Finding Liebig's law of the minimum.

Liebig's law of the minimum (LLM) is often used to interpret empirical biological growth data and model multiple substrates co-limited growth. However, its mechanistic foundation is rarely discussed, even though its validity has been questioned since its introduction in the 1820s. Here we first show that LLM is a crude approximation of the law of mass action, the state of art theory of biochemical reactions, and the LLM model is less accurate than two other approximations of the law of mass action: the synthesizing unit model and the additive model. We corroborate this conclusion using empirical data sets of algae and plants grown under two co-limiting substrates. Based on our analysis, we show that when growth is modeled directly as a function of substrate uptake, the LLM model improperly restricts the organism to be of fixed elemental stoichiometry, making it incapable of consistently resolving biological adaptation, ecological evolution, and community assembly. When growth is modeled as a function of the cellular nutrient quota, the LLM model may obtain good results at the risk of incorrect model parameters as compared to those inferred from the more accurate synthesizing unit model. However, biogeochemical models that implement these three formulations are needed to evaluate which formulation is acceptably accurate and their impacts on predicted long-term ecosystem dynamics. In particular, studies are needed that explore the extent to which parameter calibration can rescue model performance when the mechanistic representation of a biogeochemical process is known to be deficient.

Orthogonal fitness benefits of nitrogen and ants for nitrogen-limited plants in the presence of herbivores.

Predictable effects of resource availability on plant growth-defense strategies provide a unifying theme in theories of direct anti-herbivore defense, but it is less clear how resource availability modulates plant indirect defense. Ant-plant-hemipteran interactions produce mutualistic trophic cascades when hemipteran-tending ants reduce total herbivory, and these interactions are a key component of plant indirect defense in most terrestrial ecosystems. Here we conducted an experiment to test how ant-plant-hemipteran interactions depend on nitrogen (N) availability by manipulating the presence of ants and aphids under different N fertilization treatments. Ants increased plant flowering success by decreasing the densities of herbivores, and the effects of ants on folivores were positively related to the density of aphids. Unexpectedly, N fertilization produced no changes in plant N concentrations. Plants grown in higher N grew and flowered more, but aphid honeydew chemistry stayed the same, and neither the density of aphids nor the rate of ant attraction per aphid changed with N addition. The positive effects of ants and N addition on plant fitness were thus independent of one another. We conclude that N was the plant's limiting nutrient and propose that addition of the limiting nutrient is unlikely to alter the strength of mutualistic trophic cascades.

Biogeochemistry and Geographical Ecology: Embracing All Twenty-Five Elements Required to Build Organisms.

Biogeochemistry is a key but relatively neglected part of the abiotic template that underlies ecology. The template has a geography, one that is increasingly being rearranged in this era of global change. Justus von Liebig's law of the minimum has played a useful role in focusing attention on biogeochemical regulation of populations, but given that ∼25+ elements are required to build organisms and that these organisms use and deplete nutrients in aggregates of communities and ecosystems, we make the case that it is time to move on. We review available models that suggest the many different mechanisms that give rise to multiple elements, or colimitation. We then review recent empirical data that show that rates of decomposition and primary productivity may be limited by multiple elements. In that light, given the tropics' high species diversity and generally more weathered soils, we predict that colimitation at community and ecosystem scales is more prevalent closer to the equator. We conclude with suggestions for how to move forward with experimental studies of colimitation.

Temporal resolution of birth rate analysis in zooplankton and its implications for identifying strong interactions in ecology.

Expanding on Haeckel's classical definition, ecology can be defined as the study of strong and weak interactions between the organism and the environment, hence the need for identifying strong interactions as major drivers of population and community dynamics. The solution to this problem is facilitated by the fact that the frequency distribution of interaction strengths is highly skewed, resulting in few or, according to Liebig's law of the minimum, just one strong interaction. However, a single strong interaction often remains elusive. One of the reasons may be that, due to the ever-present dynamics of ecological systems, a single strong interaction is likely to exist only on relatively short time intervals, so methods with sufficient temporal resolution are required. In this paper, we study the temporal resolution of contribution analysis of birth rate in zooplankton, a method to assess the relative strength of bottom-up (food) versus top-down (predation) effects. Birth rate is estimated by the Edmondson-Paloheimo model. Our test system is a population of the cladoceran Bosmina longirostris inhabiting a small northern lake with few planktivorous predators, and thus likely controlled by food. We find that the method's temporal resolution in detecting bottom-up effects corresponds well to the species' generation time, and the latter seems comparable to the lifetime of a single strong interaction. This enables one to capture a single strong interaction "on the fly," right during its time of existence. We suggest that this feature, the temporal resolution of about the lifetime of a single strong interaction, may be a generally desirable property for any method, not only the one studied here, intended to identify and assess strong interactions. Success in disentangling strong interactions in ecological communities, and thus solving one of the key issues in ecology, may critically depend on the temporal resolution of the methods used.

Modelling of Lemna minor L. growth as influenced by nutrient supply, supplemental light, CO2 and harvest intervals for a continuous indoor cultivation.

Given the proper conditions, Lemna spp. rapidly produce a high amount of valuable biomass which is considered as an alternative source for feed and food. For a continuous and long-term indoor production under controlled conditions, environmental and harvest parameters have to be optimized to suppress algal growth and constantly yield a high-quality product. Experimentally assessing the effect of a larger number of parameters on the growth rate ri is impossible due to the theoretically high number of parameter combinations. Thus, a SIMILE® - based model has been developed. This enables production parameters to be assessed individually for its effect on the growth rate r i by a differential equation. Start values for numerical integration were taken from measured data and analytical solutions of the differential growth equation. At 400 ppm CO2, the regrowth rate ri in an optimized laboratory set-up amounted to 216 g FM·m-2d-1, harvesting one third of the biomass at intervals of 5 days. In up-scaled set-ups, lower regrowth rates ri of about 173 g FM·m-2d-1 (Kalkar) and 190 g FM·m-2d-1 (Berlin) were obtained, because temperature and light conditions were below optimum. At 3,500 ppm CO2, the regrowth rate ri in laboratory set-up increased to 323 g FM·m-2d-1 by shortening the harvest interval to three days. Maximum growth rates ri were obtained with an NH4 +/NO3 - ratio of 1/9 at 1.14 mM total N concentration. The results indicate how to optimize culture conditions and harvest intervals. Model runs closely match the experimental data taken from the three different approaches and thus confirm the validity of the model.

Reconciling the Mitscherlich's law of diminishing returns with Liebig's law of the minimum. Some results on crop modeling.

Reliable fertilizer recommendations depend on the correctness of the crop production models fitted to the data, but generally the crop models are built empirically, neglecting important physiological aspects related with response to fertilizers, or they are based in laws of plant mineral nutrition seen by many authors as conflicting theories: the Liebig's Law of the Minimum and Mitscherlich's Law of Diminishing Returns. We developed a new approach to modelling the crop response to fertilizers that reconcile these laws. In this study, the Liebig's Law is applied at the cellular level to explain plant production and, as a result, crop models compatible with the Law of Diminishing Returns are derived. Some classical crop models appear here as special cases of our methodology, and a new interpretation for Mitscherlich's Law is also provided.

Unified theory of Alzheimer's disease (UTAD): implications for prevention and curative therapy.

The aim of this review is to propose a Unified Theory of Alzheimer's disease (UTAD) that integrates all key behavioural, genetic and environmental risk factors in a causal chain of etiological and pathogenetic events. It is based on three concepts that emanate from human's evolutionary history: (1) The grandmother-hypothesis (GMH), which explains human longevity due to an evolutionary advantage in reproduction by trans-generational transfer of acquired knowledge. Consequently it is argued that mental health at old-age must be the default pathway of humans' genetic program and not development of AD. (2) Therefore, mechanism like neuronal rejuvenation (NRJ) and adult hippocampal neurogenesis (AHN) that still function efficiently even at old age provide the required lifelong ability to memorize personal experiences important for survival. Cumulative evidence from a multitude of experimental and epidemiological studies indicate that behavioural and environmental risk factors, which impair productive AHN, result in reduced episodic memory performance and in reduced psychological resilience. This leads to avoidance of novelty, dysregulation of the hypothalamic-pituitary-adrenal (HPA)-axis and cortisol hypersecretion, which drives key pathogenic mechanisms of AD like the accumulation and oligomerization of synaptotoxic amyloid beta, chronic neuroinflammation and neuronal insulin resistance. (3) By applying to AHN the law of the minimum (LOM), which defines the basic requirements of biological growth processes, the UTAD explains why and how different lifestyle deficiencies initiate the AD process by impairing AHN and causing dysregulation of the HPA-axis, and how environmental and genetic risk factors such as toxins or ApoE4, respectively, turn into disease accelerators under these unnatural conditions. Consequently, the UTAD provides a rational strategy for the prevention of mental decline and a system-biological approach for the causal treatment of AD, which might even be curative if the systemic intervention is initiated early enough in the disease process. Hence an individualized system-biological treatment of patients with early AD is proposed as a test for the validity of UTAD and outlined in this review.

Validation of phlebotomine cardinal temperatures and humidities in the region of Rio Arinos, Mato Grosso, Brazil

The purpose of this study was to validate the phlebotomine cardinal temperatures and humidities, reported by Campelo Júnior et al. (2014), using different collection data, obtained in a study on the number of these insects, captured in the Arinos region, in Nova Mutum, Mato Grosso, Brazil, according to spatial (100 m to 1000 m) and temporal (June 2011 to April 2012) variability. Phlebotomines were captured in the riparian forest, by means of 10 traps positioned approximately every 100 m, northwards from the road along the river bank, with samples obtained bimonthly during three consecutive nights for a period of 12 months. Average relative humidity and temperature during the periods when the traps remained at the collection points were measured using a digital thermometer-hygrometer. The phlebotomine sand fly fauna was highly diversified, presenting 31 species, of which Lutzomyia antunesi was the most prevalent (45.4%). L. flaviscutellata, L. whitmani and L. umbratilis, known vectors of Leishmania spp., were also found. There was a marked variation in the quantity of phlebotomines captured throughout the consecutive collection days, as each sampling was affected by different factors determining a different maximum value for the number of insects present in each situation, as demonstrated for temperature and air humidity.