To realize the potential of materials comprising living organisms, bioengineers require a holistic understanding of the reciprocal relationship between environmental conditions and the biochemical and biophysical processes that influence development and behaviour. Mathematical modelling has a critical part to play in managing the complexity of biological dynamical systems and attaining higher degrees of control over their trajectories and endpoints. To support the development of mycelium-based engineered living materials, this paper reviews the literature of growth models for filamentous fungi with emphasis on the connection between morphogenesis and metabolism.

We would like to correct the statement of Lemma 4.1 in [BDK+18].

We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similar to the classical lattice growth models, the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free-branching birth rate.

Weed seeds were germinated in incubators at constant temperatures ranging from 4 to 32 C increments. Percent germination per day was regressed against temperature with the x-intercept representing the low threshold temperature for development. Low threshold temperatures for development (low TTD's) calculated for wild proso millet (Panicum miliaceum L. # PANMI), barnyardgrass [Echinochloa crus-galli (L.) Beauv. # ECHCG], common lambsquarters (Chenopodium album L. # CHEAL), and redroot pigweed (Amaranthus retroflexus L. # AMARE) were 6.9, 9.7, 6.0, and 10.0 C, respectively.

Success of postemergence weed management often depends upon application timing and weed seedling size. To develop a predictive tool for estimating green foxtail development and optimizing timing of management operations, seedling growth was monitored in fields for two years, as well as in a single greenhouse experiment, and compared with elapsed thermal time (growing degree days, GDD, base 10 C). The relationship between seedling height (mm) and GDD was similar both years and could be described by the following equation: Height = (-0.27 + 0.033 * GDD)2. A comparable equation described seedling growth in a greenhouse. Leaf number was linearly related to GDD. Green foxtail in corn was controlled with nicosulfuron applied at seven intervals between 100 and 450 GDD after corn planting in 1993 and 1994. In 1993 corn yield losses due to green foxtail interference were least when nicosulfuron was applied 200 to 300 GDD after planting, at which time green foxtail height was 50 to 100 mm. In 1994 corn yield losses were minimized if nicosulfuron was applied any time before 300 GDD.

We consider a network of interacting individuals, whose actions or transitions are determined by the states (behavior) of their neighbors as well as their own personal decisions. Specifically, we develop a model according to two simple decision-making rules that can describe the growth of the user population of a newly launched product or service. We analyze 22 sets of real-world historical growth data of a variety of products and services, and show that they all follow the growth equation. The numerical procedure for finding the model parameters allows the market size, and the relative effectiveness of customer service and promotional efforts to be estimated from the available historical growth data. We study the growth profiles of products and find that for a product or service to reach a mature stage within a reasonably short time in its user growth profile, the user growth rate corresponding to influenced transitions must exceed a certain threshold. Furthermore, results show that individuals in the group of celebrities having numerous friends become users of a new product or service at a much faster rate than those connected to ordinary individuals having fewer friends.

The effects of several production/management, price and risk factors upon channel catfish profitability are analyzed with a multiperiod mixed-integer linear programming model. Factors analyzed include pond size and optimal stocking rates, alternate levels and trends in catfish prices, pond production losses and level of family consumption withdrawals. Model results indicate that channel catfish offer the potential to significantly increase farm rates of return while providing an avenue of intensive farm growth, without expanding the land base of the farm. However, the long range financial success of the firm was very sensitive to several of the management and risk factors examined.

Small-scale fish farming in tropical Africa is mainly based on pond culture of Nile tilapia Oreochromis niloticus with supplementary organic fertilisation. Until recently, the ‘high’ stocking densities practised (2 fish·m–2) led to stunted populations and very low yields. Since 1996, rural fish farming developed significantly in Côte d’Ivoire. Only a dramatic decrease in stocking densities allowed fish farmers to produce marketable-sized tilapia with reasonable yield in extensive culture. Density control is achieved through tilapia monosex male culture and stocking the predator Hemichromis fasciatus. Further development of low-input tilapia farming requires improvement of production results. A growth model based on maximal growth and ingestion, maintenance needs and efficiency of food for growth was developed to explain and help optimise production results. The model was validated with farm and experimental data and demonstrated that, for a given rearing period (from 30–50 g fingerling, to market-size), yield increased with density, but then decreased beyond an optimal density. When market-weight target is set, the same variation of yield according to stocking density is observed. Densities of 2 to 3 fish·m–2 markedly reduce tilapia yield in extensive culture. Moreover, increasing market weight from 150 to 450 g·fish–1 will only induce a limited decrease in maximal yield (around 20 %) if the density is lowered and the rearing period lengthened. This decrease is more than compensated by the higher price of large tilapia. Using rearing cycle data, the model can predict the results of alternate combinations of stocking density and duration of rearing period under the same pond management. Thus, production results can be optimised given the objectives and constraints of each fish farmer. This model is a valuable tool to develop extensive tilapia farming in tropical areas, and raises questions for researchers.

This paper considers a germ-grain model for a random system of non-overlapping spheres in ℝd for d = 1, 2 and 3. The centres of the spheres (i.e. the ‘germs’ for the ‘grains’) form a stationary Poisson process; the spheres result from a uniform growth process which starts at the same instant in all points in the radial direction and stops for any sphere when it touches any other sphere. Upper and lower bounds are derived for the volume fraction of space occupied by the spheres; simulation yields the values 0.632, 0.349 and 0.186 for d = 1, 2 and 3. The simulations also provide an estimate of the tail of the distribution function of the volume of a randomly chosen sphere; these tails are compared with those of two exponential distributions, of which one is a lower bound and is an asymptote at the origin, and the other has the same mean as the simulated distribution. An upper bound on the tail of the distribution is also an asymptote at the origin but has a heavier tail than either of these exponential distributions. More detailed information for the one-dimensional case has been found by Daley, Mallows and Shepp; relevant information is summarized, including the volume fraction 1 - e-1 = 0.63212 and the tail of the grain volume distribution e-yexp(e-y - 1), which is closer to the simulated tails for d = 2 and 3 than the exponential bounds.

An adaptation of the von Bertalanffy growth model is formulated to describe the phenotypic plasticity of fish somatic growth in relation to trophic conditions. The model is developed for the North sea Downs herring (Clupea harengus). It suggests that annual growth variability during 1974-1990 was mainly due to the combined effects of herring abundance and wind-induced turbulence (coincident with the spring stratification of the water column). Springtime turbulences cause reduced and delayed planktonic blooms preceding the annual foraging period of Downs herring. The negative relation observed between herring abundance and growth is hypothesized to be due to intra-specific competition for trophic resources. Incorporated into the calculation of yield per recruit, the established growth model provides slightly more optimistic diagnoses while dropping the classic assumption of constant weight at age.

Feeding guides for salmonid fishes have been available from various sources for many years. These feeding guides have originated in one way or another from earlier feeding charts of the 1950-60s when meal-meat mixture diets were widely used. Few of the feeding guides available today are based on actual bioenergetics data at different water temperatures and are adapted to high energy diets. New feeding standards have been developed based on principles of nutritional energetics in which the digestible energy content of diet, digestible protein and energy ratio and the amount of digestible energy required per unit of live weight gain are taken into account. The gain expressed as retained energy in carcass and maintenance energy at different water temperatures is the main criteria for energy and feed allocations. Series of bioenergetic models were developed based on these principles and a stand-alone multimedia program was written to facilitate computation of the models. This program predicts growth and energy, nitrogen and phosphorus retention, requirements and excretions to determine feeding standards, waste outputs and effluent water quality based on a biological method. The models require initial and final body weights, water temperature, growth coefficient, carcass energy content and waste coefficients to estimate input and output. Accurate determinations of the thermal-unit growth coefficient, apparent digestibility coefficients and retention efficiencies are essential and these coefficients are determined by biological experiments in the laboratory and field. Oxygen requirement is included to aid environmental control in fish culture system. The Fish-PrFEQ program also contains modules for production records, performance calculations and data base management for input and output data which may be exported for further data and graphic manipulations.

A model to estimate the waste production from sea cage culture was established. Using known feed inputs of nitrogen, phosphorus and organic matter, the model quantifies waste discharge from seabream culture. Daily feed intake and growth in Sparus aurata fed a commercial diet with known composition were measured and found to be dependent on fish weight and water temperature. Digestibility of the commercial feed was measured using chromic oxide as a marker and collection of feces by stripping. The proximate composition of Sparus aurata at different sizes was determined and nitrogen and phosphorus content were on average 28.5 and 7.2 g·kg−1 body mass, respectively. Excretion of ammonia-nitrogen and inorganic phosphorus after metabolic processes was calculated as the difference.

An experiment was designed to test the prediction that two genetically-very-different kinds of pigs would retain the same amounts of protein in their bodies when given the same allowances of the same feed for the same period of time, when these allowances were limiting for both. An allowance of 33·957 kg of a feed with 12·76 MJ metabolizable energy (ME) and 189 g crude protein (N × 6·25)/kg feed was given to Large White × Landrace (LW ×) and Chinese Meishan (CM) female pigs over three different periods of time: (1) ad lib. (AL) with the time taken by individual pigs to consume the allowance being a variable, (2) over a period of 7 weeks (H) and (3) over a period of 9 weeks (L). In addition, in a fourth treatment, pigs of both breeds received the same allowance but supplemented with starch also over a period of 7 weeks (HS). The performance of the pigs on treatment AL was affected by pig breed, with CM pigs gaining protein at a slower, and lipid at a faster, rate than LW × pigs. On treatments L, H and HS the average amounts of protein retained were 2·693 and 2·655 kg for the LW × (n 15) and CM (n 15) pigs respectively (SED 0·106 kg). There was a statistical indication that the LW × pigs may have been more efficient on L, and less efficient on HS, than the CM pigs but we have been unable to propose any biological reason for such an effect, if it was in fact a real one. Thus, the efficiency with which ideal protein was utilized was close to being constant, and apparently at its maximum, for the two breeds. However, although CM pigs had the same protein gain, and the same live weights, on the same feed allowances as the LW × pigs, they gained significantly more lipid. This was attributed in part to their digesting their feed better and in part to their having a lower energy requirement for maintenance through a lower level of physical activity. Given that these two very different kinds of pigs use limiting protein with the same efficiency, it is suggested that it is safe to make the assumption in models of pig growth that the material efficiency of using limiting protein is constant across genotypes of pig.

The problems of predicting the growth, body conformation and feed intake of a flock of growing chickens are analysed in order to identify the key components needed to produce an effective model. Distinctions are made between the problems of a bird at one time, a bird over time, and a group of birds at a time. When considering a bird at a time a series of sub-problems is identified, including the prediction of the potential for growth and the way in which body composition should be taken into account. Given solutions to these problems, those of predicting the requirement of the bird for the resources of energy and nutrients for maintenance, growth and fattening then arise. For a bird fed ad libitum the rate of feed intake needs to be accurately predicted by the model if it is to be successful in predicting growth rate and efficiency. An approach to this problem is outlined, together with an initial approach to the problems raised when attempting to model populations of birds.