Broken Stick Model Research Articles

Distributional Properties of Generalized Diversity Index Based on two-key Species Abundance Models

In the area of ecological research, the study of species diversity of a community or population seems to have been fully developed. However, the problem of how the distributions and expectations of the sample diversity indices are affected by population diversity has received little attention. This paper is concerned with methods of moments of improved generalized diversity index, N(α,β) due to Shamia's (2013) proposal which includes special cases. This improved index is a further generalization due to Good as described by Backowski et al., (1997). In this article, the first four central moments of N(α,β) are derived for both general species relative abundance models: the Broken-Stick model and Sequential-Breakage model within a range of (α,β) considered. This allows the determination of the skewness and kurtosis of N(α,β) and thus gives information about the behaviour of the distribution of the improved index. The results are applied for comparing the diversities of the communities based on the samples n>s, and they yielded certain desirable monotonicity properties for large samples. It can be also shown that such indices are asymptotically normally distributed.

Reliability of Nonlinear least square broken stick model in quantifying the effects of temperature and photoperiod on flowering of pigeonpea genotypes (Cajanus cajan (L.) Millsp.)

Reliability of Nonlinear least square broken stick model in quantifying the effects of temperature and photoperiod on flowering of pigeonpea genotypes (Cajanus cajan (L.) Millsp.)

Species-Abundance Models for the Early Postfire Succession of Subalpine Shrub Grassland

Fire is one of the principal factors influencing subalpine ecosystem succession. Species numbers and plant compositions are used to determine postfire disturbance, vegetation, structural change, and succession. Ecologists also integrate species diversity and mathematical models to enable researchers to obtain increasingly detailed insights into habitats during post-disturbance restoration processes. This study employed five species-abundance models, namely the niche preemption model, the broken-stick model, the log-normal model, the Zipf model, and the Zipf–Mandelbrot model, to perform fitting analysis on the abundance data of postfire species coverage in shrub grasslands near 369 Hut at Xue Mountain in Shei-Pa National Park, Taiwan. We performed the logarithmic transformation on plant-coverage areas for each period of postfire shrub-grassland succession, and then, based on histograms drawn for species–coverage distribution modes, the test results consistently showed normal distributions (p < 0.05). Species-coverage histograms measuring various periods showed that there were comparatively higher numbers of common species during postfire succession and that the numbers of rare species progressively increased. The fitting results of the five species-abundance models showed that although the most suitable abundance models for each period of postfire succession varied, the majority of these periods demonstrated decent fitting with respect to the Zipf–Mandelbrot model. These findings showed that fuel consumption provided nutrients in a manner that facilitated postfire regeneration. Moreover, dominant species, such as Yushania niitakayamensis, and Miscanthus transmorrisonensis, did not fully occupy growing spaces and resource availabilities; consequently, seeded species were able to grow.

Lying posture as a behavioural indicator of heat stress in dairy cows

Dairy cows tend to stand as a heat stress response, but the increased tendency to stand adversely affects their productivity and welfare. Thus, taking measures against heat stress before cows spend more time standing is important. Therefore, this study focused on the lying postures of cows (lying with the head turned back (HB) and lying with the head up and still (HS)) as behavioural indicators of countermeasures. It is predicted that if cows adopt a posture that exposes a large body surface area to the outside air as an adaptive response to heat stress when they are in a lying position, the expression time of HB will decrease. Six Holstein dairy cows which had calved two or three times were observed using video filming, and their behaviour was recorded for 12 days throughout the year. The temperature and humidity in the cow barn were measured and used to calculate the temperature-humidity index (THI). Standing, lying down, rumination, and HB were recorded continuously, and HS was instantaneously sampled every 30 s. Lying, standing, and rumination durations, and the time ratios of HB and HS while lying down were calculated. The data obtained from 19:30 h to 4:30 h and from 10:00 h to 15:00 h were used as nighttime and daytime data, respectively; however, data obtained from the dry milk period were excluded. Data on each behaviour during the daytime or nighttime were applied to four linear mixed models (linear, quadratic, and cubic regressions, and broken stick), including THI and milk yield as explanatory variables, and the model with the lowest value of Akaike’s information criterion was selected. A broken-stick model was selected for the analysis of lying and THI in the nighttime, and the result showed that lying time decreased with a THI value of 75 as a boundary. A linear model was selected for the analysis of HB and THI in the nighttime, and the result showed that the time ratio of HB while lying down decreased with increasing THI. These results suggest HB may be a behavioural indicator of heat stress before cows spend more time standing as a heat stress response.

Longitudinal individual predictions from irregular repeated measurements data

Intensive longitudinal data can be used to explore important associations and patterns between various types of inputs and outcomes. Nonlinear relations and irregular measurement occasions can pose problems to develop an accurate model for these kinds of data. This paper focuses on the development, fitting and evaluation of a prediction model with irregular intensive longitudinal data. A three-step process for developing a prediction tool for (daily) monitoring and prediction is outlined and illustrated for intensive weight measurements in piglets. Step 1 addresses a nonlinear relation in the data by developing and applying a normalizing transformation. Step 2 addresses the intermittent nature of the time points by aligning the measurement times to a common time grid with a broken-stick model. Step 3 addresses the prediction problem by selecting and evaluating inputs and covariates in the model to obtain accurate predictions. The final model predicts future outcomes accurately, while allowing for nonlinearities between input and output and for different measurement histories of individuals. The methodology described can be used to develop a tool to deal with intensive irregular longitudinal data that uses the available information in an optimal way. The resulting tool demonstrated to perform well for piglet weight prediction and can be adapted to many different applications.

Broken Stick Model for Irregular Longitudinal Data

Many longitudinal studies collect data that have irregular observation times, often requiring the application of linear mixed models with time-varying outcomes. This paper presents an alternative that splits the quantitative analysis into two steps. The first step converts irregularly observed data into a set of repeated measures through the broken stick model. The second step estimates the parameters of scientific interest from the repeated measurements at the subject level. The broken stick model approximates each subject's trajectory by a series of connected straight lines. The breakpoints, specified by the user, divide the time axis into consecutive intervals common to all subjects. Specification of the model requires just three variables: time, measurement and subject. The model is a special case of the linear mixed model, with time as a linear B-spline and subject as the grouping factor. The main assumptions are: Subjects are exchangeable, trajectories between consecutive breakpoints are straight, random effects follow a multivariate normal distribution, and unobserved data are missing at random. The R package brokenstick v2.5.0 offers tools to calculate, predict, impute and visualize broken stick estimates. The package supports two optimization methods, including options to constrain the variance-covariance matrix of the random effects. We demonstrate six applications of the model: Detection of critical periods, estimation of the time-to-time correlations, profile analysis, curve interpolation, multiple imputation and personalized prediction of future outcomes by curve matching.

Diatom-based paleoenvironmental reconstruction in Lake Balaton, Hungary (Tó34f)

A high-resolution diatom assemblage’s database was built on a 65 cm long sediment core (Tó34f), obtained from the Siófok Basin of Lake Balaton in 2017. Light microscope photo-documentation was developed out of 15,797 diatom valves. The pictures were arranged according to taxonomy from centric diatoms via araphids, monoraphids to biraphid forms. 30 categories were established to group the diatom taxa instead of species level identification requiring high level of expertise. Some (1) characteristic, and easily identifiable taxa (Karayevia clevei, Cavinula scutelloides) were distinguished on species level, (2) taxa were grouped at genus level (like Amphora, Aulacoseira, Neidium), while (3) were joined based on their morphological features. Two large groups were created based on this approach, the “light fragilarioids” and the “heavy fragilarioids”. Both groups contain diatoms with taxonomic problems, e.g. Staurosira, Staurosirella genera and other fragilarioids. This approach allowed us to make paleo-ecological reconstruction on (1) rough taxonomic data and (2) apply trait-based methods. Diatom assemblage’s zones were defined by CONISS clustering method, validated by the broken stick model. Though the planktonic trait (referring the high lake level) is insignificant (< 5%) in most of the studied record, but some peaks (>35%) point to high water level. The most recent trend of increasing number of planktonic diatoms is hypothesized to be due to the recent global warming. We demonstrated that traits are a good alternative to time and expertise demanding species-level determination of diatoms, thus a quick method is found for paleo-ecological reconstructions, while the photo-base good for detailed taxonomic work at a future time.

Structure–function correlates of vision loss in neuromyelitis optica spectrum disorders

Optic neuritis (ON) in neuromyelitis optica spectrum disorders (NMOSD) regularly leads to more profound vision loss compared to multiple sclerosis (MS) and myelin-oligodendrocyte-glycoprotein-antibody associated disease (MOGAD). Here we investigate ON-related vision loss in NMOSD compared to MS and MOGAD in order to identify neuroaxonal and retinal contributors to visual dysfunction. In this retrospective study we included patients with aquaporin-4-antibody seropositive NMOSD (n = 28), MOGAD (n = 14), MS (n = 29) and controls (n = 14). We assessed optic nerve damage and fovea morphometry by optical coherence tomography. Visual function was assessed as high (HCVA) and low contrast visual acuity (LCVA), and visual fields' mean deviation (MD). In all diseases, lower visual function was associated with peripapillary retinal nerve fiber layer (pRNFL) and ganglion cell and inner plexiform layer (GCIP) thinning following a broken stick model, with pRNFL and GCIP cutoff point at ca. 60 µm. HCVA loss per µm pRNFL and GCIP thinning was stronger in NMOSD compared with MOGAD. Foveal inner rim volume contributed to MD and LCVA in NMOSD eyes, only. Together these data supports that visual dysfunction in NMOSD is associated with neuroaxonal damage beyond the effect seen in MS and MOGAD. A primary retinopathy, respectively Müller cell pathology, may contribute to this effect.

Species-Abundance Distribution Patterns of Plant Communities in the Gurbantünggüt Desert, China

It is important to study the species-abundance distribution pattern in a community to reveal the mechanism of community assembly. Six abundance models (log-normal distribution model, Zipf model, Zipf–Mandelbrot model, broken stick model, niche preemption model, and Volkov model) were used to fit the species-abundance distribution pattern of six scales (10 m × 10 m, 20 m × 20 m, 40 m ×40 m, 60 m × 60 m, 80 m × 80 m, 100 m × 100 m) in fixed, semifixed, and mobile sand dunes in the Gurbantünggüt Desert, respectively. The best-fitting model was determined using the K-S test, the Chi-square test, and the Akaike information criterion. The results showed that the values of soil salinity, nutrients, water content, Shannon–Wiener diversity index (H′), Pielou evenness index (E), and Simpson index (D) were ranked in all three habitats as fixed dunes > semifixed dunes > mobile dunes. The rank curves span a narrow range on the horizontal axis at scales of 10 m × 10 m and 20 m × 20 m, and species richness is minimal. As the scale increases, the span range of the curve gradually increases, and species richness becomes higher at scales of 40 m × 40 m, 60 m × 60 m, 80 m × 80 m, and 100 m × 100 m. At the 10 m × 10 m and 20 m × 20 m scales, the broken stick model fits best in the three dune habitats. At the 40 m × 40 m and 60 m × 60 m scales, the niche preemption model fits best in the three dune habitats. At the 80 m × 80 m and 100 m × 100 m scales, the Volkov neutral model fits best in the fixed and semifixed dune habitats, and the niche preemption model fits best in the mobile dune habitats. In fixed, semifixed, and mobile dunes, both niche and neutral processes played important roles in community construction, reflecting the manifestation of the community niche-neutral continuum.

A validation of abstracted dive profiles relayed via the Argos satellite system: a case study of a loggerhead turtle

Satellite telemetry devices can record movement data of animals along with the environmental data. Such data are relayed remotely via satellite systems, but are constrained by the limited bandwidth availability. A satellite relay data logger (SRDL) that can abstract dive profiles and compress the data for transmission using a broken stick model (BSM) has been widely used in studies on dive behavior and physiology of marine animals. However, there is still uncertainty in the abstracted dive profiles. Here, we aimed to evaluate the certainty of abstracted dive profiles (via satellite communication) in terms of dive performance (dive depth, duration, and dive type) by comparing it with the actual dive data (from the retrieved tag) in a loggerhead turtle deployed with the SRDL throughout a 1.4-year foraging period. There was no significant difference in the maximum dive depth between the retrieved and satellite transmission data; however, there was a slight but significant difference in the dive duration. The dives from both datasets were classified into five types. Inconsistent dive classifications occurred in 1.7% of the data. There was no significant difference in the proportion of time spent diving between the retrieved and satellite transmission data for each type during the common recording period. In monthly scale comparisons, however, a significant difference was detected when the amount of data via satellite transmission was the smallest. Our results demonstrated that the dive data abstracted using BSM almost reconstructed the actual dive profiles with certainty in a loggerhead turtle, although slight inconsistencies were observed.

Evidence for the intermediate disturbance hypothesis and exponential decay in replacement in Streptococcus pneumoniae following use of conjugate vaccines

Understanding how pneumococci respond to pneumococcal conjugate vaccines (PCVs) is crucial to predict the impact of upcoming higher-valency vaccines. However, stages in pneumococcal community succession following disturbance are poorly understood as long-time series on carriage are scarce and mostly evaluated at end-point measurements. We used a 20-year cross-sectional dataset of pneumococci carried by Portuguese children, and methods from community ecology, to study community assembly and diversity following use of PCV7 and PCV13. Two successional stages were detected upon introduction of each PCV: one in which non-vaccine serotypes increased in abundance, fitted by a broken-stick model, and a second in which the community returned to the original structure, fitted by a geometric series, but with different serotype profile and a drop in richness as great as 24%. A peak in diversity was observed for levels of intermediate vaccine uptake (30–40%) in agreement with the intermediate disturbance hypothesis. Serotype replacement was fitted by an exponential decay model (R2 = 80%, P < 0.001). The half-life for replacement was 8 years for PCV7 and 10 years for PCV13. The structure of the pneumococcal community is resilient to vaccine pressure. The increasing loss of diversity, however, suggests it could eventually reach a threshold beyond which it may no longer recover.

Improved soil structural stability under no-tillage is related to increased soil carbon in rice paddies: Evidence from literature review and field experiment

Improving soil structural stability (SSS) and soil organic carbon (SOC) are critical for soil health and environmental pollution mitigation. No-tillage alters many soil properties (e.g., SOC), however, its effects on SSS in rice paddies are unclear. Therefore, we used field experiment and meta-analysis to determine the effects of no-tillage on wet stability of aggregates (WSA), clay dispersibility (ClayDis), mean weight diameter (MWD), and aggregate SOC distribution and mineralization in rice paddies. The field experiment included four tillage practices: no-tillage, rotary tillage and moldboard plow tillage with rice straw retention (NTS, RTS and CTS respectively), and moldboard plow tillage with rice straw removal (CT). The WSA at 0–5 cm soil depth was significantly higher under NTS compared with CTS. The ClayDis at 5–10 cm soil depth under NTS was 36% lower ( P < 0.05) than CTS. The relationship between SOC and WSA fits a broken stick model, with an inflection point of clay/SOC ratio at 12.5. Higher SOC under no-tillage might result from the protection of >2 mm aggregates (macroaggregates) and lower SOC mineralization of < 2 mm aggregates. Additionally, the meta-analysis showed that no-tillage increased ( P < 0.05) the macroaggregate content, WSA and MWD. However, the current research regarding tillage effects on paddy ClayDis is insufficient. In rice paddies, the increased macroaggregate content may contribute to increasing SOC, which improves SSS under no-tillage. • No-tillage in rice cropping increased soil structural stability. • Aggregate stability increases with SOC content and its mineralization. • SOC mineralizability of <2 mm aggregates was low under no-tillage. • No-tillage increased SOC storage in >2 mm aggregates. • Carbon mineralization did not differ among aggregate size classes.

Species-abundance distribution patterns of Quercus aliena var. acutiserrata forest in Taibai Mountain, China.

The statistical model (log-normal model), niche models (Zipf model, broken stick mo-del, niche preemption model), and neutral model were used to fit the species-abundance distribution patterns based on the measurements of environmental factors and inventory data of trees with DBH≥1 cm in a 1.5 hm2 plot in the primary forest (PF) and a 1.5 hm2 plot in the secondary forest (SF). The results showed that species-abundance distribution was affected by habitat heterogeneity in Q. aliena var. acutiserrata forest. Topography had a predominant impact on the species-abundance distribution in PF. Species distribution was affected by both neutral and niche processes, with neutral process having a less prominent effect in large convexity habitats. While the neutral model was rejected by the K-S and Chi-square test in low convexity habitats, the species-abundance distribution satisfied the assumption of niche theory. Niche process and neutral process were equally important in the community in areas with steep slopes, while niche differentiation was the dominant in flat areas. In SF, the main factors affecting species distribution were soil nutrients. The niche process was the mainly ecological process affected species-abundance distribution in habitats with high soil available phosphorus, while the niche and neutral processes existed simultaneously in habitats with low soil phosphorus availability. There was a significant scale effect on the species-abundance distribution pattern of Q. aliena var. acutiserrata forests in Taibai Mountain. The niche and neutral processes could protect the species-abundance distribution at the 20 m×20 m scale in PF, while the niche process could explain the species-abundance distribution at the 40 m×40 m and 70 m×70 m scales. The niche and neutral processes combined acted on the species abundance distribution at the 20 m×20 m, 40 m×40 m and 70 m×70 m scales in SF, with niche process being more important than neutral process. Moreover, besides the scale and habitat heterogeneity, the species-abundance distribution patterns of Q. aliena var. acutiserrata forests differed significantly between primary forest and secondary forest under anthropogenic disturbance.

Riparian vegetation dynamics in protected and unprotected areas, Kumawu District—Ashanti Region (Ghana)

The aim of the study was to explore the response of plant assemblages to environmental drivers among four riparian zones (Amobia, Ninian, Pame and Owname), in Ashanti Region, Ghana, West Africa. A 120 sample plots of 10 × 10 m2 for trees and shrubs and 0.5 × 2 m2 for grasses and herbs, were randomly laid perpendicular to the environmental gradients, and from both sides of the four classified riparian zones. Number of individuals were counted per plot and percentage cover estimated per species. MacArthur broken stick model (BS), Chao-1 estimates and Hill numbers were calculated to quantify community assemblages, while constrained ordination (CCA) was applied to examine the relationship between species assemblages and the distribution of associated environmental factors. A total of 1589 individuals belonging to 48 families and 141 species were registered. Species from the Fabaceae, were the highest (14.2%). Overall, species abundance, richness and diversity, differed significantly across the four zones. Aspilia africana and Panicum maximum were the single most abundant tree and grass species, respectively. Infrequent species including Bussea occidentalis, Celtis zenkarii constituted 0.4% of the total species sampled. Although Pame was found to be species poor, it tended to be the most diverse, while Ninian was the least diverse. CCA analysis showed that farming, bushfire, erosion and logging, accounted for 43.13% (axis I = 23.24% and axis II = 19.89%) patterns of species variability across sites. Though disturbances tend to promote diversity through the creation of evenness in species distribution and richness, but in severe scenarios, sensitive indigenous species may go extinct, leaving only stress-tolerant alien invasive like Arthraxon hispidus and Chromolaena odorota.

Analysing species abundance distribution patterns across sampling scales in three natural forests in Northeastern China

Understanding how and why species abundance distributions (SADs) vary with sampling scale has been a long-standing issue in ecology. By fitting various SAD models with observations collected in three large forest field plots, the objective of this study is to explore how the shape of SADs and the predictive ability of SAD models vary with sampling scales. Based on a large dataset collected in the Changbaishan, Jiaohe and Liangshui forests in northeastern China, observed SADs were compared with SADs estimated using five different models (log-normal, broken stick, Zipf, niche preemption and neutral model) at four sampling scales (10 × 10 m, 30 × 30 m, 60 × 60 m and 90 × 90 m). The results show that the studied SADs are scale dependent. Niche-based models provided a better fit at small sample sizes, the predictive ability decreasing with increasing sampling scale. The neutral model performed better at large sample sizes, the predictive ability increasing with increasing sampling scale. We identify the models that provided the best fit to observed species abundance distributions across spatial scales, and conclude that there is not one best SAD model for all spatial scales. Future studies should consider the scale effects on the species abundance distribution.

Vegetation structure and floristic composition (Case study: Mala Galeh Protected area, Fars Province, Iran)

Identifying flora of each region is fundamental for accomplishing other pure and applied researches in biology. Especially, in the ecological conditions of protected area of Male Gale. Data were collected in 96 sampling plots using systematic­_ random method. The size of sampling plot was 20 m × 50 m for the tree and shrub species, and 8 m × 8 m for herbaceous species. In this study area, 162 species, 122 genera and 43 families were identified. The largest families were Asteraceae (26 species) and Fabaceae (25 species). The frequency of Asteraceae may be due to grazing in some areas of the region. The life form spectrum includes: Hemichryptophytes (14/01 %), Therophytes (65/4 %), Cryptophytes (76/9 %), Chamaephytes (7.1 %) and Phanerophytes (5.8 %). The abundance of Therophytes and Asteraceae family is refered to destruction of forests in the study area. The highest value of the SIV tree and shrub species layer belong to Quercus brantii species and ZIziphus Mummularia. The highest value of the FIV herbaceous layer belong to Asteraceae family. The Species Important Value (SIV) of vegetation cover indicated that tree, shrubs species and herbaceous species had geometric distribution, broken stick model and lognormal distribution in this area.

THE ABUNDANCE AND DIVERSITY OF GRASSHOPPER (ORTHOPTERA: CAELIFERA) ALONG AN ALTITUDINAL GRADIENT IN JIJEL DISTRICT, ALGERIA

Grasshoppers (Orthoptera: Caelifera) diversity were studied in three sites at different altitude in Jijel district (North East Algeria). The insects were captured with sweep net weekly from April to August 2016. It appears that 30 Grasshopper species belonging to 4 families and 11 subfamilies were identified amongst 712 individuals. Acrididae species (25) were the most frequent. The species richness was higher at medium altitude (23 species) and high altitude (22 species) than at low altitude (18 species). Species abundance distribution fitted the Broken stick model at low and high altitude while it fitted the Geometric or Motumura model at medium altitude. Grasshopper abundance increased with the altitude while diversity was not correlated with increasing altitude since diversity indices values were high in medium altitude.

Relationship between peripapillary vessel density and visual field in glaucoma: a broken-stick model

Background/AimsTo determine the tipping point at which peripapillary vessel density (pVD), measured using optical coherence tomography angiography (OCT-A), is associated with detectable visual field (VF) loss in cases of open-angle...

Species-abundance distributions and Taylor’s power law of fluctuation scaling

Two widely investigated areas of theory in ecology over the past half century are species-abundance distributions (SADs) and Taylor’s power law of fluctuation scaling (TL). This paper connects TL with a classic SAD, MacArthur’s broken-stick model. Each of these models is more than 60 years old, but apparently the connection has not been observed previously. For large numbers of species, the broken-stick model asymptotically obeys TL with exponent 2: the variance of species abundance equals the square of the mean species abundance. Equivalently, in the broken-stick model, the coefficient of variation of abundance is asymptotically 1. Because both the broken-stick model and TL have interpretations and applications beyond ecology, the connection established here has broader than purely ecological interest. This simple but previously unnoticed relationship between the broken-stick model and the power-law variance function raises the question of how other species-abundance distributions are related to power law or other variance functions.

Ecological and toxicological assessment of heavy metal pollution of the Bienda-Stemme Lake (West Spitsbergen)

According to the literature, linear-exponential mathematical models have been developed that link the magnitude of the risks (probabilities) of fatal outcomes when metal cations affect daphnia in a wide range of concentration variations. The approach to a comprehensive assessment of heavy metal pollution of surface waters of land has been improved (risk of combined exposure). The classification of water quality is given depending on the magnitude of the combined risks. The broken-stick model was used in order to classify water quality according to metal contamination levels. The developed approach was applied for an interannual assessment of lake pollution. The results of ecological and toxicological assessment of the dynamics of metal pollution (such as iron, manganese, zinc, copper, nickel, cobalt, lead, chromium, mercury and cadmium) of the Bienda-Stemme lake, located in Western Spitsbergen (Svalbard), in the spring of 2003-2019 are presented. It was established that the quality of the Bienda-Stemme lake water varied from “good” in 2003-2004, 2013-2015 to “satisfactory” in 2017 and 2018. In the period of 2007-2012, as well as in 2019, the water quality of the lake was characterized as “very good”. On average for the period of 2003-2019 the water quality of the lake in the spring was characterized as “good”. The main contribution to the metal pollution of the Bienda-Stemme lake is due to compounds of copper, mercury and zinc. A significant advantage of the considered approach to assessing the pollution of the Bienda-Stemme lake by metals is that this approach does not use the system of federal standards for MPC (maximum permissible concentrations). Moreover, up to present, regional standards have not been developed in Russia.