A 2-dimensional Geometry for Biological Time

This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal ...) and properly biological (heart beating, respiration, metabolic ...). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The "visual" representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3-dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for "representation time", with a cognitive significance.Comment: Presented in an invited Lecture, conference "Biologie e selezioni naturali", Florence, December 4-8, 200

The structure of maturity: immature trees may drive the productivity of mature forests

Relating forest productivity to local variations in forest structure has been a long-standing challenge. Previous studies often focused on the connection between forest structure and stand-level photosynthesis (GPP). However, biomass production (NPP) and net ecosystem exchange (NEE) are also subject to respiration and other carbon losses, which vary with local conditions and life history traits. Here, we use a simulation approach to study how these losses impact forest productivity and reveal themselves in forest structure. We fit the process-based forest model Formind to a 25ha inventory of an old-growth temperate forest in China and classify trees as "mature" (full-grown) or "immature" based on their intrinsic carbon use efficiency. Our results reveal a strong negative connection between the stand-level carbon use efficiency and the prevalence of mature trees: GPP increases with the total basal area, whereas NPP and NEE are driven by the basal area of immature trees. Accordingly, the basal area entropy - a structural proxy for the prevalence of immature trees - correlated well with NPP and NEE and had higher predictive power than other structural characteristics such as Shannon diversity and height standard deviation. Our results were robust across spatial scales (0.04-1ha) and yield promising hypotheses field studies and new theoretical work

Estimating forest structure in a tropical forest using field measurements, a synthetic model and discrete return lidar data

Tropical forests are huge reservoirs of terrestrial carbon and are experiencing rapid degradation and deforestation. Understanding forest structure proves vital in accurately estimating both forest biomass and also the natural disturbances and remote sensing is an essential method for quantification of forest properties and structure in the tropics. Our objective is to examine canopy vegetation profiles formulated from discrete return LIght Detection And Ranging (lidar) data and examine their usefulness in estimating forest structural parameters measured during a field campaign. We developed a modeling procedure that utilized hypothetical stand characteristics to examine lidar profiles. In essence, this is a simple method to further enhance shape characteristics from the lidar profile. In this paper we report the results comparing field data collected at La Selva, Costa Rica (10° 26′ N, 83° 59′ W) and forest structure and parameters calculated from vegetation height profiles and forest structural modeling. We developed multiple regression models for each measured forest biometric property using forward stepwise variable selection that used Bayesian information criteria (BIC) as selection criteria. Among measures of forest structure, ranging from tree lateral density, diameter at breast height, and crown geometry, we found strong relationships with lidar canopy vegetation profile parameters. Metrics developed from lidar that were indicators of height of canopy were not significant in estimating plot biomass (p-value = 0.31, r2 = 0.17), but parameters from our synthetic forest model were found to be significant for estimating many of the forest structural properties, such as mean trunk diameter (p-value = 0.004, r2 = 0.51) and tree density (p-value = 0.002, r2 = 0.43). We were also able to develop a significant model relating lidar profiles to basal area (p-value = 0.003, r2 = 0.43). Use of the full lidar profile provided additional avenues for the prediction of field based forest measure parameters. Our synthetic canopy model provides a novel method for examining lidar metrics by developing a look-up table of profiles that determine profile shape, depth, and height. We suggest that the use of metrics indicating canopy height derived from lidar are limited in understanding biomass in a forest with little variation across the landscape and that there are many parameters that may be gleaned by lidar data that inform on forest biometric properties

Entropy Stress Based on Organ and Mitochondrial Metabolic Loading

he energy for sustaining life is released through the oxidation of glucose, fats, and proteins. A part of the energy released within each cell is stored as chemical energy of Adenosine Tri- Phosphate molecules, which is called work currency of the body, while the remainder is released as heat. Earlier literature introduced availability concepts from thermodynamics, related the specific irreversibility and entropy generation rate to metabolic efficiency, and energy release rate of each organ, and computed whole body specific entropy generation rate at any given age as a sum of entropy generation within four vital organs; Brain, Heart, Kidney, Liver and the rest of organs. The current work includes the effects of i) two additional organs: adipose tissue and skeletal muscles, for application to athletes, ii) proportions of nutrients oxidized which affects blood temperature and metabolic efficiencies, iii) converts the entropy stress from organ/cellular level to mitochondrial level, and iv) relates these parameters as biomarkers in biological aging process. Based on 7 organ model, considering a male of 84 kg steady mass, the lifetime energy expenditure is estimated to be 2726.46 MJ/kg body mass, with contributions of 86.4, 825.8, 274.8, 131.4, 316.4, 661.1, 430.4 MJ to each unit body mass by Adipose Tissue, Brain, Heart, Kidney, Liver, Rest of Mass, Skeletal Muscle, while lifetime entropy generated 6051 kJ/(K kg body mass) with contributions of 191.7, 1832.7, 610, 291.7, 702.3, 1467.2, 955.2 kJ/K to each unit body mass. Based on mitochondrial volume and 5 organ model, the lifetime energy expenditure is estimated to be 15529.6 MJ/ cm3 of mitochondrial volume of whole body, with contributions of 8250, 2435, 3040, 1805, 1.9E-05 MJ to each unit volume of mitochondria in organs, serving as biomarkers in the biological aging process of organs, while lifetime entropy generated is 34465 kJ/(K cm^3 of mitochondrial volume) with contributions of 18310, 5400, 6740, 4010.5, 4.3E-05 kJ/K respectively to each unit of mitochondrial volume. The organ entropy stress ranking based on unit volume of mitochondria within an organ {kJ/ (K cm^3 of mito of organ k) show brain being highest and liver lowest