PeerJ Preprints: Mathematical Biologyhttps://peerj.com/preprints/index.atom?journal=peerj&subject=1900Mathematical Biology articles published in PeerJ PreprintsOptimizing pedigrees: Using a biasing system to determine likely inheritance systemshttps://peerj.com/preprints/28712017-04-092017-04-09Justin Ang
Pedigrees, though straightforward and versatile, lack the ability to tell us information about many individuals. Though numerical systems have been developed, there is currently no system to quantify the probability of a pedigree following certain inheritance systems. My system intends to fulfill that chasm by creating a flexible numerical system and testing it for variance. First, my system attempts to adapt inheritance system to known pedigree data. Then, it calculates the difference between the calculated values and the known pedigree data. It aggregates these values, then it uses a chi-squared analysis in order to determine the likelihood of said inheritance system. This is done for many different systems, until we have a general idea of which systems are probable and which are not.
Pedigrees, though straightforward and versatile, lack the ability to tell us information about many individuals. Though numerical systems have been developed, there is currently no system to quantify the probability of a pedigree following certain inheritance systems. My system intends to fulfill that chasm by creating a flexible numerical system and testing it for variance. First, my system attempts to adapt inheritance system to known pedigree data. Then, it calculates the difference between the calculated values and the known pedigree data. It aggregates these values, then it uses a chi-squared analysis in order to determine the likelihood of said inheritance system. This is done for many different systems, until we have a general idea of which systems are probable and which are not.Biodiversity collapse and early warning indicators in a spatial phase transition between neutral and niche communitieshttps://peerj.com/preprints/15892017-03-212017-03-21Leonardo A SaraviaFernando R Momo
The dynamics of ecological communities have been described by neutral and niche theories that are now increasingly integrated into unified models. It is known that a critical transition exists between these two states, but the spatial aspect of this transition has not been studied. Our aim is to study the spatial aspect of the transition and propose early warning signals to detect it. We used a stochastic, spatially explicit model that spans a continuum from neutral to niche communities, and is driven by the intensity of hierarchical competition. The transition is indicated by the emergence of a large patch formed by one species that connects the whole area. The properties of this patch can be used as early warning indicators of a critical transition. If competition intensity increases beyond the critical point, our model shows a sudden decrease of the Shannon diversity index and a gentle decline in species richness. The critical point occurs at a very low value of competitive intensity, with the rate of migration from the metacommunity greatly influencing the position of this critical point. As an example, we apply our new method of early warning indicators to the Barro Colorado Tropical forest, which, as expected, appears to be far from a critical transition. Low values of competitive intensity were also reported by previous studies for different high-diversity real communities, suggesting that these communities are located before the critical point. A small increase of competitive interactions could push them across the transition, however, to a state in which diversity is much lower. Thus this new early warnings indicator could be used to monitor high diversity ecosystems that are still undisturbed.
The dynamics of ecological communities have been described by neutral and niche theories that are now increasingly integrated into unified models. It is known that a critical transition exists between these two states, but the spatial aspect of this transition has not been studied. Our aim is to study the spatial aspect of the transition and propose early warning signals to detect it. We used a stochastic, spatially explicit model that spans a continuum from neutral to niche communities, and is driven by the intensity of hierarchical competition. The transition is indicated by the emergence of a large patch formed by one species that connects the whole area. The properties of this patch can be used as early warning indicators of a critical transition. If competition intensity increases beyond the critical point, our model shows a sudden decrease of the Shannon diversity index and a gentle decline in species richness. The critical point occurs at a very low value of competitive intensity, with the rate of migration from the metacommunity greatly influencing the position of this critical point. As an example, we apply our new method of early warning indicators to the Barro Colorado Tropical forest, which, as expected, appears to be far from a critical transition. Low values of competitive intensity were also reported by previous studies for different high-diversity real communities, suggesting that these communities are located before the critical point. A small increase of competitive interactions could push them across the transition, however, to a state in which diversity is much lower. Thus this new early warnings indicator could be used to monitor high diversity ecosystems that are still undisturbed.Jumping performance of Locusta migratoria and relationship between jumping performance and ground roughnesshttps://peerj.com/preprints/28772017-03-162017-03-16Xiaojuan MoWenjie GeDonato RomanoElisa DonatiCesare StefaniniPaolo Dario
Locusts are famous for its excellent jumping performance. Jumping helps locusts avoid predators and initiate flight. In this paper, high-speed videos are recorded to analyze the jumping performance of Locusta migratoria Linnaeus from ground with different roughness. By the established simplified theoretical model, we calculated L.migratoria normally can get 1.8318 m/s takeoff velocity and maximum acceleration about 66.72 m/s2 with takeoff angle at about 36°. Locusts are prone to slip when jumping from smooth surface especially for locusts with only one leg. The analyzed results show that locusts can increase their takeoff acceleration to get bigger takeoff velocity to adapt to different terrains, and takeoff velocity has no connection with takeoff angle while bigger takeoff angle have the possibility to help locusts to jump successfully with only one leg left or from smooth surface.
Locusts are famous for its excellent jumping performance. Jumping helps locusts avoid predators and initiate flight. In this paper, high-speed videos are recorded to analyze the jumping performance of Locusta migratoriaLinnaeus from ground with different roughness. By the established simplified theoretical model, we calculated L.migratoria normally can get 1.8318 m/s takeoff velocity and maximum acceleration about 66.72 m/s2 with takeoff angle at about 36°. Locusts are prone to slip when jumping from smooth surface especially for locusts with only one leg. The analyzed results show that locusts can increase their takeoff acceleration to get bigger takeoff velocity to adapt to different terrains, and takeoff velocity has no connection with takeoff angle while bigger takeoff angle have the possibility to help locusts to jump successfully with only one leg left or from smooth surface.Density estimates of monarch butterflies overwintering in central Mexicohttps://peerj.com/preprints/28322017-02-282017-02-28Wayne ThogmartinJay E DiffendorferLaura Lopez-HoffmanKaren OberhauserJohn PleasantsBrice Xavier SemmensDarius SemmensOrley R TaylorRuscena Wiederholt
Given the rapid population decline and recent petition for listing of the monarch butterfly (Danaus plexippus L.) under the Endangered Species Act, an accurate estimate of the Eastern, migratory population size is needed. Because of difficulty in counting individual monarchs, the number of hectares occupied by monarchs in the overwintering area is commonly used as a proxy for population size, which is then multiplied by the density of individuals per hectare to estimate population size. There is, however, considerable variation in published estimates of overwintering density, ranging from 6.9–60.9 million ha-1. We develop a probability distribution for overwinter density of monarch butterflies from six published density estimates. The mean density among the mixture of the six published estimates was ~27.9 million butterflies ha-1 (95% CI: 2.4–80.7 million ha-1); the mixture distribution is approximately log-normal, and as such is better represented by the median (21.1 million butterflies ha-1). Based upon assumptions regarding the number of milkweed needed to support monarchs, the amount of milkweed (Asclepias spp.) lost (0.86 billion stems) in the northern U.S. plus the amount of milkweed remaining (1.34 billion stems), we estimate >1.8 billion stems is needed to return monarchs to an average population size of 6 ha. Considerable uncertainty exists in this required amount of milkweed because of the considerable uncertainty occurring in overwinter density estimates. Nevertheless, the estimate is on the same order as other published estimates. The studies included in our synthesis differ substantially by year, location, method, and measures of precision. A better understanding of the factors influencing overwintering density across space and time would be valuable for increasing the precision of conservation recommendations.
Given the rapid population decline and recent petition for listing of the monarch butterfly (Danaus plexippus L.) under the Endangered Species Act, an accurate estimate of the Eastern, migratory population size is needed. Because of difficulty in counting individual monarchs, the number of hectares occupied by monarchs in the overwintering area is commonly used as a proxy for population size, which is then multiplied by the density of individuals per hectare to estimate population size. There is, however, considerable variation in published estimates of overwintering density, ranging from 6.9–60.9 million ha-1. We develop a probability distribution for overwinter density of monarch butterflies from six published density estimates. The mean density among the mixture of the six published estimates was ~27.9 million butterflies ha-1 (95% CI: 2.4–80.7 million ha-1); the mixture distribution is approximately log-normal, and as such is better represented by the median (21.1 million butterflies ha-1). Based upon assumptions regarding the number of milkweed needed to support monarchs, the amount of milkweed (Asclepias spp.) lost (0.86 billion stems) in the northern U.S. plus the amount of milkweed remaining (1.34 billion stems), we estimate >1.8 billion stems is needed to return monarchs to an average population size of 6 ha. Considerable uncertainty exists in this required amount of milkweed because of the considerable uncertainty occurring in overwinter density estimates. Nevertheless, the estimate is on the same order as other published estimates. The studies included in our synthesis differ substantially by year, location, method, and measures of precision. A better understanding of the factors influencing overwintering density across space and time would be valuable for increasing the precision of conservation recommendations.Linearization improves the repeatability of quantitative Dynamic Contrast-Enhanced MRIhttps://peerj.com/preprints/28242017-02-212017-02-21Kyle M. JonesMarisa H. BordersKimberly A. FitzpatrickMark D. PagelJulio Cárdenas-Rodríguez
We studied the effect of linearization on the repeatability of the Tofts and reference region models (RRM) for Dynamic Contrast-Enhanced MRI (DCE MRI). We compared the repeatabilities of these two linearized models, the standard non-linear version, and semi-quantitative methods of analysis. Simulated and experimental DCE MRI data from 12 rats with a flank tumor of C6 glioma acquired over three consecutive days were analyzed using four quantitative and semi-quantitative DCE MRI metrics. The quantitative methods used were: 1) Linear Tofts model (LTM), 2) Non-linear Tofts model (NTM), 3) Linear RRM (LRRM), and 4) Non-linear RRM (NRRM). The following semi-quantitative metrics were used: 1) Maximum enhancement ratio (MER), 2) time to peak (TTP), 3) initial area under the curve (iauc64), and 4) slope. LTM and NTM were used to estimate Ktrans, while LRRM and NRRM were used to estimate Ktrans relative to muscle (RKtrans). Repeatability was assessed by calculating the within-subject coefficient of variation (wSCV) and the percent intra-subject variation (iSV) determined with the Gage repeatability and reproducibility (R&R) analysis. The iSV for RKtrans using LRRM was two-fold lower compared to NRRM at all simulated and experimental conditions. A similar trend was observed for the Tofts model, where LTM was at least 50% more repeatable than the NTM under all experimental and simulated conditions. The semi-quantitative metrics iauc64 and MER were as equally reproducible as Ktrans and RKtrans estimated by LTM and LRRM respectively. The iSV for iauc64 and MER were significantly lower than the iSV for slope and TTP. In simulations and experimental results, linearization improves the repeatability of quantitative DCE MRI by at least 30%, making it as repeatable as semi-quantitative metrics.
Westudied the effect of linearization on the repeatability of the Tofts and reference region models (RRM) for Dynamic Contrast-Enhanced MRI (DCE MRI). We compared the repeatabilities of these two linearized models, the standard non-linear version, and semi-quantitative methods of analysis. Simulated and experimental DCE MRI data from 12 rats with a flank tumor of C6 glioma acquired over three consecutive days were analyzed using four quantitative and semi-quantitative DCE MRI metrics. The quantitative methods used were: 1) Linear Tofts model (LTM), 2) Non-linear Tofts model (NTM), 3) Linear RRM (LRRM), and 4) Non-linear RRM (NRRM). The following semi-quantitative metrics were used: 1) Maximum enhancement ratio (MER), 2) time to peak (TTP), 3) initial area under the curve (iauc64), and 4) slope. LTM and NTM were used to estimate Ktrans, while LRRM and NRRM were used to estimate Ktrans relative to muscle (RKtrans). Repeatability was assessed by calculating the within-subject coefficient of variation (wSCV) and the percent intra-subject variation (iSV) determined with the Gage repeatability and reproducibility (R&R) analysis. The iSV for RKtrans using LRRM was two-fold lower compared to NRRM at all simulated and experimental conditions. A similar trend was observed for the Tofts model, where LTM was at least 50% more repeatable than the NTM under all experimental and simulated conditions. The semi-quantitative metrics iauc64 and MER were as equally reproducible as Ktrans and RKtrans estimated by LTM and LRRM respectively. The iSV for iauc64 and MER were significantly lower than the iSV for slope and TTP. In simulations and experimental results, linearization improves the repeatability of quantitative DCE MRI by at least 30%, making it as repeatable as semi-quantitative metrics.Which method is more accurate? or errors have error barshttps://peerj.com/preprints/26932017-01-032017-01-03Jan H Jensen
This document is my attempt at distilling some of the information in two papers published by Anthony Nicholls (J. Comput. Aided Mol. Des. 2014, 28, 887; ibid 2016, 30, 103). Anthony also very kindly provided some new equations, not found in the papers, in response to my questions. The paper describes how one determines whether the difference in accuracy of two methods in predicting some properties for the same data set is statistically significant using root-mean-square errors, mean absolute errors, mean errors, and Pearsons r values.
This document is my attempt at distilling some of the information in two papers published by Anthony Nicholls (J. Comput. Aided Mol. Des. 2014, 28, 887; ibid 2016, 30, 103). Anthony also very kindly provided some new equations, not found in the papers, in response to my questions. The paper describes how one determines whether the difference in accuracy of two methods in predicting some properties for the same data set is statistically significant using root-mean-square errors, mean absolute errors, mean errors, and Pearsons r values.Phylogenetic factorization of compositional data yields lineage-level associations in microbiome datasetshttps://peerj.com/preprints/26852017-01-032017-01-03Alex D WashburneJustin D SilvermanJonathan W LeffDominic J BennettJohn L DarcySayan MukherjeeNoah FiererLawrence A David
Marker gene sequencing of microbial communities has generated big datasets of microbial relative abundances varying across environmental conditions, sample sites and treatments. These data often come with putative phylogenies, providing unique opportunities to investigate how shared evolutionary history affects microbial abundance patterns. Here, we present a method to identify the phylogenetic factors driving patterns in microbial community composition. We use the method, "phylofactorization", to re-analyze datasets from the human body and soil microbial communities, demonstrating how phylofactorization is a dimensionality-reducing tool, an ordination-visualization tool, and an inferential tool for identifying edges in the phylogeny along which putative functional ecological traits may have arisen.
Marker gene sequencing of microbial communities has generated big datasets of microbial relative abundances varying across environmental conditions, sample sites and treatments. These data often come with putative phylogenies, providing unique opportunities to investigate how shared evolutionary history affects microbial abundance patterns. Here, we present a method to identify the phylogenetic factors driving patterns in microbial community composition. We use the method, "phylofactorization", to re-analyze datasets from the human body and soil microbial communities, demonstrating how phylofactorization is a dimensionality-reducing tool, an ordination-visualization tool, and an inferential tool for identifying edges in the phylogeny along which putative functional ecological traits may have arisen.How patch size and refuge availability change interaction strength and population dynamics: a combined individual- and population-based modeling experimenthttps://peerj.com/preprints/21902016-11-292016-11-29Yuanheng LiUlrich BroseKatrin MeyerBjörn C Rall
Knowledge on how functional responses (a measurement of feeding interaction strength) are affected by patch size and habitat complexity (represented by refuge availability) is crucial for understanding food-web stability and subsequently biodiversity. Due to their laborious character, it is almost impossible to carry out systematic empirical experiments on functional responses across wide gradients of patch sizes and refuge availabilities. Here we overcame this issue by using an individual-based model (IBM) to simulate feeding experiments. The model is based on empirically measured traits such as body size dependent speed and capture success. We simulated these experiments in patches ranging from size of petri dishes to natural patches in the field. Moreover, we varied the refuge availability within the patch independently of patch size, allowing for an independent analyses of both variables. The maximum feeding rate (the maximum number of prey a predator can consume in a given time frame) is independent of patch size and refuge availability, as it is the physiological upper limit of feeding rates. Moreover, the results of these simulations revealed that a type III functional response, which is known to have a stabilizing effect on population dynamics, fits the data best. The half saturation density (the prey density where a predator consumes half of its maximum feeding rate) increased with refuge availability but was only marginally influenced by patch size. Subsequently, we investigated how patch size and refuge availability influence stability and coexistence of predator-prey systems. Following common practice, we used an allometric scaled Rosenzweig-MacArthur predator-prey model based on results from our in silico IBM experiments. The results suggested that densities of both populations are nearly constant across the range of patch sizes simulated, resulting from the constant interaction strength across the patch sizes. However, constant densities with decreasing patch sizes mean a decrease of absolute number of individuals, consequently leading to extinction of predators in smallest patches. Moreover, increasing refuge availabilities also allowed predator and prey to coexist by decreased interaction strengths. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.
Knowledge on how functional responses (a measurement of feeding interaction strength) are affected by patch size and habitat complexity (represented by refuge availability) is crucial for understanding food-web stability and subsequently biodiversity. Due to their laborious character, it is almost impossible to carry out systematic empirical experiments on functional responses across wide gradients of patch sizes and refuge availabilities. Here we overcame this issue by using an individual-based model (IBM) to simulate feeding experiments. The model is based on empirically measured traits such as body size dependent speed and capture success. We simulated these experiments in patches ranging from size of petri dishes to natural patches in the field. Moreover, we varied the refuge availability within the patch independently of patch size, allowing for an independent analyses of both variables. The maximum feeding rate (the maximum number of prey a predator can consume in a given time frame) is independent of patch size and refuge availability, as it is the physiological upper limit of feeding rates. Moreover, the results of these simulations revealed that a type III functional response, which is known to have a stabilizing effect on population dynamics, fits the data best. The half saturation density (the prey density where a predator consumes half of its maximum feeding rate) increased with refuge availability but was only marginally influenced by patch size. Subsequently, we investigated how patch size and refuge availability influence stability and coexistence of predator-prey systems. Following common practice, we used an allometric scaled Rosenzweig-MacArthur predator-prey model based on results from our in silico IBM experiments. The results suggested that densities of both populations are nearly constant across the range of patch sizes simulated, resulting from the constant interaction strength across the patch sizes. However, constant densities with decreasing patch sizes mean a decrease of absolute number of individuals, consequently leading to extinction of predators in smallest patches. Moreover, increasing refuge availabilities also allowed predator and prey to coexist by decreased interaction strengths. Our results underline the need for protecting large patches with high habitat complexity to sustain biodiversity.Systmod II: Approaching a real dynamic computer model for fish stock assessment and development of fishery strategieshttps://peerj.com/preprints/26042016-11-212016-11-21Kristin HamreSteinar MoenJohannes Hamre
Simulating development of fish stocks may be as complex as calculation of the development of the atmosphere, which is treated in meteorology as an initial value problem in physics. This approach was first proposed by Abbe and Bjerknes in the beginning of the 20 th century and today huge systems of differential equations are used to predict the weather. A similar approach to fisheries biology and ecology requires a real dynamic population model, which calculates the development of fish stocks from an initial state with equations that are independent of time. Here we present Systmod II, which uses a length-based growth function with a parameter for environmental variation and length-based data structure. The model uses monthly time steps to integrate population growth by moving fish to higher length groups as they grow. Since fish growth and maturity correlate more with length than with age, this gives comprehensive and clear results. The model was validated for Norwegian Spring-Spawning herring, using observed data from ICES working groups, and correlations (R2) between simulated and observed stock (total stock, spawning stock and catchable stock, numbers and biomass) were above 0.93. At present, the model makes reliable predictions on the short term (3 year for herring). For long term forecasts, better predictions of recruitment are needed . Since length is the main variable of the growth function, the state of the fish stock, including variability in length per yearclass, can be measured in situ, using hydro-acoustic trawl surveys. Data for modelling of many of the relations are still lacking, but can be filled in from future field studies.
Simulating development of fish stocks may be as complex as calculation of the development of the atmosphere, which is treated in meteorology as an initial value problem in physics. This approach was first proposed by Abbe and Bjerknes in the beginning of the 20 th century and today huge systems of differential equations are used to predict the weather. A similar approach to fisheries biology and ecology requires a real dynamic population model, which calculates the development of fish stocks from an initial state with equations that are independent of time. Here we present Systmod II, which uses a length-based growth function with a parameter for environmental variation and length-based data structure. The model uses monthly time steps to integrate population growth by moving fish to higher length groups as they grow. Since fish growth and maturity correlate more with length than with age, this gives comprehensive and clear results. The model was validated for Norwegian Spring-Spawning herring, using observed data from ICES working groups, and correlations (R2) between simulated and observed stock (total stock, spawning stock and catchable stock, numbers and biomass) were above 0.93. At present, the model makes reliable predictions on the short term (3 year for herring). For long term forecasts, better predictions of recruitment are needed . Since length is the main variable of the growth function, the state of the fish stock, including variability in length per yearclass, can be measured in situ, using hydro-acoustic trawl surveys. Data for modelling of many of the relations are still lacking, but can be filled in from future field studies.Making inference from wildlife collision data: inferring predator absence from prey strikeshttps://peerj.com/preprints/25722016-11-032016-11-03Peter CaleyGeoffrey R HosackSimon C Barry
Wildlife collision data are ubiquitous, though challenging for making ecological inference due to typically irreducible uncertainty relating to the sampling process. We illustrate a new approach that is useful for generating inference from predator data arising from wildlife collisions. By simply conditioning on a second prey species sampled via the same collision process, and by using a biologically realistic numerical response functions, we can produce a coherent numerical response relationship between predator and prey. This relationship can then be used to make inference on the population size of the predator species, including the probability of extinction. The statistical conditioning enables us to account for unmeasured variation in factors influencing the runway strike incidence for individual airports and to enable valid comparisons. A practical application of the approach for testing hypotheses about the distribution and abundance of a predator species is illustrated using the hypothesized red fox incursion into Tasmania, Australia. We estimate that conditional on the numerical response between fox and lagomorph runway strikes on mainland Australia, the predictive probability of observing no runway strikes of foxes in Tasmania after observing 15 lagomorph strikes is 0.001. We conclude there is enough evidence to safely reject the null hypothesis that there is a widespread red fox population in Tasmania at a population density consistent with prey availability. The method is novel and has potential wider application.
Wildlife collision data are ubiquitous, though challenging for making ecological inference due to typically irreducible uncertainty relating to the sampling process. We illustrate a new approach that is useful for generating inference from predator data arising from wildlife collisions. By simply conditioning on a second prey species sampled via the same collision process, and by using a biologically realistic numerical response functions, we can produce a coherent numerical response relationship between predator and prey. This relationship can then be used to make inference on the population size of the predator species, including the probability of extinction. The statistical conditioning enables us to account for unmeasured variation in factors influencing the runway strike incidence for individual airports and to enable valid comparisons. A practical application of the approach for testing hypotheses about the distribution and abundance of a predator species is illustrated using the hypothesized red fox incursion into Tasmania, Australia. We estimate that conditional on the numerical response between fox and lagomorph runway strikes on mainland Australia, the predictive probability of observing no runway strikes of foxes in Tasmania after observing 15 lagomorph strikes is 0.001. We conclude there is enough evidence to safely reject the null hypothesis that there is a widespread red fox population in Tasmania at a population density consistent with prey availability. The method is novel and has potential wider application.