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Papers by James Matis

Bulletin of Mathematical Biology, Aug 1, 1974

... 448 JH MATIS, M. CARDENAS AND RL KODELL p2(t), pa(t), N], where p3(t) -- 1 - kpl(t ) - p~(t),... more ... 448 JH MATIS, M. CARDENAS AND RL KODELL p2(t), pa(t), N], where p3(t) -- 1 - kpl(t ) - p~(t), and as an immediate conse-quence the means, variances and covariances of the peripheral compartments arc: E[X~(t)] = NPl(t), (6) V[X,(t)] = Npl(t)[1 - pl(t)], (7) and Coy [Xt(t), Xj(t ...

Springer eBooks, 1988

Linear compartmental models are being widely used to model pharmacokinetic systems. Most of these... more Linear compartmental models are being widely used to model pharmacokinetic systems. Most of these models are deterministic and the statistical analysis of such models has been studied extensively. Many deterministic models are illustrated in other papers of this volume, and recent reviews are also given by Gibaldi and Perrier (1982), Godfrey (1983), and Jacquez (1985).

Ecological Modelling, Apr 1, 1992

ABSTRACT This paper develops a semi-Markov process model for describing ecological data, and demo... more ABSTRACT This paper develops a semi-Markov process model for describing ecological data, and demonstrates the utility of the model by fitting it to data on the migration of a marked population of shrimp. Gamma transit time distributions are selected for the model by reason of the qualitative properties of their transfer rate functions. Occupancy probabilities, mean residence times and other related parameters are estimated from the data for the assumed semi-Markov process model. These results are compared to those for a corresponding Markov process model which is widely used and was previously fitted to the same data. The semi-Markov process model provides a better fit for the data with substantial increases in the precision of corresponding parameter estimates. Further generalizations of this compartmental modeling approach to other semi-Markov process models are also discussed.

Mathematical biosciences, Oct 1, 2008

Mechanistic models in which the per-capita death rate of a population is proportional to cumulati... more Mechanistic models in which the per-capita death rate of a population is proportional to cumulative past size have been shown to describe adequately the population size curves for a number of aphid species. Such previous cumulative-sized based models have not included immigration. The inclusion of immigration is suggested biologically as local aphid populations are initiated by migration of winged aphids and as reproduction is temperature-dependent. This paper investigates two models with constant immigration, one with continuous immigration and the other with restricted immigration. Cases of the latter are relatively simple to fit to data. The results from these two immigration models are compared for data sets on the mustard aphid in India.

Canadian Journal of Animal Science, Dec 1, 1984

A stochastic model provided a better fit than did two deterministic, exponential models of in vit... more A stochastic model provided a better fit than did two deterministic, exponential models of in vitro digestion of fiber of varied size particles produced by ingestive mastication. Variations in rates of digestion within and among such varied size particles suggest rumen fiber digestion is a highly stochastic process. Key words: Rumen, microbial, fiber, models, stochastic

Water Resources Research, Aug 1, 1973

ABSTRACT

Journal of Animal Science, 1990

Two experiments were conducted to measure effects of source and level of roughage on the flow of ... more Two experiments were conducted to measure effects of source and level of roughage on the flow of corn residues through the gastrointestinal tract of cattle. In Exp. 1, steers (195 kg) were fed diets of ground corn with 0, 30 or 60% of ground Coastal bermudagrass hay (Cynodon dactylon) [L.] Pers.) at intakes of 1, 1.5 or 2% of BW in a 9 x 9 Latin square. Experiment 2 consisted of two 4 x 4 Latin squares with either rice hulls (square 1) or ground Coastal bermudagrass hay (square 2) providing 0, 7.5, 15 or 30% of the total diet fed at 1.5% of BW. After a 28-d adjustment period, a portion of the corn in one meal was replaced with cracked corn stained with brilliant green. The concentrations of stained corn residues appearing in the feces subsequent to dosing were fitted to a one-compartment, age-dependent model and compartmental mean residence time (CMRT) and time delay (tau) were estimated. In Exp. 1, increasing the level of intake of the ration from 1% to 1.5 or 2.0% of BW increased (P less than .05) CMRT by 52% and reduced (P less than .05) tau by 41%. In Exp. 2, source of roughage had no effect (P = .95) on CMRT or tau. Combined results of the two experiments indicated that increasing proportion (P) of either roughage was associated with an exponential decline in CMRT of stained corn residues (CMRT = 1211 * e-.0315P) from rations consumed at 1.5 and 2.0% of BW. No consistent effect of roughage type or proportion was noted on time delay in the two experiments collectively. These results indicate that increasing the proportion of roughage in the diet exponentially reduces residence time of corn residues in the ruminoreticulum (CMRT) without affecting residence time in the postgastric segments (tau).

Journal of Applied Ecology, Apr 1, 1983

Journal of Fish Biology, Jul 1, 1975

The effects were studied of a 24 h exposure to a subacute concentration of parathion (0.33 p.p.m.... more The effects were studied of a 24 h exposure to a subacute concentration of parathion (0.33 p.p.m., which is approximately equivalent to 0.5 of the 48-h LC,& on the locomotor orientation of mature goldfish C i i r~r~~i i i s aurmtu~ L , 26-30 cm long, in response to a food odour and a water flow differential, singly and in combination, in a free choice situation. Prior to exposure, food odour alone was significantly attractive but the combination ' food oduur with increased water flow ', as compared mth thc control situation, was avoided. Factorial analysis demomtrated interaction betwccn odour and increased flow. Aftcr exposure to parathion the food odour ceaqed to be attractive and was significantly avoided. This avoidance was not prescnt in thc + food odour-increased flow. combination. The parathion exposure did not affect the response to the flow conditions per SY but reversed the interaction between food odour and increased flow. In addition, the exposure to the pesticide itself, in a second order interaction, interacted with ' food odour-flow ' response. Hence, the short term exposure to the subacute organophosphate concentration affected not only the perception of food odour and flow individually, but also the interaction between these commoii environniental stimuli.

Ecological Modelling, Aug 1, 2009

Density dependent feedback, based on cumulative population size, has been advocated to explain an... more Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize "boom and bust" population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl-Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.

Water Resources Research, Dec 1, 1972

The locomotor response of goldfish, largemouth bass, and channel catfish to ‘copper-polluted’ wat... more The locomotor response of goldfish, largemouth bass, and channel catfish to ‘copper-polluted’ water at a maximum concentration of 50 μg/l Cu++ in an open field, free choice situation was monitored. The rate of water flow was 1.8 cm/sec. The largemouth bass were unaffected, but the goldfish and the channel catfish tended to orient themselves toward the source of the ion. The degree of this orientation was less, however, than that found in shallower gradients of the same copper concentration as described by Kleerekoper et al. in 1972. When goldfish were exposed to the copper ion in a uniform field so that neither avoidance of nor attraction to the polluted mass was possible, no change in orientation was observed. It is concluded that the slope of the copper gradient between ‘clean’ and ‘polluted’ water rather than the eventual highest concentration of the ion (50 μg/1) affected the orientation and the locomotor behavior of the catfish and the goldfish.

Theoretical Population Biology, Feb 1, 1998

The deterministic power law logistic model is used to describe density-dependent population growt... more The deterministic power law logistic model is used to describe density-dependent population growth in cases where the ordinary logistic model is insufficient. This paper investigates an analogous stochastic power law logistic model. The exact (unconditional) population size distributions and the cumulant functions for this stochastic model are intractable for large population sizes. Approximating cumulant functions are derived for populations of any size, and are illustrated with examples of assumed Africanized honey bee population dynamics. Outstanding among the findings is that the approximations for the cumulant functions are very accurate for these examples. The stochastic power law logistic model is very general and may be applied to describe the growth of many other natural populations.

Journal of Comparative Physiology A-neuroethology Sensory Neural and Behavioral Physiology, 1975

The locomotor response of juvenileGinglymostoma cirratum, the nurse shark, to six covert, discret... more The locomotor response of juvenileGinglymostoma cirratum, the nurse shark, to six covert, discrete sources of an attractant chemical stimulus (fresh shrimp extract) was monitored in a tank (5×5×0.5 m) by means of a square matrix of 1936 photocells embedded in the floor and an on line computer. The experiments were done in flowing (1.17 cm/s) and stagnant water in order

Journal of the Fisheries Research Board of Canada, 1972

In slowly flowing water, seven naive goldfish 30-cm long changed their locomotor behavior upon en... more In slowly flowing water, seven naive goldfish 30-cm long changed their locomotor behavior upon entering a mass of water containing shallow gradients of copper chloride. The concentration was 11–17 μg/liter Cu++ in most of this mass, with small isolated pockets containing maximally 50 μg/liter. The amount of time spent by the fish, the average size of turn, and the variance of the size of turn increased in the "polluted" region. The orientation of the fish in this region deviated consistently in the upstream direction resulting in the increase in time spent in the area of highest concentration. Comparison of the locomotor behavior of the fish in sodium chloride of the same concentration and in laboratory water established that the changes mentioned were in response to the copper rather than the chloride ion.

CRC Press eBooks, Feb 1, 2011

The well-known Verhulst-Pearl model in ecology, (()) () N Nt Nt = where N(t) denotes current popu... more The well-known Verhulst-Pearl model in ecology, (()) () N Nt Nt = where N(t) denotes current population size, has a solution which may be written in the form of a logistic cumulative distribution function (cdf). It is widely used to describe population growth curves (Renshaw, 1991). An alternative model

Lecture notes in statistics, 2000

Consider now adding births to the previous linear multidimensional models discussed in Chapters 1... more Consider now adding births to the previous linear multidimensional models discussed in Chapters 10 and 11. The assumptions are then 1 Prob{Xiwill increase by 1 due to immigration{ = I i Δt 2 Prob{Xiwill decrease by 1 due to death{=µ i X i Δt 3 Prob {Xiwill increase by 1 due to birth{=λ i X i Δt 4 Prob{Xiwill increase by 1 and Xjwill decrease by 1 due to migration{= k ij X j Δt for i,j=1,2 with i ≠ j

This paper describes a new and innovative approach to the instruction of applied stochastic proce... more This paper describes a new and innovative approach to the instruction of applied stochastic processes at institutions of higher education and a method for introducing this topic to K-12 students for pre-course motivation. This approach consists of incorporating laboratory modules via digital video media that present real-world applications of stochastic processes into coursework. The modules engage the students in problem solving, thereby creating a conceptual framework for learning the subject. The pedagogy behind this instructional approach and module content is described in this paper. Preliminary evaluations are presented for assessment purposes from a pilot implementation of the modules at the collegiate level.

Bulletin of Mathematical Biology, Nov 1, 1981

ABSTRACT

Soil Science Society of America Journal, Mar 1, 1985

Bulletin of Mathematical Biology, Aug 1, 1974

... 448 JH MATIS, M. CARDENAS AND RL KODELL p2(t), pa(t), N], where p3(t) -- 1 - kpl(t ) - p~(t),... more ... 448 JH MATIS, M. CARDENAS AND RL KODELL p2(t), pa(t), N], where p3(t) -- 1 - kpl(t ) - p~(t), and as an immediate conse-quence the means, variances and covariances of the peripheral compartments arc: E[X~(t)] = NPl(t), (6) V[X,(t)] = Npl(t)[1 - pl(t)], (7) and Coy [Xt(t), Xj(t ...

Springer eBooks, 1988

Linear compartmental models are being widely used to model pharmacokinetic systems. Most of these... more Linear compartmental models are being widely used to model pharmacokinetic systems. Most of these models are deterministic and the statistical analysis of such models has been studied extensively. Many deterministic models are illustrated in other papers of this volume, and recent reviews are also given by Gibaldi and Perrier (1982), Godfrey (1983), and Jacquez (1985).

Ecological Modelling, Apr 1, 1992

ABSTRACT This paper develops a semi-Markov process model for describing ecological data, and demo... more ABSTRACT This paper develops a semi-Markov process model for describing ecological data, and demonstrates the utility of the model by fitting it to data on the migration of a marked population of shrimp. Gamma transit time distributions are selected for the model by reason of the qualitative properties of their transfer rate functions. Occupancy probabilities, mean residence times and other related parameters are estimated from the data for the assumed semi-Markov process model. These results are compared to those for a corresponding Markov process model which is widely used and was previously fitted to the same data. The semi-Markov process model provides a better fit for the data with substantial increases in the precision of corresponding parameter estimates. Further generalizations of this compartmental modeling approach to other semi-Markov process models are also discussed.

Mathematical biosciences, Oct 1, 2008

Mechanistic models in which the per-capita death rate of a population is proportional to cumulati... more Mechanistic models in which the per-capita death rate of a population is proportional to cumulative past size have been shown to describe adequately the population size curves for a number of aphid species. Such previous cumulative-sized based models have not included immigration. The inclusion of immigration is suggested biologically as local aphid populations are initiated by migration of winged aphids and as reproduction is temperature-dependent. This paper investigates two models with constant immigration, one with continuous immigration and the other with restricted immigration. Cases of the latter are relatively simple to fit to data. The results from these two immigration models are compared for data sets on the mustard aphid in India.

Canadian Journal of Animal Science, Dec 1, 1984

A stochastic model provided a better fit than did two deterministic, exponential models of in vit... more A stochastic model provided a better fit than did two deterministic, exponential models of in vitro digestion of fiber of varied size particles produced by ingestive mastication. Variations in rates of digestion within and among such varied size particles suggest rumen fiber digestion is a highly stochastic process. Key words: Rumen, microbial, fiber, models, stochastic

Water Resources Research, Aug 1, 1973

ABSTRACT

Journal of Animal Science, 1990

Two experiments were conducted to measure effects of source and level of roughage on the flow of ... more Two experiments were conducted to measure effects of source and level of roughage on the flow of corn residues through the gastrointestinal tract of cattle. In Exp. 1, steers (195 kg) were fed diets of ground corn with 0, 30 or 60% of ground Coastal bermudagrass hay (Cynodon dactylon) [L.] Pers.) at intakes of 1, 1.5 or 2% of BW in a 9 x 9 Latin square. Experiment 2 consisted of two 4 x 4 Latin squares with either rice hulls (square 1) or ground Coastal bermudagrass hay (square 2) providing 0, 7.5, 15 or 30% of the total diet fed at 1.5% of BW. After a 28-d adjustment period, a portion of the corn in one meal was replaced with cracked corn stained with brilliant green. The concentrations of stained corn residues appearing in the feces subsequent to dosing were fitted to a one-compartment, age-dependent model and compartmental mean residence time (CMRT) and time delay (tau) were estimated. In Exp. 1, increasing the level of intake of the ration from 1% to 1.5 or 2.0% of BW increased (P less than .05) CMRT by 52% and reduced (P less than .05) tau by 41%. In Exp. 2, source of roughage had no effect (P = .95) on CMRT or tau. Combined results of the two experiments indicated that increasing proportion (P) of either roughage was associated with an exponential decline in CMRT of stained corn residues (CMRT = 1211 * e-.0315P) from rations consumed at 1.5 and 2.0% of BW. No consistent effect of roughage type or proportion was noted on time delay in the two experiments collectively. These results indicate that increasing the proportion of roughage in the diet exponentially reduces residence time of corn residues in the ruminoreticulum (CMRT) without affecting residence time in the postgastric segments (tau).

Journal of Applied Ecology, Apr 1, 1983

Journal of Fish Biology, Jul 1, 1975

The effects were studied of a 24 h exposure to a subacute concentration of parathion (0.33 p.p.m.... more The effects were studied of a 24 h exposure to a subacute concentration of parathion (0.33 p.p.m., which is approximately equivalent to 0.5 of the 48-h LC,& on the locomotor orientation of mature goldfish C i i r~r~~i i i s aurmtu~ L , 26-30 cm long, in response to a food odour and a water flow differential, singly and in combination, in a free choice situation. Prior to exposure, food odour alone was significantly attractive but the combination ' food oduur with increased water flow ', as compared mth thc control situation, was avoided. Factorial analysis demomtrated interaction betwccn odour and increased flow. Aftcr exposure to parathion the food odour ceaqed to be attractive and was significantly avoided. This avoidance was not prescnt in thc + food odour-increased flow. combination. The parathion exposure did not affect the response to the flow conditions per SY but reversed the interaction between food odour and increased flow. In addition, the exposure to the pesticide itself, in a second order interaction, interacted with ' food odour-flow ' response. Hence, the short term exposure to the subacute organophosphate concentration affected not only the perception of food odour and flow individually, but also the interaction between these commoii environniental stimuli.

Ecological Modelling, Aug 1, 2009

Density dependent feedback, based on cumulative population size, has been advocated to explain an... more Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize "boom and bust" population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl-Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.

Water Resources Research, Dec 1, 1972

The locomotor response of goldfish, largemouth bass, and channel catfish to ‘copper-polluted’ wat... more The locomotor response of goldfish, largemouth bass, and channel catfish to ‘copper-polluted’ water at a maximum concentration of 50 μg/l Cu++ in an open field, free choice situation was monitored. The rate of water flow was 1.8 cm/sec. The largemouth bass were unaffected, but the goldfish and the channel catfish tended to orient themselves toward the source of the ion. The degree of this orientation was less, however, than that found in shallower gradients of the same copper concentration as described by Kleerekoper et al. in 1972. When goldfish were exposed to the copper ion in a uniform field so that neither avoidance of nor attraction to the polluted mass was possible, no change in orientation was observed. It is concluded that the slope of the copper gradient between ‘clean’ and ‘polluted’ water rather than the eventual highest concentration of the ion (50 μg/1) affected the orientation and the locomotor behavior of the catfish and the goldfish.

Theoretical Population Biology, Feb 1, 1998

The deterministic power law logistic model is used to describe density-dependent population growt... more The deterministic power law logistic model is used to describe density-dependent population growth in cases where the ordinary logistic model is insufficient. This paper investigates an analogous stochastic power law logistic model. The exact (unconditional) population size distributions and the cumulant functions for this stochastic model are intractable for large population sizes. Approximating cumulant functions are derived for populations of any size, and are illustrated with examples of assumed Africanized honey bee population dynamics. Outstanding among the findings is that the approximations for the cumulant functions are very accurate for these examples. The stochastic power law logistic model is very general and may be applied to describe the growth of many other natural populations.

Journal of Comparative Physiology A-neuroethology Sensory Neural and Behavioral Physiology, 1975

The locomotor response of juvenileGinglymostoma cirratum, the nurse shark, to six covert, discret... more The locomotor response of juvenileGinglymostoma cirratum, the nurse shark, to six covert, discrete sources of an attractant chemical stimulus (fresh shrimp extract) was monitored in a tank (5×5×0.5 m) by means of a square matrix of 1936 photocells embedded in the floor and an on line computer. The experiments were done in flowing (1.17 cm/s) and stagnant water in order

Journal of the Fisheries Research Board of Canada, 1972

In slowly flowing water, seven naive goldfish 30-cm long changed their locomotor behavior upon en... more In slowly flowing water, seven naive goldfish 30-cm long changed their locomotor behavior upon entering a mass of water containing shallow gradients of copper chloride. The concentration was 11–17 μg/liter Cu++ in most of this mass, with small isolated pockets containing maximally 50 μg/liter. The amount of time spent by the fish, the average size of turn, and the variance of the size of turn increased in the "polluted" region. The orientation of the fish in this region deviated consistently in the upstream direction resulting in the increase in time spent in the area of highest concentration. Comparison of the locomotor behavior of the fish in sodium chloride of the same concentration and in laboratory water established that the changes mentioned were in response to the copper rather than the chloride ion.

CRC Press eBooks, Feb 1, 2011

The well-known Verhulst-Pearl model in ecology, (()) () N Nt Nt = where N(t) denotes current popu... more The well-known Verhulst-Pearl model in ecology, (()) () N Nt Nt = where N(t) denotes current population size, has a solution which may be written in the form of a logistic cumulative distribution function (cdf). It is widely used to describe population growth curves (Renshaw, 1991). An alternative model

Lecture notes in statistics, 2000

Consider now adding births to the previous linear multidimensional models discussed in Chapters 1... more Consider now adding births to the previous linear multidimensional models discussed in Chapters 10 and 11. The assumptions are then 1 Prob{Xiwill increase by 1 due to immigration{ = I i Δt 2 Prob{Xiwill decrease by 1 due to death{=µ i X i Δt 3 Prob {Xiwill increase by 1 due to birth{=λ i X i Δt 4 Prob{Xiwill increase by 1 and Xjwill decrease by 1 due to migration{= k ij X j Δt for i,j=1,2 with i ≠ j

This paper describes a new and innovative approach to the instruction of applied stochastic proce... more This paper describes a new and innovative approach to the instruction of applied stochastic processes at institutions of higher education and a method for introducing this topic to K-12 students for pre-course motivation. This approach consists of incorporating laboratory modules via digital video media that present real-world applications of stochastic processes into coursework. The modules engage the students in problem solving, thereby creating a conceptual framework for learning the subject. The pedagogy behind this instructional approach and module content is described in this paper. Preliminary evaluations are presented for assessment purposes from a pilot implementation of the modules at the collegiate level.

Bulletin of Mathematical Biology, Nov 1, 1981

ABSTRACT

Soil Science Society of America Journal, Mar 1, 1985