Selectivity, pulse fishing and endogenous lifespan in Beverton-Holt models

Optimal management in a multi-cohort Beverton-Holt model with any number of age classes and imperfect selectivity is equivalent to finding the optimal fish lifespan by chosen fallow cycles. Optimal policy differs in two main ways from the optimal lifespan rule with perfect selectivity. First, weight gain is valued in terms of the whole population structure. Second, the cost of waiting is the interest rate adjusted for the increase in the pulse length. This point is especially relevant for assessing the role of selectivity. Imperfect selectivity reduces the optimal lifespan and the optimal pulse length. We illustrate our theoretical findings with a numerical example. Results obtained using global numerical methods select the optimal pulse length predicted by the optimal lifespan rule.

Length-frequency estimation for yellowfin tuna (Thunnus albacares) caught by commercial fishing gear in the Eastern Pacific Ocean

ENGLISH: Methods of collecting samples for the purpose of estimating the numbers and weights of fish caught, by length interval, are described. Several models for two-stage sampling are described, and the equations for the estimators and their variances are given. The results from a brief simulation study are used to show the differences between estimates made with the different models. Estimators for the average weights of fish in the catch and their variances are also described. These average weights are used to provide improved estimates of the total annual catches of yellowfin taken from the eastern Pacific Ocean, east of 150°W, between 1955 and 1990. SPANISH: Se describen los métodos de recoger de muestreo para estimar el número o peso de peces capturados, por intervalo de talla. Se describen varios modelos para el muestreo de dos etapas, y se presentan las ecuaciones para los estimadores y sus varianzas. Se usan los resultados de un breve estudio de simulación para indicar las diferencias entre estimaciones realizadas con los distintosmodelos. También se describe un estimador para el peso promedio de peces en la captura y su varianza. Se usan estos estimadores para calcular estimaciones mejoradas de las capturas anuales totales de aleta amarilla tomadas del Océano Pacífico oriental, al este de 150°W, entre 1955 y 1990. (PDF contains 41 pages.)

An evaluation of length-frequency sampling procedures and subsequent data analysis for purse seine-caught yellowfin tuna in the Eastern Pacific Ocean

ENGLISH: A two-stage sampling design is used to estimate the variances of the numbers of yellowfin in different age groups caught in the eastern Pacific Ocean. For purse seiners, the primary sampling unit (n) is a brine well containing fish from a month-area stratum; the number of fish lengths (m) measured from each well are the secondary units. The fish cannot be selected at random from the wells because of practical limitations. The effects of different sampling methods and other factors on the reliability and precision of statistics derived from the length-frequency data were therefore examined. Modifications are recommended where necessary. Lengths of fish measured during the unloading of six test wells revealed two forms of inherent size stratification: 1) short-term disruptions of existing pattern of sizes, and 2) transition zones between long-term trends in sizes. To some degree, all wells exhibited cyclic changes in mean size and variance during unloading. In half of the wells, it was observed that size selection by the unloaders induced a change in mean size. As a result of stratification, the sequence of sizes removed from all wells was non-random, regardless of whether a well contained fish from a single set or from more than one set. The number of modal sizes in a well was not related to the number of sets. In an additional well composed of fish from several sets, an experiment on vertical mixing indicated that a representative sample of the contents may be restricted to the bottom half of the well. The contents of the test wells were used to generate 25 simulated wells and to compare the results of three sampling methods applied to them. The methods were: (1) random sampling (also used as a standard), (2) protracted sampling, in which the selection process was extended over a large portion of a well, and (3) measuring fish consecutively during removal from the well. Repeated sampling by each method and different combinations indicated that, because the principal source of size variation occurred among primary units, increasing n was the most effective way to reduce the variance estimates of both the age-group sizes and the total number of fish in the landings. Protracted sampling largely circumvented the effects of size stratification, and its performance was essentially comparable to that of random sampling. Sampling by this method is recommended. Consecutive-fish sampling produced more biased estimates with greater variances. Analysis of the 1988 length-frequency samples indicated that, for age groups that appear most frequently in the catch, a minimum sampling frequency of one primary unit in six for each month-area stratum would reduce the coefficients of variation (CV) of their size estimates to approximately 10 percent or less. Additional stratification of samples by set type, rather than month-area alone, further reduced the CV's of scarce age groups, such as the recruits, and potentially improved their accuracy. The CV's of recruitment estimates for completely-fished cohorts during the 198184 period were in the vicinity of 3 to 8 percent. Recruitment estimates and their variances were also relatively insensitive to changes in the individual quarterly catches and variances, respectively, of which they were composed. SPANISH: Se usa un diseño de muestreo de dos etapas para estimar las varianzas de los números de aletas amari11as en distintos grupos de edad capturados en el Océano Pacifico oriental. Para barcos cerqueros, la unidad primaria de muestreo (n) es una bodega de salmuera que contenía peces de un estrato de mes-área; el numero de ta11as de peces (m) medidas de cada bodega es la unidad secundaria. Limitaciones de carácter practico impiden la selección aleatoria de peces de las bodegas. Por 10 tanto, fueron examinados los efectos de distintos métodos de muestreo y otros factores sobre la confiabilidad y precisión de las estadísticas derivadas de los datos de frecuencia de ta11a. Se recomiendan modificaciones donde sean necesarias. Las ta11as de peces medidas durante la descarga de seis bodegas de prueba revelaron dos formas de estratificación inherente por ta11a: 1) perturbaciones a corto plazo en la pauta de ta11as existente, y 2) zonas de transición entre las tendencias a largo plazo en las ta11as. En cierto grado, todas las bodegas mostraron cambios cíclicos en ta11a media y varianza durante la descarga. En la mitad de las bodegas, se observo que selección por ta11a por los descargadores indujo un cambio en la ta11a media. Como resultado de la estratificación, la secuencia de ta11as sacadas de todas las bodegas no fue aleatoria, sin considerar si una bodega contenía peces de un solo lance 0 de mas de uno. El numero de ta11as modales en una bodega no estaba relacionado al numero de lances. En una bodega adicional compuesta de peces de varios lances, un experimento de mezcla vertical indico que una muestra representativa del contenido podría estar limitada a la mitad inferior de la bodega. Se uso el contenido de las bodegas de prueba para generar 25 bodegas simuladas y comparar los resultados de tres métodos de muestreo aplicados a estas. Los métodos fueron: (1) muestreo aleatorio (usado también como norma), (2) muestreo extendido, en el cual el proceso de selección fue extendido sobre una porción grande de una bodega, y (3) medición consecutiva de peces durante la descarga de la bodega. EI muestreo repetido con cada método y distintas combinaciones de n y m indico que, puesto que la fuente principal de variación de ta11a ocurría entre las unidades primarias, aumentar n fue la manera mas eficaz de reducir las estimaciones de la varianza de las ta11as de los grupos de edad y el numero total de peces en los desembarcos. El muestreo extendido evito mayormente los efectos de la estratificación por ta11a, y su desempeño fue esencialmente comparable a aquel del muestreo aleatorio. Se recomienda muestrear con este método. El muestreo de peces consecutivos produjo estimaciones mas sesgadas con mayores varianzas. Un análisis de las muestras de frecuencia de ta11a de 1988 indico que, para los grupos de edad que aparecen con mayor frecuencia en la captura, una frecuencia de muestreo minima de una unidad primaria de cada seis para cada estrato de mes-área reduciría los coeficientes de variación (CV) de las estimaciones de ta11a correspondientes a aproximadamente 10% 0 menos. Una estratificación adicional de las muestras por tipo de lance, y no solamente mes-área, redujo aun mas los CV de los grupos de edad escasos, tales como los reclutas, y mejoró potencialmente su precisión. Los CV de las estimaciones del reclutamiento para las cohortes completamente pescadas durante 1981-1984 fueron alrededor de 3-8%. Las estimaciones del reclutamiento y sus varianzas fueron también relativamente insensibles a cambios en las capturas de trimestres individuales y las varianzas, respectivamente, de las cuales fueron derivadas. (PDF contains 70 pages)

Force chains, friction, and flow: Behavior of granular media across length scales

We study the behavior of granular materials at three length scales. At the smallest length scale, the grain-scale, we study inter-particle forces and "force chains". Inter-particle forces are the natural building blocks of constitutive laws for granular materials. Force chains are a key signature of the heterogeneity of granular systems. Despite their fundamental importance for calibrating grain-scale numerical models and elucidating constitutive laws, inter-particle forces have not been fully quantified in natural granular materials. We present a numerical force inference technique for determining inter-particle forces from experimental data and apply the technique to two-dimensional and three-dimensional systems under quasi-static and dynamic load. These experiments validate the technique and provide insight into the quasi-static and dynamic behavior of granular materials.

At a larger length scale, the mesoscale, we study the emergent frictional behavior of a collection of grains. Properties of granular materials at this intermediate scale are crucial inputs for macro-scale continuum models. We derive friction laws for granular materials at the mesoscale by applying averaging techniques to grain-scale quantities. These laws portray the nature of steady-state frictional strength as a competition between steady-state dilation and grain-scale dissipation rates. The laws also directly link the rate of dilation to the non-steady-state frictional strength.

At the macro-scale, we investigate continuum modeling techniques capable of simulating the distinct solid-like, liquid-like, and gas-like behaviors exhibited by granular materials in a single computational domain. We propose a Smoothed Particle Hydrodynamics (SPH) approach for granular materials with a viscoplastic constitutive law. The constitutive law uses a rate-dependent and dilation-dependent friction law. We provide a theoretical basis for a dilation-dependent friction law using similar analysis to that performed at the mesoscale. We provide several qualitative and quantitative validations of the technique and discuss ongoing work aiming to couple the granular flow with gas and fluid flows.

Transmission matrices and lumped parameter models for continuous systems

The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

Spontaneous and stimulated light emission due to radiative recombination in forward biased lead telluride P-N junctions

Since the discovery in 1962 of laser action in semiconductor diodes made from GaAs, the study of spontaneous and stimulated light emission from semiconductors has become an exciting new field of semiconductor physics and quantum electronics combined. Included in the limited number of direct-gap semiconductor materials suitable for laser action are the members of the lead salt family, i.e . PbS, PbSe and PbTe. The material used for the experiments described herein is PbTe . The semiconductor PbTe is a narrow band- gap material (E_g = 0.19 electron volt at a temperature of 4.2°K). Therefore, the radiative recombination of electron-hole pairs between the conduction and valence bands produces photons whose wavelength is in the infrared (λ ≈ 6.5 microns in air).

The p-n junction diode is a convenient device in which the spontaneous and stimulated emission of light can be achieved via current flow in the forward-bias direction. Consequently, the experimental devices consist of a group of PbTe p-n junction diodes made from p –type single crystal bulk material. The p - n junctions were formed by an n-type vapor- phase diffusion perpendicular to the (100) plane, with a junction depth of approximately 75 microns. Opposite ends of the diode structure were cleaved to give parallel reflectors, thereby forming the Fabry-Perot cavity needed for a laser oscillator. Since the emission of light originates from the recombination of injected current carriers, the nature of the radiation depends on the injection mechanism.

The total intensity of the light emitted from the PbTe diodes was observed over a current range of three to four orders of magnitude. At the low current levels, the light intensity data were correlated with data obtained on the electrical characteristics of the diodes. In the low current region (region A), the light intensity, current-voltage and capacitance-voltage data are consistent with the model for photon-assisted tunneling. As the current is increased, the light intensity data indicate the occurrence of a change in the current injection mechanism from photon-assisted tunneling (region A) to thermionic emission (region B). With the further increase of the injection level, the photon-field due to light emission in the diode builds up to the point where stimulated emission (oscillation) occurs. The threshold current at which oscillation begins marks the beginning of a region (region C) where the total light intensity increases very rapidly with the increase in current. This rapid increase in intensity is accompanied by an increase in the number of narrow-band oscillating modes. As the photon density in the cavity continues to increase with the injection level, the intensity gradually enters a region of linear dependence on current (region D), i.e. a region of constant (differential) quantum efficiency.

Data obtained from measurements of the stimulated-mode light-intensity profile and the far-field diffraction pattern (both in the direction perpendicular to the junction-plane) indicate that the active region of high gain (i.e. the region where a population inversion exists) extends to approximately a diffusion length on both sides of the junction. The data also indicate that the confinement of the oscillating modes within the diode cavity is due to a variation in the real part of the dielectric constant, caused by the gain in the medium. A value of τ ≈ 10^-9 second for the minority- carrier recombination lifetime (at a diode temperature of 20.4°K) is obtained from the above measurements. This value for τ is consistent with other data obtained independently for PbTe crystals.

Data on the threshold current for stimulated emission (for a diode temperature of 20. 4°K) as a function of the reciprocal cavity length were obtained. These data yield a value of J’_th = (400 ± 80) amp/cm² for the threshold current in the limit of an infinitely long diode-cavity. A value of α = (30 ± 15) cm^-1 is obtained for the total (bulk) cavity loss constant, in general agreement with independent measurements of free- carrier absorption in PbTe. In addition, the data provide a value of n_s ≈ 10% for the internal spontaneous quantum efficiency. The above value for n_s yields values of t_b ≈ τ ≈ 10^-9 second and t_s ≈ 10^-8 second for the nonradiative and the spontaneous (radiative) lifetimes, respectively.

The external quantum efficiency (n_d) for stimulated emission from diode J-2 (at 20.4° K) was calculated by using the total light intensity vs. diode current data, plus accepted values for the material parameters of the mercury- doped germanium detector used for the measurements. The resulting value is n_d ≈ 10%-20% for emission from both ends of the cavity. The corresponding radiative power output (at λ = 6.5 micron) is 120-240 milliwatts for a diode current of 6 amps.

Length and sex effects on the spatial structure of catches of Pacific halibut (Hippoglossus stenolepis) on longline gear

Field experiments were conducted to test the hypotheses that Pacific halibut (Hippoglossus stenolepis) display small-scale spatial structure within longline catches, relative to other species and empty hooks, or within-species based on sex or length. Sequential hook-by-hook inventories, along with length and sex data, were taken at thirty-one survey stations. Two-dimensional spatial statistics were used to test for 1) aggregation, defined as the clustering of individuals within a given demographic of size or sex over small intervals of distance; and 2) segregation, defined as the sequential occurrence of individuals within a given demographic of size or sex, uninterrupted by other observations, irrespective of the distance between individuals. Statistically significant structure was detected within catches that is more commonly associated with fish length than sex. Significant spatial structuring occurred at 60% of all stations tested. Significant aggregation of halibut of legal length for commercial retention (≥82 cm) was detected at 44% of stations and aggregation of sublegal-size halibut was detected at 11%. Maleand female-based aggregations were observed at 22% and 11% of stations, respectively. Significant segregation of females was observed at 20% of stations, male segregation occurred at 8% of stations, and segregation by size at 16% of stations. Understanding small-scale spatial structure within longline catches may help us interpret changes in survey and commercial catch data. If structure is generated by behavior, then observed size-at-age or relative sex-ratios may be biased relative to underlying distributions. Although physical processes such as gape limitation should remain stable over the time, dynamic processes may be spatially and temporally variabl

Interactions of age-dependent mortality and selectivity functions in age-based stock assessment models

The natural mortality rate (M) of fish varies with size and age, although it is often assumed to be constant in stock assessments. Misspecification of M may bias important assessment quantities. We simulated fishery data, using an age-based population model, and then conducted stock assessments on the simulated data. Results were compared to known values. Misspecification of M had a negligible effect on the estimation of relative stock depletion; however, misspecification of M had a large effect on the estimation of parameters describing the stock recruitment relationship, age-specific selectivity, and catchability. If high M occurs in juvenile and old fish, but is misspecified in the assessment model, virgin biomass and catchability are often poorly estimated. In addition, stock recruitment relationships are often very difficult to estimate, and steepness values are commonly estimated at the upper bound (1.0) and overfishing limits tend to be biased low. Natural mortality can be estimated in assessment models if M is constant across ages or if selectivity is asymptotic. However if M is higher in old fish and selectivity is dome-shaped, M and the selectivity cannot both be adequately estimated because of strong interactions between M and selectivity.

Age and growth of spiny dogfish (Squalus acanthias) in the Gulf of Alaska: analysis of alternative growth models

Ten growth models were fitted to age and growth data for spiny dogfish (Squalus acanthias) in the Gulf of Alaska. Previous studies of spiny dogfish growth have all fitted the t0 formulation of the von Bertalanffy model without examination of alternative models. Among the alternatives, we present a new two-phase von Bertalanffy growth model formulation with a logistically scaled k parameter and which estimates L0. A total of 1602 dogfish were aged from opportunistic collections with longline, rod and reel, set net, and trawling gear in the eastern and central Gulf of Alaska between 2004 and 2007. Ages were estimated from the median band count of three independent readings of the second dorsal spine plus the estimated number of worn bands for worn spines. Owing to a lack of small dogfish in the samples, lengths at age of small individuals were back-calculated from a subsample of 153 dogfish with unworn spines. The von Bertalanffy, two-parameter von Bertalanffy, two-phase von Bertalanffy, Gompertz, two-parameter Gompertz, and logistic models were fitted to length-at-age data for each sex separately, both with and without back-calculated lengths at age. The two-phase von Bertalanffy growth model produced the statistically best fit for both sexes of Gulf of Alaska spiny dogfish, resulting in L∞ = 87.2 and 102.5 cm and k= 0.106 and 0.058 for males and females, respectively.

Age- and length-at-maturity of female arrowtooth flounder (Atheresthes stomias) in the Gulf of Alaska

Arrowtooth flounder (Atheresthes stomias) has had the highest abundance of any groundfish species in the Gulf of Alaska since the 1970s (Matarese et al., 2003; Turnock et al., 2005; Blood et al., 2007); however, commercial catches have been restricted because Pacific halibut (Hippoglossus stenolepis) are caught as bycatch in the fishery. Arrowtooth flounder plays a key role in the ecosystem because it is a dominant organism within the food web, both as an apex predator of fish and invertebrates, as well as an important prey for walleye pollock (Theragra chalcogramma; Aydin et al., 2002). Walleye pollock is the dominant groundfish in the Bering Sea, a principal groundfish in the Gulf of Alaska, and the primary prey for marine mammals. The distribution of arrowtooth flounder extends from Cape Navarin and the eastern Sea of Okhotsk in Russia, across the Bering Sea, Aleutian Islands, Gulf of Alaska, and south to the coast of central California (Shuntov, 1964; Britt and Martin, 2001; Chetvergov, 2001; Weinberg et al., 2002; Zenger, 2004). Because of the importance of arrowtooth flounder in the marine ecosystem of A laska, a maturity study of this species was undertaken to determine age-at-maturity, which is essential for age-based stock management models. Before these results, management has had to rely upon a length-at-maturity-based estimate (Zimmermann, 1997) to manage stocks in the Gulf of Alaska (GOA), Bering Sea, and Aleutian Islands. The central GOA was selected as the location for this maturity study Age- and length-at-maturity of female arrowtooth flounder (Atheresthes stomias) in the Gulf of Alaska because it contains approximately 70% of the total Gulf of Alaska arrowtooth flounder biomass (1.9×106 t, age 3 and older)— the highest percentage in the world (Shuntov, 1964; Britt and Martin, 2001; Weinberg et al., 2002; Wilderbuer and Nichol, 2006).

Natural mortality rate, annual fecundity, and maturity at length for Greenland halibut (Reinhardtius hippoglossoides) from the northeastern Pacific Ocean

Mortality, fecundity, and size at maturity are important life history traits, and their interactions determine the evolution of life history strategies (Roff, 1992; Stearns, 1992; Charnov, 2002). These same traits are also important for population dynamics models (Hunter et al., 1992; Clark, 1999). It is increasingly important to accurately determine Greenland halibut (Reinhardtius hippoglossoides) life history traits and to correctly assess the status of its stocks because low recruitment or low biomass estimates have led to catch restrictions in the Bering Sea and Aleutian Islands (Ianelli et al.1), the Northeastern Arctic (Ådlandsvik et al., 2004), and the Northwest Atlantic (Bowering and Nedreaas, 2000).

Parameterizing probabilities for estimating age-composition distributions for mixture models

When estimating parameters that constitute a discrete probability distribution {pj}, it is difficult to determine how constraints should be made to guarantee that the estimated parameters { pˆj} constitute a probability distribution (i.e., pˆj>0, Σ pˆj =1). For age distributions estimated from mixtures of length-at-age distributions, the EM (expectationmaximization) algorithm (Hasselblad, 1966; Hoenig and Heisey, 1987; Kimura and Chikuni, 1987), restricted least squares (Clark, 1981), and weak quasisolutions (Troynikov, 2004) have all been used. Each of these methods appears to guarantee that the estimated distribution will be a true probability distribution with all categories greater than or equal to zero and with individual probabilities that sum to one. In addition, all these methods appear to provide a theoretical basis for solutions that will be either maximum-likelihood estimates or at least convergent to a probability distribut

Length-girth relationships of Barbodes gonionotus and Hampala macrolepidota in the Jatiluhur reservoir, Indonesia

The length-girth relationships of Javanese carp (Barbodes gonionotus) and hampal carp (Hampala macrolepidota) in the Jatilujur Reservoir, Indonesia were examined. The equations derived from estimating the maximum girth of Javanese carp are G sub(m) = -1.19 + 0.80L, and for the hampal carp, G super(m) = -0.47 + 0.62L. Models relating head girth to total length are also given. The relationship between G sub(m) (maximum girth) of fish caught and gillnet mesh size is also briefly discussed.

Length-weight Relationships of Dolphinfish, Coryphaena hippurus, and Wahoo, Acanthocybium solandri: Seasonal Effects of Spawning and Possible Migration in the Central North Pacific

Weight-on-length (W-L) relationships for 2,482 dolphinfish, Coryphaena hippurus, and 1,161 wahoo, Acanthocybium solandri, were examined. Data on fork length, whole (round) weight, and sex were collected for dolphinfish at the Honolulu fish auction from March 1988 through November 1989. Unsexed weight and length data for wahoo were collected at the auction from July 1988 through November 1989. We also used sex specific weight and length data of 171 wahoo collected during 1977–1985 research cruises for analysis. Coefficients of W-L regressions were significantly different between the sexes for dolphinfish. Coefficients did not significantly differ between the sexes for wahoo based on research cruise data. In a general linear model evaluating month as a categorical factor, month was significant for female dolphinfish, male dolphinfish, and wahoo with sexes pooled. W-L and length-on-weight (L-W) relationships were fitted by nonlinear regression for all dolphinfish, female dolphinfish, male dolphinfish, and all wahoo sexes pooled. W-L relationships for monthly samples of female dolphinfish, male dolphinfish, and all wahoo with sexes pooled were also fitted by nonlinear regression. Predicted mean weight at length for wahoo was highest at the beginning of the spawning season in June and lowest after the spawning season in September. Maximum and minimum predicted mean weight at length for both sexes of dolphinfish did not correspond with the peak spawning period (March–May). Plausible migration models in conjunction with reproductive behavior were examined to explain the variability in monthly predicted mean weight at length for dolphinfish.

Human muscle spindles act as forward sensory models.

Modern theories of motor control incorporate forward models that combine sensory information and motor commands to predict future sensory states. Such models circumvent unavoidable neural delays associated with on-line feedback control. Here we show that signals in human muscle spindle afferents during unconstrained wrist and finger movements predict future kinematic states of their parent muscle. Specifically, we show that the discharges of type Ia afferents are best correlated with the velocity of length changes in their parent muscles approximately 100-160 ms in the future and that their discharges vary depending on motor sequences in a way that cannot be explained by the state of their parent muscle alone. We therefore conclude that muscle spindles can act as "forward sensory models": they are affected both by the current state of their parent muscle and by efferent (fusimotor) control, and their discharges represent future kinematic states. If this conjecture is correct, then sensorimotor learning implies learning how to control not only the skeletal muscles but also the fusimotor system.