formation of viable heterozygotes between the rearranged and parental karyotypes, albeit with decreased fertility. Evolutionary dynamics calculations suggest that if the resulting heterozygous organisms have a selective advantage in an adjoining or overlapping ecological niche from that of the parental strain, despite the reproductive disadvantage of the population carrying the altered karyotype, it may accumulate sufficiently that homozygotes begin to emerge. At this point the reproductive disadvantage of the rearranged karyotype disappears, and a single population has been replaced by two populations that are partially reproductively isolated. This definition of species as populations that differ from other, closely related, species by karyotypic changes is consistent with the classical definition of a species as a population that is capable of interbreeding to produce fertile progeny. Even modest degrees of reproductive impairment of heterozygotes between two related populations may lead to speciation by this mechanism, and geographical isolation is not necessary for the process.
A mechanism is proposed by which speciation may occur without the need to postulate geographical isolation of the diverging populations. Closely related species that occupy overlapping or adjacent ecological niches often have an almost identical genome but differ by chromosomal rearrangements that result in reproductive isolation. The mitotic spindle assembly checkpoint normally functions to prevent gametes with non-identical karyotypes from forming viable zygotes. Unless gametes from two individuals happen to undergo the same chromosomal rearrangement at the same place and time, a most improbable situation, there has been no satisfactory explanation of how such rearrangements can propagate. Consideration of the dynamics of the spindle assembly checkpoint suggest that chromosomal fission or fusion events may occur that allow formation of viable heterozygotes between the rearranged and parental karyotypes, albeit with decreased fertility. Evolutionary dynamics calculations suggest that if the resulting heterozygous organisms have a selective advantage in an adjoining or overlapping ecological niche from that of the parental strain, despite the reproductive disadvantage of the population carrying the altered karyotype, it may accumulate sufficiently that homozygotes begin to emerge. At this point the reproductive disadvantage of the rearranged karyotype disappears, and a single population has been replaced by two populations that are partially reproductively isolated. This definition of species as populations that differ from other, closely related, species by karyotypic changes is consistent with the classical definition of a species as a population that is capable of interbreeding to produce fertile progeny. Even modest degrees of reproductive impairment of heterozygotes between two related populations may lead to speciation by this mechanism, and geographical isolation is not necessary for the process.Size matters: micro-evolution in Polynesian rats highlights body size changes as initial stage in evolutionhttps://peerj.com/articles/90762020-04-282020-04-28Alexandra A.E. van der Geer
Microevolutionary patterns in populations of introduced rodent species have often been the focus of analytic studies for their potential relevance to understanding vertebrate evolution. The Polynesian rat (Rattus exulans) is an excellent proxy species because of its wide geographic and temporal distribution: its native and introduced combined range spans half the globe and it has been living for at least seven centuries wherever it was introduced. The objective of this study was to assess the effects of long-term isolation (insularity; up to 4,000 years) and geographic variables on skull shape variation using geometric morphometrics. A sample of 513 specimens from 103 islands and four mainland areas was analysed. This study, to my knowledge the first to extensively sample introduced rats, analysed 59 two-dimensional landmarks on the skull. Landmarks were obtained in three separate aspects (dorsal, lateral, ventral skull view). The coordinate data were then subjected to a multivariate ordination analysis (principal components analysis, or PCA), multivariate regressions, and a canonical variates analysis (CVA). Three measures of disparity were evaluated for each view. The results show that introduced Polynesian rats evolve skull shapes that conform to the general mammalian interspecific pattern of cranial evolutionary allometry (CREA), with proportionally longer snouts in larger specimens. In addition, larger skulls are more tubular in shape than the smaller skulls, which are more balloon-shaped with a rounder and wider braincase relative to those of large skulls. This difference is also observed between the sexes (sexual dimorphism), due to the slightly larger average male size. Large, tubular skulls with long snouts are typical for Polynesia and Remote Oceania, where no native mammals occur. The greater disparity of Polynesian rats on mammal species-poor islands (’exulans-only’ region) provides further insight into how diversity may affect diversification through ecological release from predators and competitors.
Microevolutionary patterns in populations of introduced rodent species have often been the focus of analytic studies for their potential relevance to understanding vertebrate evolution. The Polynesian rat (Rattus exulans) is an excellent proxy species because of its wide geographic and temporal distribution: its native and introduced combined range spans half the globe and it has been living for at least seven centuries wherever it was introduced. The objective of this study was to assess the effects of long-term isolation (insularity; up to 4,000 years) and geographic variables on skull shape variation using geometric morphometrics. A sample of 513 specimens from 103 islands and four mainland areas was analysed. This study, to my knowledge the first to extensively sample introduced rats, analysed 59 two-dimensional landmarks on the skull. Landmarks were obtained in three separate aspects (dorsal, lateral, ventral skull view). The coordinate data were then subjected to a multivariate ordination analysis (principal components analysis, or PCA), multivariate regressions, and a canonical variates analysis (CVA). Three measures of disparity were evaluated for each view. The results show that introduced Polynesian rats evolve skull shapes that conform to the general mammalian interspecific pattern of cranial evolutionary allometry (CREA), with proportionally longer snouts in larger specimens. In addition, larger skulls are more tubular in shape than the smaller skulls, which are more balloon-shaped with a rounder and wider braincase relative to those of large skulls. This difference is also observed between the sexes (sexual dimorphism), due to the slightly larger average male size. Large, tubular skulls with long snouts are typical for Polynesia and Remote Oceania, where no native mammals occur. The greater disparity of Polynesian rats on mammal species-poor islands (’exulans-only’ region) provides further insight into how diversity may affect diversification through ecological release from predators and competitors.Understanding the spread of de novo and transmitted macrolide-resistance in Mycoplasma genitaliumhttps://peerj.com/articles/89132020-04-072020-04-07Dominique CadoschVictor GarciaJørgen S. JensenNicola LowChristian L. Althaus
Background
The rapid spread of azithromycin resistance in sexually transmitted Mycoplasma genitalium infections is a growing concern. It is not yet clear to what degree macrolide resistance in M. genitalium results from the emergence of de novo mutations or the transmission of resistant strains.
Methods
We developed a compartmental transmission model to investigate the contribution of de novo macrolide resistance mutations to the spread of antimicrobial-resistant M. genitalium. We fitted the model to resistance data from France, Denmark and Sweden, estimated the time point of azithromycin introduction and the rates at which infected individuals receive treatment, and projected the future spread of resistance.
Results
The high probability of de novo resistance in M. genitalium accelerates the early spread of antimicrobial resistance. The relative contribution of de novo resistance subsequently decreases, and the spread of resistant infections in France, Denmark and Sweden is now mainly driven by transmitted resistance. If treatment with single-dose azithromycin continues at current rates, macrolide-resistant M. genitalium infections will reach 25% (95% confidence interval, CI [9–30]%) in France, 84% (95% CI [36–98]%) in Denmark and 62% (95% CI [48–76]%) in Sweden by 2025.
Conclusions
Blind treatment of urethritis with single-dose azithromycin continues to select for the spread of macrolide resistant M. genitalium. Clinical management strategies for M. genitalium should limit the unnecessary use of macrolides.
Background
The rapid spread of azithromycin resistance in sexually transmitted Mycoplasma genitalium infections is a growing concern. It is not yet clear to what degree macrolide resistance in M. genitalium results from the emergence of de novo mutations or the transmission of resistant strains.
Methods
We developed a compartmental transmission model to investigate the contribution of de novo macrolide resistance mutations to the spread of antimicrobial-resistant M. genitalium. We fitted the model to resistance data from France, Denmark and Sweden, estimated the time point of azithromycin introduction and the rates at which infected individuals receive treatment, and projected the future spread of resistance.
Results
The high probability of de novo resistance in M. genitalium accelerates the early spread of antimicrobial resistance. The relative contribution of de novo resistance subsequently decreases, and the spread of resistant infections in France, Denmark and Sweden is now mainly driven by transmitted resistance. If treatment with single-dose azithromycin continues at current rates, macrolide-resistant M. genitalium infections will reach 25% (95% confidence interval, CI [9–30]%) in France, 84% (95% CI [36–98]%) in Denmark and 62% (95% CI [48–76]%) in Sweden by 2025.
Conclusions
Blind treatment of urethritis with single-dose azithromycin continues to select for the spread of macrolide resistant M. genitalium. Clinical management strategies for M. genitalium should limit the unnecessary use of macrolides.Modelling the effective reproduction number of vector-borne diseases: the yellow fever outbreak in Luanda, Angola 2015–2016 as an examplehttps://peerj.com/articles/86012020-02-272020-02-27Shi ZhaoSalihu S. MusaJay T. HebertPeihua CaoJinjun RanJiayi MengDaihai HeJing Qin
The burden of vector-borne diseases (Dengue, Zika virus, yellow fever, etc.) gradually increased in the past decade across the globe. Mathematical modelling on infectious diseases helps to study the transmission dynamics of the pathogens. Theoretically, the diseases can be controlled and eventually eradicated by maintaining the effective reproduction number, (
${\mathcal{R}}_{\mathrm{eff}}$
R
eff
), strictly less than 1. We established a vector-host compartmental model, and derived (
${\mathcal{R}}_{\mathrm{eff}}$
R
eff
) for vector-borne diseases. The analytic form of the (
${\mathcal{R}}_{\mathrm{eff}}$
R
eff
) was found to be the product of the basic reproduction number and the geometric average of the susceptibilities of the host and vector populations. The (
${\mathcal{R}}_{\mathrm{eff}}$
R
eff
) formula was demonstrated to be consistent with the estimates of the 2015–2016 yellow fever outbreak in Luanda, and distinguished the second minor epidemic wave. For those using the compartmental model to study the vector-borne infectious disease epidemics, we further remark that it is important to be aware of whether one or two generations is considered for the transition “from host to vector to host” in reproduction number calculation.
The burden of vector-borne diseases (Dengue, Zika virus, yellow fever, etc.) gradually increased in the past decade across the globe. Mathematical modelling on infectious diseases helps to study the transmission dynamics of the pathogens. Theoretically, the diseases can be controlled and eventually eradicated by maintaining the effective reproduction number, (
${\mathcal{R}}_{\mathrm{eff}}$
R
eff
), strictly less than 1. We established a vector-host compartmental model, and derived (
${\mathcal{R}}_{\mathrm{eff}}$
R
eff
) for vector-borne diseases. The analytic form of the (
${\mathcal{R}}_{\mathrm{eff}}$
R
eff
) was found to be the product of the basic reproduction number and the geometric average of the susceptibilities of the host and vector populations. The (
${\mathcal{R}}_{\mathrm{eff}}$
R
eff
) formula was demonstrated to be consistent with the estimates of the 2015–2016 yellow fever outbreak in Luanda, and distinguished the second minor epidemic wave. For those using the compartmental model to study the vector-borne infectious disease epidemics, we further remark that it is important to be aware of whether one or two generations is considered for the transition “from host to vector to host” in reproduction number calculation.Fasciola gigantica, F. hepatica and Fasciola intermediate forms: geometric morphometrics and an artificial neural network to help morphological identificationhttps://peerj.com/articles/85972020-02-182020-02-18Suchada SumruaypholPraphaiphat SiribatJean-Pierre DujardinSébastien DujardinChalit KomalamisraUrusa Thaenkham
Background
Fasciola hepatica and F. gigantica cause fascioliasis in both humans and livestock. Some adult specimens of Fasciola sp. referred to as “intermediate forms” based on their genetic traits, are also frequently reported. Simple morphological criteria are unreliable for their specific identification. In previous studies, promising phenotypic identification scores were obtained using morphometrics based on linear measurements (distances, angles, curves) between anatomical features. Such an approach is commonly termed “traditional” morphometrics, as opposed to “modern” morphometrics, which is based on the coordinates of anatomical points.
Methods
Here, we explored the possible improvements that modern methods of morphometrics, including landmark-based and outline-based approaches, could bring to solving the problem of the non-molecular identification of these parasites. F. gigantica and Fasciola intermediate forms suitable for morphometric characterization were selected from Thai strains following their molecular identification. Specimens of F. hepatica were obtained from the Liverpool School of Tropical Medicine (UK). Using these three taxa, we tested the taxonomic signal embedded in traditional linear measurements versus the coordinates of anatomical points (landmark- and outline-based approaches). Various statistical techniques of validated reclassification were used, based on either the shortest Mahalanobis distance, the maximum likelihood, or the artificial neural network method.
Results
Our results revealed that both traditional and modern morphometric approaches can help in the morphological identification of Fasciola sp. We showed that the accuracy of the traditional approach could be improved by selecting a subset of characters among the most contributive ones. The influence of size on discrimination by shape was much more important in traditional than in modern analyses. In our study, the modern approach provided different results according to the type of data: satisfactory when using pseudolandmarks (outlines), less satisfactory when using landmarks. The different reclassification methods provided approximately similar scores, with a special mention to the neural network, which allowed improvements in accuracy by combining data from both morphometric approaches.
Conclusion
We conclude that morphometrics, whether traditional or modern, represent a valuable tool to assist in Fasciola species recognition. The general level of accuracy is comparable among the various methods, but their demands on skills and time differ. Based on the outline method, our study could provide the first description of the shape differences between species, highlighting the more globular contours of the intermediate forms.
Background
Fasciola hepatica and F. gigantica cause fascioliasis in both humans and livestock. Some adult specimens of Fasciola sp. referred to as “intermediate forms” based on their genetic traits, are also frequently reported. Simple morphological criteria are unreliable for their specific identification. In previous studies, promising phenotypic identification scores were obtained using morphometrics based on linear measurements (distances, angles, curves) between anatomical features. Such an approach is commonly termed “traditional” morphometrics, as opposed to “modern” morphometrics, which is based on the coordinates of anatomical points.
Methods
Here, we explored the possible improvements that modern methods of morphometrics, including landmark-based and outline-based approaches, could bring to solving the problem of the non-molecular identification of these parasites. F. gigantica and Fasciola intermediate forms suitable for morphometric characterization were selected from Thai strains following their molecular identification. Specimens of F. hepatica were obtained from the Liverpool School of Tropical Medicine (UK). Using these three taxa, we tested the taxonomic signal embedded in traditional linear measurements versus the coordinates of anatomical points (landmark- and outline-based approaches). Various statistical techniques of validated reclassification were used, based on either the shortest Mahalanobis distance, the maximum likelihood, or the artificial neural network method.
Results
Our results revealed that both traditional and modern morphometric approaches can help in the morphological identification of Fasciola sp. We showed that the accuracy of the traditional approach could be improved by selecting a subset of characters among the most contributive ones. The influence of size on discrimination by shape was much more important in traditional than in modern analyses. In our study, the modern approach provided different results according to the type of data: satisfactory when using pseudolandmarks (outlines), less satisfactory when using landmarks. The different reclassification methods provided approximately similar scores, with a special mention to the neural network, which allowed improvements in accuracy by combining data from both morphometric approaches.
Conclusion
We conclude that morphometrics, whether traditional or modern, represent a valuable tool to assist in Fasciola species recognition. The general level of accuracy is comparable among the various methods, but their demands on skills and time differ. Based on the outline method, our study could provide the first description of the shape differences between species, highlighting the more globular contours of the intermediate forms.Ecosystem antifragility: beyond integrity and resiliencehttps://peerj.com/articles/85332020-02-112020-02-11Miguel EquihuaMariana Espinosa AldamaCarlos GershensonOliver López-CoronaMariana MunguíaOctavio Pérez-MaqueoElvia Ramírez-Carrillo
We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.
We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.Gini coefficients for measuring the distribution of sexually transmitted infections among individuals with different levels of sexual activityhttps://peerj.com/articles/84342020-01-202020-01-20Sandro GsteigerNicola LowPam SonnenbergCatherine H. MercerChristian L. Althaus
Objectives
Gini coefficients have been used to describe the distribution of Chlamydia trachomatis (CT) infections among individuals with different levels of sexual activity. The objectives of this study were to investigate Gini coefficients for different sexually transmitted infections (STIs), and to determine how STI control interventions might affect the Gini coefficient over time.
Methods
We used population-based data for sexually experienced women from two British National Surveys of Sexual Attitudes and Lifestyles (Natsal-2: 1999–2001; Natsal-3: 2010–2012) to calculate Gini coefficients for CT, Mycoplasma genitalium (MG), and human papillomavirus (HPV) types 6, 11, 16 and 18. We applied bootstrap methods to assess uncertainty and to compare Gini coefficients for different STIs. We then used a mathematical model of STI transmission to study how control interventions affect Gini coefficients.
Results
Gini coefficients for CT and MG were 0.33 (95% CI [0.18–0.49]) and 0.16 (95% CI [0.02–0.36]), respectively. The relatively small coefficient for MG suggests a longer infectious duration compared with CT. The coefficients for HPV types 6, 11, 16 and 18 ranged from 0.15 to 0.38. During the decade between Natsal-2 and Natsal-3, the Gini coefficient for CT did not change. The transmission model shows that higher STI treatment rates are expected to reduce prevalence and increase the Gini coefficient of STIs. In contrast, increased condom use reduces STI prevalence but does not affect the Gini coefficient.
Conclusions
Gini coefficients for STIs can help us to understand the distribution of STIs in the population, according to level of sexual activity, and could be used to inform STI prevention and treatment strategies.
Objectives
Gini coefficients have been used to describe the distribution of Chlamydia trachomatis (CT) infections among individuals with different levels of sexual activity. The objectives of this study were to investigate Gini coefficients for different sexually transmitted infections (STIs), and to determine how STI control interventions might affect the Gini coefficient over time.
Methods
We used population-based data for sexually experienced women from two British National Surveys of Sexual Attitudes and Lifestyles (Natsal-2: 1999–2001; Natsal-3: 2010–2012) to calculate Gini coefficients for CT, Mycoplasma genitalium (MG), and human papillomavirus (HPV) types 6, 11, 16 and 18. We applied bootstrap methods to assess uncertainty and to compare Gini coefficients for different STIs. We then used a mathematical model of STI transmission to study how control interventions affect Gini coefficients.
Results
Gini coefficients for CT and MG were 0.33 (95% CI [0.18–0.49]) and 0.16 (95% CI [0.02–0.36]), respectively. The relatively small coefficient for MG suggests a longer infectious duration compared with CT. The coefficients for HPV types 6, 11, 16 and 18 ranged from 0.15 to 0.38. During the decade between Natsal-2 and Natsal-3, the Gini coefficient for CT did not change. The transmission model shows that higher STI treatment rates are expected to reduce prevalence and increase the Gini coefficient of STIs. In contrast, increased condom use reduces STI prevalence but does not affect the Gini coefficient.
Conclusions
Gini coefficients for STIs can help us to understand the distribution of STIs in the population, according to level of sexual activity, and could be used to inform STI prevention and treatment strategies.Assessment of a Takagi–Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometryhttps://peerj.com/articles/81732020-01-062020-01-06Hector A. Echavarria-HerasJuan R. Castro-RodriguezCecilia Leal-RamirezEnrique Villa-Diharce
Background
The traditional allometric analysis relies on log- transformation to contemplate linear regression in geometrical space then retransforming to get Huxley’s model of simple allometry. Views assert this induces bias endorsing multi-parameter complex allometry forms and nonlinear regression in arithmetical scales. Defenders of traditional approach deem it necessary since generally organismal growth is essentially multiplicative. Then keeping allometry as originally envisioned by Huxley requires a paradigm of polyphasic loglinear allometry. A Takagi-Sugeno-Kang fuzzy model assembles a mixture of weighted sub models. This allows direct identification of break points for transition between phases. Then, this paradigm is seamlessly appropriate for efficient allometric examination of polyphasic loglinear allometry patterns. Here, we explore its suitability.
Methods
Present fuzzy model embraces firing strength weights from Gaussian membership functions and linear consequents. Weights are identified by subtractive clustering and consequents through recursive least squares or maximum likelihood. Intersection of firing strength factors set criterion to estimate breakpoints. A multi-parameter complex allometry model follows by adapting firing strengths by composite membership functions and linear consequents in arithmetical space.
Results
Takagi-Sugeno-Kang surrogates adapted complexity depending on analyzed data set. Retransformation results conveyed reproducibility strength of similar proxies identified in arithmetical space. Breakpoints were straightforwardly identified. Retransformed form implies complex allometry as a generalization of Huxley’s power model involving covariate depending parameters. Huxley reported a breakpoint in the log–log plot of chela mass vs. body mass of fiddler crabs (Uca pugnax), attributed to a sudden change in relative growth of the chela approximately when crabs reach sexual maturity. G.C. Packard implied this breakpoint as putative. However, according to present fuzzy methods existence of a break point in Huxley’s data could be validated.
Conclusions
Offered scheme bears reliable analysis of zero intercept allometries based on geometrical space protocols. Endorsed affine structure accommodates either polyphasic or simple allometry if whatever turns required. Interpretation of break points characterizing heterogeneity is intuitive. Analysis can be achieved in an interactive way. This could not have been obtained by relying on customary approaches. Besides, identification of break points in arithmetical scale is straightforward. Present Takagi-Sugeno-Kang arrangement offers a way to overcome the controversy between a school considering a log-transformation necessary and their critics claiming that consistent results can be only obtained through complex allometry models fitted by direct nonlinear regression in the original scales.
Background
The traditional allometric analysis relies on log- transformation to contemplate linear regression in geometrical space then retransforming to get Huxley’s model of simple allometry. Views assert this induces bias endorsing multi-parameter complex allometry forms and nonlinear regression in arithmetical scales. Defenders of traditional approach deem it necessary since generally organismal growth is essentially multiplicative. Then keeping allometry as originally envisioned by Huxley requires a paradigm of polyphasic loglinear allometry. A Takagi-Sugeno-Kang fuzzy model assembles a mixture of weighted sub models. This allows direct identification of break points for transition between phases. Then, this paradigm is seamlessly appropriate for efficient allometric examination of polyphasic loglinear allometry patterns. Here, we explore its suitability.
Methods
Present fuzzy model embraces firing strength weights from Gaussian membership functions and linear consequents. Weights are identified by subtractive clustering and consequents through recursive least squares or maximum likelihood. Intersection of firing strength factors set criterion to estimate breakpoints. A multi-parameter complex allometry model follows by adapting firing strengths by composite membership functions and linear consequents in arithmetical space.
Results
Takagi-Sugeno-Kang surrogates adapted complexity depending on analyzed data set. Retransformation results conveyed reproducibility strength of similar proxies identified in arithmetical space. Breakpoints were straightforwardly identified. Retransformed form implies complex allometry as a generalization of Huxley’s power model involving covariate depending parameters. Huxley reported a breakpoint in the log–log plot of chela mass vs. body mass of fiddler crabs (Uca pugnax), attributed to a sudden change in relative growth of the chela approximately when crabs reach sexual maturity. G.C. Packard implied this breakpoint as putative. However, according to present fuzzy methods existence of a break point in Huxley’s data could be validated.
Conclusions
Offered scheme bears reliable analysis of zero intercept allometries based on geometrical space protocols. Endorsed affine structure accommodates either polyphasic or simple allometry if whatever turns required. Interpretation of break points characterizing heterogeneity is intuitive. Analysis can be achieved in an interactive way. This could not have been obtained by relying on customary approaches. Besides, identification of break points in arithmetical scale is straightforward. Present Takagi-Sugeno-Kang arrangement offers a way to overcome the controversy between a school considering a log-transformation necessary and their critics claiming that consistent results can be only obtained through complex allometry models fitted by direct nonlinear regression in the original scales.Another look at the eigenvalues of a population matrix modelhttps://peerj.com/articles/80182019-11-112019-11-11Brenda HanleyPatrick ConnellyBrian Dennis
Population matrix models are important tools in resource management, in part because they are used to calculate the finite rate of growth (“dominant eigenvalue”). But understanding how a population matrix model converts life history traits into the finite rate of growth can be tricky. We introduce interactive software (“IsoPOPd”) that uses the characteristic equation to display how vital rates (survival and fertility) contribute to the finite rate of growth. Higher-order interactions among vital rates complicate the linkage between a management intervention and a population’s growth rate. We illustrate the use of the software for investigating the consequences of three management interventions in a 3-stage model of white-tailed deer (Odocoileus virginianus). The software is applicable to any species with 2- or 3-stages, but the mathematical concepts underlying the software are applicable to a population matrix model of any size. The IsoPOPd software is available at: https://cwhl.vet.cornell.edu/tools/isopopd.
Population matrix models are important tools in resource management, in part because they are used to calculate the finite rate of growth (“dominant eigenvalue”). But understanding how a population matrix model converts life history traits into the finite rate of growth can be tricky. We introduce interactive software (“IsoPOPd”) that uses the characteristic equation to display how vital rates (survival and fertility) contribute to the finite rate of growth. Higher-order interactions among vital rates complicate the linkage between a management intervention and a population’s growth rate. We illustrate the use of the software for investigating the consequences of three management interventions in a 3-stage model of white-tailed deer (Odocoileus virginianus). The software is applicable to any species with 2- or 3-stages, but the mathematical concepts underlying the software are applicable to a population matrix model of any size. The IsoPOPd software is available at: https://cwhl.vet.cornell.edu/tools/isopopd.Enforced symmetry: the necessity of symmetric waxing and waninghttps://peerj.com/articles/80112019-11-062019-11-06Niklas HohmannEmilia Jarochowska
A fundamental question in ecology is how the success of a taxon changes through time and what drives this change. This question is commonly approached using trajectories averaged over a group of taxa. Using results from probability theory, we show analytically and using examples that averaged trajectories will be more symmetric as the number of averaged trajectories increases, even if none of the original trajectories they were derived from is symmetric. This effect is not only based on averaging, but also on the introduction of noise and the incorporation of a priori known origination and extinction times. This implies that averaged trajectories are not suitable for deriving information about the processes driving the success of taxa. In particular, symmetric waxing and waning, which is commonly observed and interpreted to be linked to a number of different paleobiological processes, does not allow drawing any conclusions about the nature of the underlying process.
A fundamental question in ecology is how the success of a taxon changes through time and what drives this change. This question is commonly approached using trajectories averaged over a group of taxa. Using results from probability theory, we show analytically and using examples that averaged trajectories will be more symmetric as the number of averaged trajectories increases, even if none of the original trajectories they were derived from is symmetric. This effect is not only based on averaging, but also on the introduction of noise and the incorporation of a priori known origination and extinction times. This implies that averaged trajectories are not suitable for deriving information about the processes driving the success of taxa. In particular, symmetric waxing and waning, which is commonly observed and interpreted to be linked to a number of different paleobiological processes, does not allow drawing any conclusions about the nature of the underlying process.