Cor Zonneveld

A cell-based model for the chlorophyll a to carbon ratio in phytoplankton.

The ratio of chlorophyll a per cell and carbon per cell is considered to be a key quantity in phytoplankton growth. The quantity varies with nutrient and light availability. The aim of this paper is to predict how the chlorophyll a to carbon ratio varies in relation to environmental conditions. A cell-based model is presented, that allows the description of carbon and chlorophyll a cell quota, and thus the chlorophyll a to carbon ratio, in nutrient-limited as well as light-limited growth. The model predictions are in line with experimental data. Variations in Chl:C result, among others, from photoacclimation. The analysis in this paper shows that the impact photoacclimation on phytoplankton growth is rather small, despite large variations in Chl:C. This is mainly due to the package effect, a phenomenon that can be easily accounted for especially in cell-based models.

Omnivory and food web dynamics

Abstract Intraguild predation is a trophic interaction in which two consumers compete for one resource and where one of the consumer species may also feed on its competitor. The intraguild predator’s diet follows from the relative strength of its interactions with its potential prey. Current view holds that weak interactions between species promote the stability of food webs. To the contrary, nutrient enrichment is predicted to destabilize ecosystems. We present a theoretical analysis of the interplay between intraguild predation and nutrient enrichment in a Marr-Pirt chemostat model of a microbial food web. We perform a two-dimensional bifurcation analysis along a gradient of allochtonous nutrient levels and a gradient of one out of two biologically plausible strategies to explore the spectrum of the intraguild predator’s foraging interactions. Both strategies show that intraguild predation may • stabilize food chains; • eliminate chaos, predicted by food chain models; • give rise to multiple stable states; • be favored in systems with low turn-over rates, where the intraguild predator has a low interaction strength and a low yield on the basal resource.

Analysis of Transect Counts to Monitor Population Size in Endangered Insects The Case of the El Segundo Blue Butterfly, Euphilotes Bernardino Allyni

Before, during and after habitat restoration from 1984 to 1994, we monitored population size of the federally listed endangered El Segundo blue butterfly, Euphilotes bernardino allyni (Shields). In the subsequent formalization of a recovery plan for the species, the U.S. Fish and Wildlife Service established several recovery criteria, including a requirement of ‘a scientifically credible monitoring plan’ to track population size annually. To avoid detrimental effects of the extensively used mark-release-recapture method on the delicate El Segundo blue butterfly, which would conflict with protection afforded by the Endangered Species Act, we chose instead to perform transect counts to estimate relative population size. Herein, we analyze the results of our transect counts by three different methods, developed by or modified from Pollard, Watt et al. and Zonneveld. Qualitatively, the three methods, which have different assumptions, produced similar results when applied to the same data. Zonnevelds model estimates death rate in addition to an index of population size, thus providing more information than the other two methods. The El Segundo blue butterflys sedentary nature and the close relationship of its adult and early stages to one foodplant permits extrapolation of the index of population size based on transect counts, to an estimate of actual population size. Our data document butterfly numbers increasing from 1984 to 1989, but then declining until the end of our observations in 1994. Based on analysis of our El Segundo blue butterfly data, we propose an implementation of a scientifically credible monitoring plan.

The embedded tumour: host physiology is important for the evaluation of tumour growth

The growth potential of a tumour can significantly depend on host features such as age, cell proliferation rates and caloric intake. Although this is widely known, existing mathematical models for tumour growth do not account for it. We therefore developed a new model for tumour growth, starting from a mathematical framework that describes the hosts physiology. The resulting tumour-in-host model allowed us to study the implications of various specific interactions between the energetics of tumour and host. The model accounts for the influence of both age and feeding regimen of the host organism on the behaviour of a tumour. Concerning the effects of a tumour on its host, it explains why tumour-mediated body-weight loss is often more dramatic than expected from the energy demands of the tumour. We also show how the model can be applied to study enhanced body-weight loss in presence of cachectic factors. Our tumour-in-host model thus appears a proper tool to unite a wide range of phenomena in tumour–host interactions.

From exposure to effect: a comparison of modeling approaches to chemical carcinogenesis.

Standardized long-term carcinogenicity tests aim to reveal the relationship between exposure to a chemical and occurrence of a carcinogenic response. The analysis of such tests may be facilitated by the use of mathematical models. To what extent current models actually achieve this purpose is difficult to evaluate. Various aspects of chemically induced carcinogenesis are treated by different modeling approaches, which proceed very much in isolation of each other. With this paper we aim to provide for the non-mathematician a comprehensive and critical overview of models dealing with processes involved in chemical carcinogenesis. We cover the entire process of carcinogenesis, from exposure to effect. We succinctly summarize the biology underlying the models and emphasize the relationship between model assumptions and model formulations. The use of mathematics is restricted as far as possible with some additional information relegated to boxes.

Cross-Sectional Growth References and Implications for the Development of an International Growth Standard for School-Aged Children and Adolescents

Normative data are needed to create a reference that indicates optimal development of weight in relation to height and age, particularly in the face of the unfolding obesity epidemic. The body-mass index (BMI) has some serious limitations: it is a relatively poor predictor of current and future fatness. Currently, however, there are few available alternatives, with the possible exception of waist circumference or skinfolds. The use of cross-sectional references to construct a BMI-reference curve is problematic when there are period and cohort effects. Ideally, a reference would be based on longitudinal data in populations with little underweight, overweight, and obesity. In the meantime cross-sectional data in appropriate populations could be used to construct BMI percentiles linking BMI values at age 5 to those at age 18 (or 21) that would correspond with adult BMI values reflecting optimal health (e.g., that would correspond to adult BMI values between 21 and 23 kg/m2).

Endocrine interactions between digenetic trematode parasites and their intermediate hosts, freshwater snails, with emphasis on the possible role of ecdysteroids

Summary The possible involvement of ecdysteroids in the endocrine interaction between digenetic trematode parasites and their intermediate hosts, freshwater snails, was studied in the combination Lymnaea stagnalis-Trichobilharzia ocellata. Measurements of ecdysteroids by radioimmunoassay in Bemax-fed and starved non-parasitized and parasitized snails showed that all tissues examined contain ecdysteroids, albeit at low levels. The highest titers of immunoreactive molecules were found in the digestive gland and gonad, Infection appeared to have no effect on the ecdysteroid titers, but the state of nutrition is important. In tissues of starved snails of non-parasitized as well as of parasitized snails the ecdysteroid titer appeared to be 2–3 times as high as in Bemax-fed snails. It is not clear whether the high titers are caused by an increased synthesis of ecdysteroids in starved snails or by an inhibited metabolism/catabolism of ecdysteroids. The distribution of 3H-ecdysone over various body parts of both ...

Erratum to “From exposure to effect: a comparison of modeling approaches to chemical carcinogenesis” ☆: [Mutat. Res. 489 (2001) 17–45]

Box 3. Multi-stage models Let N0 denote the number of susceptible normal cells (stem cells) and J the random variable ‘time until a certain cell gives rise to a tumor cell’. The probability that an organism is tumor free at time t equals the probability that not any cell transforms into a tumor cell before time t. Under the assumption that cells transform independently of each other, this implies that GT (t) equals the product of N0 times GJ (t) or, equivalently, GT (t) = GJ (t)0 = {1 − FJ (t)}N0 . In terms of the hazard rates this means hT (t) = N0hJ (t). Exact formula: If two changes are required to transform a certain cell, the time to transformation equals the sum of the waiting time until the first change (K1) and the waiting time between the first and the second change (K2). The variables K1 and K2 follow an exponential distribution with parameters p1 and p2, respectively. F ′ J can be expressed in terms ofF ′ K1 andF ′ K2 , as follows:F ′ J (t) = ∫ t 0F ′ K1 (s)F ′ K2(t−s) ds = p1p2{e−p1t−e−p2t }/(p2−p1). Integration gives an exact expression for FJ and, thus, also for GT = {1 − FJ }N0 . Approximate formula: From Eq. (3), we have GJ (t) = −hJ (t)GJ (t). Because of the relation FJ = 1 − GJ , this is equivalent to F ′ J (t) = hJ (t){1 − FJ (t)}. In this context, the assumption that transformation is a rare phenomenon means (1 − FJ ) ≈ 1 or equivalently, hJ (t) ≈ F ′ J (t). The hazard for T then yields: hT (t) = N0hJ (t) ≈ N0F ′ J (t) = p1p2N0{e−p1t − e−p2t }/(p2 − p1). Based on expansion in Taylor series about t = 0 and the assumption that p1 and p2 are small, this expression reduces to: hT (t) ≈ p1p2N0t . Thus, for the two stage model μ = p1p2N0 (Eq. (9)).