Delta-lognormal Model Research Articles

Application of Fishery-independent Data as an Alternative Source for Determining Relative Abundance Indices of Blue Marlin, Makaira nigricans (Actinopterygii: Perciformes: Istiophoridae) in the North-eastern Indian Ocean

The present study aimed to determine the abundance index of blue marlin, Makaira nigricans (Lacepède, 1802) utilizing fishery-independent data, i.e., scientific observer, and attempted to bridge the research's gap for low coverage information in the north eastern Indian Ocean. A total of 2,984 set-by-set observer data from 2006-2018, spatially disaggregated by one-degree blocks, were obtained from the Indonesian scientific observer program following commercial longline fleets. A delta-lognormal model was chosen to fit the dataset, using catch as the response variable with seven covariates. A backward procedure based on AIC, BIC and R2 were used to select the best model. Overall, the delta-Gamma performs better when modelling data with a high proportion of zeros than other traditional models. The blue marlin CPUE trend is relatively stable over time, despite the inter-annual fluctuations, which are likely a result of natural variation in the population as opposed to operational changes or inter-annual environmental variation. Given the low spatial coverage compared to logbook data, scientific observer data performed well and produced a robust abundance index of blue marlin in the northeastern Indian Ocean.

Shortfin mako hot sets – Defining high bycatch conditions as a basis for bycatch mitigation

Shortfin mako sharks, Isurus oxyrinchus, were listed under Appendix II of CITES in 2019 in part due to the results of the last stock assessment for the North Atlantic population, which determined the population is overfished and experiencing overfishing. With population numbers expected to continue to decline, the managing body, the International Commission for the Conservation of Atlantic Tunas (ICCAT), has called for efforts to reduce shortfin mako bycatch. We evaluate the potential for reducing mako bycatch by identifying mako hot sets, those with particularly high shortfin mako bycatch. Environmental conditions were evaluated for their influence on catch per unit effort (CPUE) of shortfin mako sharks. Standardized CPUEs were calculated from the US pelagic longline observer program (2004–2012) using a generalized additive model (GAM) with a delta-lognormal approach applied to the environmental variables sea surface height, sea surface temperature, bathymetry, and chlorophyll-a concentration. Quantile regression (QR) was also performed to evaluate whether environmental variables can predict fishing conditions with high CPUE. The results of the GAM and QR methods were compared and assessed for their ability to predict and identify locations where shortfin mako CPUE is particularly high. The results suggest that using the binomial portion of the delta-lognormal model, the probability of positive bycatch, is the best basis to define an algorithm to avoid setting in conditions that might have high mako bycatch. Bycatch avoidance strategies built from probability of positive bycatch perform well enough at identifying hot sets to avoid half the shortfin mako bycatch with only a 20% reduction in effort.

An unbiased estimator of coefficient of variation of streamflow

Given increasing demand for high frequency streamflow series (HFSS) at daily and subdaily time scales there is increasing need for reliable metrics of relative variability for such series. HFSS can exhibit enormous relative variability especially in comparison with low frequency streamflow series formed by aggregation of HFSS. The product moment estimator of the coefficient of variation C, defined as the ratio of sample standard deviation to sample mean, as well as ten other common estimators of C, are shown to provide severely downward biased and highly variable estimates of C for very long records of highly skewed and periodic HFSS particularly for rivers which exhibit zeros. Resorting to the theory of compound distributions, we introduce an estimator of C corresponding to a mixture of monthly zero-inflated lognormal distributions denoted as a delta lognormal monthly mixture ΔLN3MM model. Through monthly stratification, our ΔLN3MM model accounts for the seasonality, skewness, multimodality, and the possible intermittency of HFSS. In comparisons among estimators, our ΔLN3MM based C estimator is shown to yield much more reliable and approximately unbiased estimates of C not only for small samples but also for very large samples (tens of thousands of observations). We document values of C in the range of [0.18, 42,000] with a median of 1.9 and an interquartile range of [1.34, 3.75] for 6807 daily streamflow series across the U.S. from GAGES-II dataset, with the highest values of C occurring in arid and semiarid regions. A multivariate analysis and national contour map reveal that extremely large values of C, never previously documented, tend to occur in arid watersheds with low runoff ratios, which tend to also exhibit a considerable number of zero streamflows.

Characteristics of bi-directional unimanual and bimanual drawing movements: The application of the Delta-Lognormal models and Sigma-Lognormal model

The use of large digitizers, allowing users to interact using both hands simultaneously, are getting more and more popular in applications requiring human computer interaction. In most of these applications, gesture commands are used and these commands to activate specific actions can provide also information about the neuromuscular system of the user. As shown for single hand interactions, understanding of the neuromotor coordination processes using both hands could improve interface design. In the present paper, we address this topic with a first study aimed to characterize the bimanual and unimanual coordination. We compare the kinematic properties of movements performed unimanually and bimanually. Rapidly drawn lines are assessed using kinematic features in addition to the parameters estimated by two models, i.e., the Delta-Lognormal model and Sigma-Lognormal model. Sixteen right-handed participants were instructed to conduct 120 rapid drawing actions with the dominant hand, non-dominant hand, and both hands simultaneously. Kinematic variables (i.e. reaction time (RT) and movement time (MT)) together with parameters of the Delta-Lognormal model and Sigma-Lognormal model were extracted from the movements. The latter parameters estimate the agonist and antagonist synergies that contribute to the overall movement production of the rapid drawn lines. A 2 × 2 repeated measures ANOVA was applied to all dependent variables with manual condition (uni- vs bimanual) and hand used (dominant vs non-dominant) as independent factors. Parameters of the Delta-Lognormal model and Sigma-Lognormal model revealed that the prolonged preparation time of the bimanual task had both a central and peripheral origin, i.e., it originated at the CNS and neuromuscular levels. Furthermore, findings from the Sigma-lognormal model suggested that the dominant and non-dominant hand contribute differently to the manual conditions, which may lead to new heuristics for implementing command systems for computer interaction systems requiring bimanual manipulation as well as designing automatic systems for rehabilitative training.

Cpue Standardization and Catch Estimate of Blue Shark by Taiwanese Large-Scale Tuna Longline Fishery in the North Pacific Ocean

The blue shark, ＂Prionace glauca＂, is a pelagic species with a circum-global distribution in tropical to temperate waters. It is the top by-catch shark species for the Taiwanese large-scale tuna longline (LTLL) fishery. However, its population status in the North Pacific Ocean is still little known. In the present study, the blue shark catch and effort data from observers’ records of Taiwanese LTLL fishing vessels operating in the North Pacific Ocean from 2004 to 2012 were analyzed. Due to the large percentage of zero blue shark catch, the catch per unit effort (CPUE) of blue shark, as the number of fish caught per 1,000 hooks, was standardized using a delta-lognormal model. The standardized CPUE of blue sharks, as an estimate of relative abundance of blue shark, decreased from 2005 to 2009 and showed an increasing trend thereafter. Back-estimated historical blue shark by-catch of Taiwanese LTLL fishery in the North Pacific Ocean ranged from 0.4 MT in 1973 to 1,447 MT in 2002. The results obtained in this study can be improved if longer time series observers' data are available and environmental factors are included in the model.

Comparison of relative abundance indices calculated from two methods of generating video count data

The use of baited remote underwater video to remotely observe fish and generate indices of relative abundance has steadily gained acceptance as a fisheries management tool particularly as survey time series have matured. Because ‘capture’ for this gear is visually derived, fish can possibly be counted multiple times and therefore different methods of estimating site abundances have been developed. We compared the performance of two video abundance estimation techniques, MaxN and MeanCount, by generating relative indices of abundance using a delta lognormal model. We demonstrated high correspondence between standardized indices produced through the years analyzed independent of the species evaluated, indicating there was little change in the information content between indices. Despite the agreement between the indices, estimates for proportion positive and coefficient of variation (CV) showed a general reduction in precision when using the MeanCount method for all species analyzed. Systematic underestimation of proportion positives and high CV values generated using MeanCount is problematic for the use of that abundance estimation method. Individual-based modeling results confirmed that MeanCount is linearly related to true abundance, while MaxN showed a power relationship. However, the MaxN estimate became linear as the area observed was increased in the model from 25% to 100%, which suggests that syncing cameras and generating counts over the entire observed area would eliminate the asymptotic relationship and simplify the use of MaxN estimators. Better understanding of catchability for optical type gears would enhance understanding of the relationship between the generated index and true population abundance, and supply assessment scientist with a clearer understanding of how to incorporate these types of survey data into assessments.

Spatiotemporal catch distribution of age-0 Pacific bluefin tuna Thunnus orientalis caught by the Japanese troll fishery in relation to surface sea temperature and seasonal migration

This study used a delta-lognormal model to analyze monthly catches of age-0 Pacific bluefin tuna by the troll fishery. The model included fixed effects of month, area, and month–area interaction, and random effects of port, year and port–year interaction. The catch patterns by month and area predicted by the statistical model (standardized catch) revealed that main fishing grounds along the Tsushima Warm Current generally shifted from north to south as the season turned from autumn to winter. In contrast, the standardized catch along the Kuroshio Current did not show such clear spatiotemporal patterns. The standardized catch along the Tsushima Warm Current is significantly associated with average monthly sea surface temperatures in the fishing grounds and consistent with migration routes revealed by tagging experiments in previous studies. These associations indicate the spatiotemporal catch pattern in the Tsushima Warm Current region partly reflects seasonal migration. Knowledge of the possible associations among fish migration, environmental factors and spatiotemporal distribution of the catch will contribute to future management of this species.

Time-dependence between upper arm muscles activity during rapid movements: Observation of the proportional effects predicted by the kinematic theory

Rapid human movements can be assimilated to the output of a neuromuscular system with an impulse response modeled by a Delta-Lognormal equation. In such a model, the main assumption concerns the cumulative time delays of the response as it propagates toward the effector following a command. To verify the validity of this assumption, delays between bursts in electromyographic (EMG) signals of agonist and antagonist muscles activated during a rapid hand movement were investigated. Delays were measured between the surface EMG signals of six muscles of the upper limb during single rapid handwriting strokes. From EMG envelopes, regressions were obtained between the timing of the burst of activity produced by each monitored muscle. High correlation coefficients were obtained supporting the proportionality of the cumulative time delays, the basic hypothesis of the Delta-Lognormal model. A paradigm governing the sequence of muscle activities in a rapid movement could, in the long run, be useful for applications dealing with the analysis and synthesis of human movements.

Population structure, distribution and relative abundance of the blue shark (Prionace glauca) in the Caribbean Sea and adjacent waters of the North Atlantic

Catch and fishing effort data from the Venezuelan Pelagic Longline Observer Program (VPLOP) in the Caribbean Sea and adjacent waters of the Atlantic were used to investigate the population structure, distribution and relative abundance of the blue shark, Prionace glauca. A total of 959 blue sharks were sampled by trained observers during the period of January 1994 to December 2007. Fork length (FL) in males ranged from 79 to 355cm and from 97 to 349cm in females. Sexual segregation at the spatial and temporal scale was observed, males dominated January–June and during October–December across all areas; while females dominated during July–September with a higher magnitude in the Atlantic side (Guyana-Amazon area). Sex ratio for mature (>180cm FL) blue shark favored females in the Caribbean Sea from July to December, and in the Guyana-Amazon area in July–September; while immature blue sharks were dominated by males across all areas. Thirty-four pregnant females were caught in the Caribbean Sea and three in the Guyana-Amazon area. Pregnant females displayed a seasonal trend which increased from September through January, where >50% of the pregnant females occurred during November–January; of the pregnant females caught in the Caribbean Sea two had embryos close to the size-at-birth [>35cm total length (TL)]. The spatial distribution of blue sharks in the Caribbean Sea was marked by high concentrations around the offshore islands of Venezuela and the Netherland Antilles year round; while in the Guyana-Amazon area the high concentrations were more seasonally localized off northeastern coast of South America but diminished progressively and by the end of the year was absent in the area. Relative abundance of blue shark was estimated from the Venezuelan pelagic longline (VPL) fleet using a General Linear Model Approach with a delta lognormal model distribution to account for the high proportion of zero observations. The variability within vessel groups was partitioned into each vessel variance and the auto-correlation within a vessel was evaluated by using a variance–covariance matrix model. Diagnostic checks and deviance table analysis were performed to identify the set of model factors and interactions that adequately explained the observed variability. The results indicated that variability of catch rates within vessels is as large as the variability among vessel groups, where smaller and medium size vessels show higher catch rates of blue sharks in the VPL fleet. Standardized catch rates indicated in general a lower relative abundance in the most recent years followed by a slight recovery that requires caution due to the predicted high variance. Fishing activities can have uneven effects in the blue shark population due to its spatial and temporal segregation in the study area; potential changes in the fishing operations of the VPL fleet can have negative effects in the population structure of blue sharks in the Caribbean Sea and adjacent waters if habitat for blue sharks are increasingly used to target other valuable species (e.g., large tunas and swordfish).

Seasonal distribution of bloater (Coregonus hoyi) in the waters of Lake Huron surrounding the Bruce Peninsula

Information about bloater (Coregonus hoyi) habitat in Lake Huron was limited to correlations between commercial yield and fishing depth, despite available information from other Great Lakes. We identified seasonal patterns of bloater habitat use in hypolimnetic waters surrounding the Bruce Peninsula, Lake Huron. We applied a delta-lognormal model to fisheries-independent survey data to evaluate whether bloater catch-per-unit-effort was related to depth, temperature, and bathymetric slope. A Bayesian variable selection technique indicated that bloater distribution was most strongly related to bottom depth and water temperature. Our study also reconfirmed a previously-described pattern of seasonal inshore movement during warmer months followed by a return to deeper offshore waters during cooler months. By focusing our sampling within the hypolimnion, we characterized intra-annual patterns of bloater habitat use with respect to a temperature gradient near the minimum thermal requirements reported for this species. Bloater distribution under these thermal conditions has not been previously reported.

Kinematic characteristics of bidirectional delta-lognormal primitives in young and older subjects

In this paper, 14 healthy subjects in two age groups have produced rapid handwriting strokes with a direction reversal. The delta-lognormal model was used to obtain a detailed description of the velocity of these movements and of the neuromuscular synergy that produces them. This modeling also allowed the derivation of new hypothesis on the nature of the slowing effect due to aging (i.e., a direct effect or a coping strategy) and on its repartition on the different steps of the movement production (i.e., its preparation versus its execution). Our analysis revealed a substantial increase of neuromuscular response delays and a decrease of the command amplitudes with age. For the parameters that show a significant decrease in performance, the agonist and antagonist systems were affected similarly. In addition, we observed that the age has a proportional effect on the various time characteristics of the movements and that even in the case of a significant slowing down of the neuromuscular systems, the elderly can still achieve optimal movement responses, characterized by the use of a single delta-lognormal primitive. This performance might be related to the preservation of some movement timing properties and relationships between the agonist and the antagonist neuromuscular systems.

Catch rates and size composition of blue sharks (Prionace glauca) caught by the Brazilian pelagic longline fleet in the southwestern Atlantic Ocean

Distribution and relative abundance of blue sharks ( Prionace glauca ) in the southwestern Atlantic Ocean was modeled based on catch-per-unit-effort (CPUE) per 1000 hooks and length frequencies of blue sharks caught by the Brazilian pelagic tuna longline fleet. As a measure of relative abundance, CPUE of blue sharks caught in 58 238 fishing sets by the Brazilian pelagic tuna longline fleet (national and chartered), from 1978 to 2009, was standardized by a Generalized Linear Model (GLM) using three different approaches: i) a negative binomial error structure (log link); ii) the traditional delta lognormal model; and iii) the Tweedie distribution, recently proposed to adjust models with a high proportion of zeros. A cluster analysis using the K-means method was used to identify target species and incorporate it as a factor into the GLM. Cluster analysis grouped the data into six different fishing clusters according to the percentage of target species. Target factor (cluster) was the most important factor explaining the variance in all three CPUE models. The Tweedie model showed a relatively better fit compared to the other models. Blue shark nominal and standardized CPUE showed a relatively stable trend from 1978 to 1995. From 1995 onwards, however, there was an increasing trend in the standardized CPUE, up to a maximum value in 2008. In general, nominal CPUE and standardized CPUE tracked well up until 2000, after which standardized CPUE’s values were at a noticeably lower level than nominal CPUE. Length frequency data were analyzed for 11 932 blue sharks measured as part of the Brazilian onboard observer program operating on the pelagic tuna longline fleet between 2006 and 2008, with sizes ranging from 91 to 224 cm fork length. Overall, blue shark size data showed clear spatial and seasonal distributions for males and females in the southwestern Atlantic Ocean, with juveniles predominantly concentrated in the most southerly latitudes.

Characterization of Bi-Directional Movement Primitives and Their Agonist-Antagonist Synergy with the Delta-Lognormal Model

A general definition of a movement primitive and of the elements that have to be taken into account in attempts to its characterization is proposed. As an example, the delta-lognormal model is used to define the kinematic primitives associated with rapid, stroke-like movements. The quantitative characteristics of the agonist-antagonist synergy that underlie a specific primitive predicted by the model, the bidirectional stroke, are described. The results reveal the existence of a universal correlation between the agonist and the antagonist neuromuscular systems that produce this primitive.

Modeling environmental, spatial, temporal, and operational effects on blue shark by-catches in the Mediterranean long-line fishery

A study was conducted from 1998 to 2001 on blue shark (Prionace glauca) by-catch of the Italian and Greek surface-drifting swordfish long-line fisheries in the Mediterranean Sea. The focus was on examining whether catches are related to some environmental, spatial, temporal or operational parameters and to what extent, applying generalized linear model (GLM) approaches. Analyses indicated that most appropriate for the dataset was the Delta-lognormal model, which is a binomial error distribution for the probability of a non-zero catch and lognormal error for positive catch rates. Spatial and temporal factors were the most influential regarding blue shark distribution and abundance, with a considerable interaction between them; the modeled environmental factors were of minor importance. Spatial distribution revealed a strong longitudinal gradient whereby blue shark occurrences increased in an east to west direction, whereas catches by latitude were higher in southern- and northern-most regions. Blue sharks were more frequently encountered in autumn and in distant open waters; however, the likelihood of making a larger catch peaked in late spring–early summer and in the vicinity of land. Catch rates differed significantly depending on the fishing gear configuration. Deeper settings (>20 m), more resilient lines and use of fish attractants increased the probability of P. glauca capture.

Application of the Tweedie distribution to zero-catch data in CPUE analysis

We focus on the zero-catch problem of CPUE (catch per unit effort) standardization. Because the traditional CPUE model with a log-normal error structure cannot be applied in this case, three methods have often been utilized as follows: (1) Ad hoc method adds a small constant value to all response variables. (2) Catch model with a Poisson or negative-binomial (NB) error structure. (3) Delta-type two-step method such as the delta-normal model (after estimating the ratio of zero-catch using a logit or probit model, a model such as CPUE log-normal or Catch-Poisson is applied to CPUE without zero-data). However, there are some statistical problems with each of these methods. In this paper, we carried out the CPUE standardization mainly using the Tweedie distribution model based on the actual by-catch data (silky shark, Carcharhimus falciformis, in the North Pacific Ocean caught by Japanese training vessels) including many observations with zero-catch (>2/3rd) and tuna fishery data as a target (yellowfin tuna, Thunnus albacares, in the Indian Ocean caught by Japanese commercial vessels) where the ratio of zero-catch is not so high (<1/3rd). The Tweedie model is an extension of compound Poisson model derived from the stochastic process where the weight of the counted objects (i.e., number of fish) has a gamma distribution and has an advantage of handling the zero-catch data in a unified way. We also compared four candidate models, the Catch-NB model, ad hoc method, Delta-lognormal model (delta-type two-step method) and Tweedie distribution, through CPUE analyses of actual fishery data in terms of the statistical performance. Square error and Pearson's correlation coefficient were calculated based on the observed CPUE and the corresponding predicted CPUE using the n-fold cross-validation. As a result, the differences in the trend of CPUE between years and model performance between the ad hoc method and Tweedie model were found to be not so large in the example of yellowfin tuna (target species). However, the statistical performance of Tweedie distribution is rather better than Delta-lognormal model, the Catch-NB distribution and ad hoc method in the example of silky shark (by-catch species). Standardized CPUE year trend of ad hoc method was found to be quite different from that of the Tweedie distribution and other two models. Model performance of the Tweedie distribution is good judging from the 5-fold cross-validation using the fishery data if including many zero-catch data such as by-catch species.

Combining shape and physical modelsfor online cursive handwriting synthesis

This paper proposes a novel learning-based approach to synthesizing cursive handwriting of a user's personal handwriting style by combining shape and physical models. In the training process, some sample paragraphs written by a user are collected and these cursive handwriting samples are segmented into individual characters by using a two-level writer-independent segmentation algorithm. Samples for each letter are then aligned and trained using shape models. In the synthesis process, a delta log-normal model based conditional sampling algorithm is proposed to produce smooth and natural cursive handwriting of the user's style from models.

Alternative error distribution models for standardization of catch rates of non-target species from a pelagic longline fishery: billfish species in the Venezuelan tuna longline fishery

Alternative error distributions were evaluated for calculating indices of relative abundance for non-target species using catch and effort data from commercial fisheries. A general procedure is presented for testing the underlying assumptions of different error distributions. Catch rates, from an observer program, of billfish caught mainly as bycatch in a pelagic tuna longline fishery in the Western Central Atlantic were standardized. Although catches of billfishes are not common in pelagic tuna longline fisheries, these fisheries are one of the main sources of fishing mortality for these stocks in the central Atlantic due to the magnitude and spatial extent of longline fishing effort. Billfish CPUE data are highly skewed with a large proportion of zero observations. Delta distribution models can accommodate this type of data, and involve modeling the probability of a non-zero observation and the catch rate given that the catch is non-zero separately. Three different Delta models were compared against other error distributions, including the lognormal, log-gamma, and Poisson. Diagnostic checks and deviance table analyses were performed to identify the best error distribution and the set of factors and interactions that most adequately explained the observed variability. The results indicated that the Delta-lognormal model (a binomial error distribution for the probability of a non-zero catch and lognormal error for the positive catch rates) complied best with the underlying characteristics of the data set. Analyses of catch rates for blue marlin, white marlin and sailfish confirmed the spatio-temporal nature of their distribution in the central Atlantic and Caribbean Sea. Also, the analyses indicated that catch rates of billfish differed among fishing vessel types; larger vessels had a higher probability of catching blue marlin, the more oceanic-oriented species, and lower probabilities of catching the more coastal-oriented species white marlin and sailfish. Standardized catch rates indicated in general a lower relative abundance for blue and white marlin in the most recent years, although estimated confidence intervals overlap through the years especially for white marlin.

Standardization of bluefin tuna, Thunnus thynnus, catch per unit effort in the baitboat fishery of the Bay of Biscay (Eastern Atlantic)

Abstract Relative indices of abundance by age class for bluefin tuna from 1975 to 2000 were estimated using generalized linear mixed models. Age class was included as a fixed factor within the model specifications, with the Year×Age interaction as a fixed factor component in order to obtain annual indices by age. Catch and effort data on bluefin tuna were available from two sources, catches by trip, and daily catches from logbooks. Catches were modelled using the delta-lognormal model. The model finally selected included the following explanatory factors: Year, Age, Year×Age, Month, number of Crew, number of Bait Tanks, and with the Year×Month interaction as a random component. Overall, year trends and coefficients of variation were similar from both datasets by age class. In general, the standardization procedure showed that vessel characteristics and technological advances related to fishing have a relatively minor explanatory effect on the observed catch rates of bluefin tuna in the fishery. Neither geographical distribution nor type of bait had an explanatory effect on the observed catch rates. The 1994 cohort stands out as an exceptionally large year class; it can be followed through the standardized series. This standardized catch rate index at age of bluefin tuna is the most complete yet available and is the only one currently used for juvenile fish in calibrating population models to evaluate the Eastern Atlantic and Mediterranean stock. It is particularly valuable because, apart from improvements in electronic technology, there are no changes in the method of exploitation during the entire series.

The 2/3 power law: When and why?

This paper presents the origin of some reported observations, which links the kinematics of handwriting with a movement trajectory, best known as the 2/3 power law. Using computer simulations, it is shown that the vectorial delta-lognormal model recently proposed to describe 2D movements can successfully simulate these phenomena. Although the power law has been found to be a good predictor in many experimental conditions, a few experiments have shown that the law does not apply to all graphic movements. Using the vectorial delta-lognormal model, the conditions under which a 2/3 power relationship can be observed are presented and the reasons why it does not seem to be verified for more general handwritten patterns are highlighted.

A new method for the analysis of simple and complex planar rapid movements

Recent developments in the field of simple human movement modelling provide new ways in which to view complete models for analysing and understanding complex movements. Based on a kinematic theory and a vectorial delta-lognormal model recently proposed by Plamondon (1993a, 1995a, b, c, 1998), a new method for exploring and understanding the inherent mechanisms that govern planar movement generation and predict human behaviour is presented here. This paper describes an approach for analysing simple as well as complex movements such as cursive handwriting. It highlights some difficulties encountered in the analysis of complex movements. Problems such as the development of robust approaches to solve the reverse engineering problem of automatic parameter extraction of a succession of time-overlapped nonlinear functions are discussed. The analysis of natural cursive handwriting shows many interesting properties of the model and proposes new ways to study perturbed movement phenomena.