Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

What limits insect fecundity? Body size- and temperature-dependent egg maturation and oviposition in a butterfly

1. Large female insects usually have high potential fecundity. Therefore selection should favour an increase in body size given that these females get opportunities to realize their potential advantage by maturing and laying more eggs. However, ectotherm physiology is strongly temperature-dependent, and activities are carried out sufficiently only within certain temperature ranges. Thus it remains unclear if the fecundity advantage of a large size is fully realized in natural environments, where thermal conditions are limiting. 2. Insect fecundity might be limited by temperature at two levels; first eggs need to mature, and then the female needs time for strategic ovipositing of the egg. Since a female cannot foresee the number of oviposition opportunities that she will encounter on a given day, the optimal rate of egg maturation will be governed by trade-offs associated with egg- and time-limited oviposition. As females of different sizes will have different amounts of body reserves, size-dependent allocation trade-offs between the mother’s condition and her egg production might be expected. 3. In the temperate butterfly Pararge aegeria , the time and temperature dependence of oviposition and egg maturation, and the interrelatedness of these two processes were investigated in a series of laboratory experiments, allowing a decoupling of the time budgets for the respective processes. 4. The results show that realized fecundity of this species can be limited by both the temperature dependence of egg maturation and oviposition under certain thermal regimes. Furthermore, rates of oviposition and egg maturation seemed to have regulatory effects upon each other. Early reproductive output was correlated with short life span, indicating a cost of reproduction. Finally, large females matured more eggs than small females when deprived of oviposition opportunities. Thus, the optimal allocation of resources to egg production seems dependent on female size. 5. This study highlights the complexity of processes underlying rates of egg maturation and oviposition in ectotherms under natural conditions. We further discuss the importance of temperature variation for egg- vs. time-limited fecundity and the consequences for the evolution of female body size in insects.

Effects of body size and lifestyle on evolution of mammal life histories

It has recently been proposed that life-history evolution is subject to a fundamental size-dependent constraint. This constraint limits the rate at which biomass can be produced so that production per unit of body mass is inevitably slower in larger organisms than in smaller ones. Here we derive predictions for how changes in body size and production rates evolve in different lifestyles subject to this constraint. Predictions are tested by using data on the mass of neonate tissue produced per adult per year in 637 placental mammal species and are generally supported. Compared with terrestrial insectivores with generalized primitive traits, mammals that have evolved more specialized lifestyles have divergent massspecific production rates: (i) increased in groups that specialize on abundant and reliable foods: grazing and browsing herbivores (artiodactyls, lagomorphs, perissoclactyls, and folivorous rodents) and flesh-eating marine mammals (pinnipeds, cetaceans); and (ii) decreased in groups that have lifestyles with reduced death rates: bats, primates, arboreal, fossorial, and desert rodents, bears, elephants, and rhinos. Convergent evolution of groups with similar lifestyles is common, so patterns of productivity across mammalian taxa reflect both ecology and phylogeny. The overall result is that groups with different lifestyles have parallel but offset relationships between production rate and body size. These results shed light on the evolution of the fast-slow life-history continuum, suggesting that variation occurs along two axes corresponding to body size and lifestyle.

The long-term stability of a possible aqueous ammonium sulfate ocean inside Titan

We model the thermal evolution of a subsurface ocean of aqueous ammonium sulfate inside Titan using a parameterized convection scheme. The cooling and crystallization of such an ocean depends on its heat flux balance, and is governed by the pressure-dependent melting temperatures at the top and bottom of the ocean. Using recent observations and previous experimental data, we present a nominal model which predicts the thickness of the ocean throughout the evolution of Titan; after 4.5 Ga we expect an aqueous ammonium sulfate ocean 56 km thick, overlain by a thick (176 km) heterogeneous crust of methane clathrate, ice I and ammonium sulfate. Underplating of the crust by ice I will give rise to compositional diapirs that are capable of rising through the crust and providing a mechanism for cryovolcanism at the surface. We have conducted a parameter space survey to account for possible variations in the nominal model, and find that for a wide range of plausible conditions, an ocean of aqueous ammonium sulfate can survive to the present day, which is consistent with the recent observations of Titan's spin state from Cassini radar data [Lorenz, R.D., Stiles, B.W., Kirk, R.L., Allison, M.D., del Marmo, P.P., Iess, L., Lunine, J.I., Ostro, S.J., Hensley, S., 2008. Science 319, 1649–1651].

Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

A new data set of soil mineralogy for dust-cycle modeling

The mineralogy of airborne dust affects the impact of dust particles on direct and indirect radiative forcing, on atmospheric chemistry and on biogeochemical cycling. It is determined partly by the mineralogy of the dust-source regions and partly by size-dependent fractionation during erosion and transport. Here we present a data set that characterizes the clay and silt-sized fractions of global soil units in terms of the abundance of 12 minerals that are important for dust–climate interactions: quartz, feldspars, illite, smectite, kaolinite, chlorite, vermiculite, mica, calcite, gypsum, hematite and goethite. The basic mineralogical information is derived from the literature, and is then expanded following explicit rules, in order to characterize as many soil units as possible. We present three alternative realizations of the mineralogical maps, taking the uncertainties in the mineralogical data into account. We examine the implications of the new database for calculations of the single scattering albedo of airborne dust and thus for dust radiative forcing.

Direct versus indirect sexual selection: genetic basis of colour, size and recruitment in a wild bird

Indirect and direct models of sexual selection make different predictions regarding the quantitative genetic relationships between sexual ornaments and fitness. Indirect models predict that ornaments should have a high heritability and that strong positive genetic covariance should exist between fitness and the ornament. Direct models, on the other hand, make no such assumptions about the level of genetic variance in fitness and the ornament, and are therefore likely to be more important when environmental sources of variation are large. Here we test these predictions in a wild population of the blue tit (Parus caeruleus), a species in which plumage coloration has been shown to be under sexual selection. Using 3 years of cross-fostering data from over 250 breeding attempts, we partition the covariance between parental coloration and aspects of nestling fitness into a genetic and environmental component. Contrary to indirect models of sexual selection, but in agreement with direct models, we show that variation in coloration is only weakly heritable (h(2) < 0.11), and that two components of offspring fitness-nestling size and fledgling recruitment-are strongly dependent on parental effects, rather than genetic effects. Furthermore, there was no evidence of significant positive genetic covariation between parental colour and offspring traits. Contrary to direct benefit models, however, we find little evidence that variation in colour reliably indicates the level of parental care provided by either males or females. Taken together, these results indicate that the assumptions of indirect models of sexual selection are not supported by the genetic basis of the traits reported on here.

Aggregation of parasitism risk in an aphid-parasitoid system: Effects of plant patch size and aphid density

Few studies have linked density dependence of parasitism and the tritrophic environment within which a parasitoid forages. In the non-crop plant-aphid, Centaurea nigra-Uroleucon jaceae system, mixed patterns of density-dependent parasitism by the parasitoids Aphidius funebris and Trioxys centaureae were observed in a survey of a natural population. Breakdown of density-dependent parasitism revealed that density dependence was inverse in smaller colonies but direct in large colonies (>20 aphids), suggesting there is a threshold effect in parasitoid response to aphid density. The CV2 of searching parasitoids was estimated from parasitism data using a hierarchical generalized linear model, and CV2>1 for A. funebris between plant patches, while for T. centaureae CV2>1 within plant patches. In both cases, density independent heterogeneity was more important than density-dependent heterogeneity in parasitism. Parasitism by T. centaureae increased with increasing plant patch size. Manipulation of aphid colony size and plant patch size revealed that parasitism by A. funebris was directly density dependent at the range of colony sizes tested (50-200 initial aphids), and had a strong positive relationship with plant patch size. The effects of plant patch size detected for both species indicate that the tritrophic environment provides a source of host density independent heterogeneity in parasitism, and can modify density-dependent responses. (c) 2007 Gessellschaft fur Okologie. Published by Elsevier GmbH. All rights reserved.

Microbe-associated molecular pattern (MAMP) signatures, synergy, size and charge: influences on perception or mobility and host defence responses

Triggering of defences by microbes has mainly been investigated using single elicitors or microbe-associated molecular patterns (MAMPs), but MAMPs are released in planta as complex mixtures together with endogenous oligogalacturonan (OGA) elicitor. We investigated the early responses in Arabidopsis of calcium influx and oxidative burst induced by non-saturating concentrations of bacterial MAMPs, used singly and in combination: flagellin peptide (flg22), elongation factor peptide (elf18), peptidoglycan (PGN) and component muropeptides, lipo-oligosaccharide (LOS) and core oligosaccharides. This revealed that some MAMPs have additive (e.g. flg22 with elf18) and even synergistic (flg22 and LOS) effects, whereas others mutually interfere (flg22 with OGA). OGA suppression of flg22-induced defences was not a result of the interference with the binding of flg22 to its receptor flagellin-sensitive 2 (FLS2). MAMPs induce different calcium influx signatures, but these are concentration dependent and unlikely to explain the differential induction of defence genes [pathogenesis-related gene 1 (PR1), plant defensin gene 1.2 (PDF1.2) and phenylalanine ammonia lyase gene 1 (PAL1)] by flg22, elf18 and OGA. The peptide MAMPs are potent elicitors at subnanomolar levels, whereas PGN and LOS at high concentrations induce low and late host responses. This difference might be a result of the restricted access by plant cell walls of MAMPs to their putative cellular receptors. flg22 is restricted by ionic effects, yet rapidly permeates a cell wall matrix, whereas LOS, which forms supramolecular aggregates, is severely constrained, presumably by molecular sieving. Thus, MAMPs can interact with each other, whether directly or indirectly, and with the host wall matrix. These phenomena, which have not been considered in detail previously, are likely to influence the speed, magnitude, versatility and composition of plant defences.

Effect of sequence distribution on the morphology, crystallization, melting, and biodegradation of poly(epsilon-caprolactone-co-epsilon-caprolactam) copolymers

Two types of poly(epsilon-caprolactone (CLo)-co-poly(epsilon-caprolactam (CLa)) copolymers were prepared by catalyzed hydrolytic ring-opening polymerization. Both cyclic comonomers were added simultaneously in the reaction medium for the First type or materials where copolymers have a random distribution of counits, as evidenced by H-1 and C-13 NMR. For the second type of copolymers, the cyclic comonomers were added sequentially, yielding diblock poly(ester-amides). The materials were characterized by differential scanning calorimetry (DSC), wide- and small-angle X-ray scattering (WAXS and SAXS), and transmission and scanning electron microscopies (TEM and SEM). Their biodegradation in compost was also studied. All copolymers were found to be miscible by the absence of structure in the melt. TEM revealed that all samples exhibited a crystalline lamellar morphology. DSC and WAXS showed that in a wide composition range (CLo contents from 6 to 55%) only the CLa units were capable of crystallization in the random copolymers. The block copolymer samples only experience a small reduction of crystallization and melting temperature with composition, and this was attributed to a dilution effect caused by the miscible noncrystalline CLo units. The comparison between block and random copolymers provided a unique opportunity to distinguish the dilution effect of the CLo units on the crystallization and melting of the polyamide phase from the chemical composition effect in the random copolymers case, where the CLa sequences are interrupted statistically by the CLo units, making the crystallization of the polyamide strongly composition dependent. Finally, the enzymatic degradation of the copolymers in composted soil indicate a synergistic behavior where much faster degradation was obtained for random copolymers witha CLo content larger than 30% than for neat PCL.

Unusually high differential attenuation at C band: Results from a two-year analysis of the French Trappes polarimetric radar data

The differential phase (ΦDP) measured by polarimetric radars is recognized to be a very good indicator of the path integrated by rain. Moreover, if a linear relationship is assumed between the specific differential phase (KDP) and the specific attenuation (AH) and specific differential attenuation (ADP), then attenuation can easily be corrected. The coefficients of proportionality, γH and γDP, are, however, known to be dependent in rain upon drop temperature, drop shapes, drop size distribution, and the presence of large drops causing Mie scattering. In this paper, the authors extensively apply a physically based method, often referred to as the “Smyth and Illingworth constraint,” which uses the constraint that the value of the differential reflectivity ZDR on the far side of the storm should be low to retrieve the γDP coefficient. More than 30 convective episodes observed by the French operational C-band polarimetric Trappes radar during two summers (2005 and 2006) are used to document the variability of γDP with respect to the intrinsic three-dimensional characteristics of the attenuating cells. The Smyth and Illingworth constraint could be applied to only 20% of all attenuated rays of the 2-yr dataset so it cannot be considered the unique solution for attenuation correction in an operational setting but is useful for characterizing the properties of the strongly attenuating cells. The range of variation of γDP is shown to be extremely large, with minimal, maximal, and mean values being, respectively, equal to 0.01, 0.11, and 0.025 dB °−1. Coefficient γDP appears to be almost linearly correlated with the horizontal reflectivity (ZH), differential reflectivity (ZDR), and specific differential phase (KDP) and correlation coefficient (ρHV) of the attenuating cells. The temperature effect is negligible with respect to that of the microphysical properties of the attenuating cells. Unusually large values of γDP, above 0.06 dB °−1, often referred to as “hot spots,” are reported for 15%—a nonnegligible figure—of the rays presenting a significant total differential phase shift (ΔϕDP > 30°). The corresponding strongly attenuating cells are shown to have extremely high ZDR (above 4 dB) and ZH (above 55 dBZ), very low ρHV (below 0.94), and high KDP (above 4° km−1). Analysis of 4 yr of observed raindrop spectra does not reproduce such low values of ρHV, suggesting that (wet) ice is likely to be present in the precipitation medium and responsible for the attenuation and high phase shifts. Furthermore, if melting ice is responsible for the high phase shifts, this suggests that KDP may not be uniquely related to rainfall rate but can result from the presence of wet ice. This hypothesis is supported by the analysis of the vertical profiles of horizontal reflectivity and the values of conventional probability of hail indexes.

Differences in glucose-dependent insulinotropic polypeptide hormone and hepatic lipase in subjects of southern and northern Europe: implications for postprandial lipaemia

The aim was to determine in 32 healthy young men from northern and southern Europe whether differences in the secretion of insulin and glucose-dependent insulinotropic polypeptide (GIP) might explain these findings through the actions of these hormones on lipoprotein lipase. In a randomized, single-blind, crossover study the effects of 2 test meals of identical macronutrient composition but different saturated fatty acid (SFA) and monounsaturated fatty acid (MUFA) contents were investigated on postprandial GIP, insulin, the ratio of incremental triacylglycerol to apolipoprotein B-48 (a marker of chylomicron size), and the activity of postheparin lipases. Fasting and postprandial GIP concentrations and postheparin hepatic lipase (HL) activities were higher in the southern Europeans (P<0.001 and P<0.02, respectively). Lipoprotein lipase activity after the SFA-rich meal was higher in the northern Europeans (P<0.01). HL activity 9 h after the SFA-rich meal and the area under the curve (AUC) for the postprandial insulin response correlated with the AUC for the postprandial GIP response (r=0.44 (P<0.04) and r=0.46 (P<0.05), respectively). There were no significant differences in chylomicron size between the 2 groups for either meal, but when the groups were combined there was a difference in chylomicron size between the SFA- and MUFA-rich meals (P<0.05), which could be due to the formation of larger chylomicrons after the MUFA-rich meal. The significantly higher GIP and insulin responses and HL activities in southern Europeans may provide an explanation for a previous report of attenuated postprandial triacylglycerol and apolipoprotein B-48 responses in them.

Modelling the time-evolution of phytoplankton size spectra from satellite remote sensing

A dynamic size-structured model is developed for phytoplankton and nutrients in the oceanic mixed layer and applied to extract phytoplankton biomass at discrete size fractions from remotely sensed, ocean-colour data. General relationships between cell size and biophysical processes (such as sinking, grazing, and primary production) of phytoplankton were included in the model through a bottom–up approach. Time-dependent, mixed-layer depth was used as a forcing variable, and a sequential data-assimilation scheme was implemented to derive model trajectories. From a given time-series, the method produces estimates of size-structured biomass at every observation, so estimates seasonal succession of individual phytoplankton size, derived here from remote sensing for the first time. From these estimates, normalized phytoplankton biomass size spectra over a period of 9 years were calculated for one location in the North Atlantic. Further analysis demonstrated that strong relationships exist between the seasonal trends of the estimated size spectra and the mixed-layer depth, nutrient biomass, and total chlorophyll. The results contain useful information on the time-dependent biomass flux in the pelagic ecosystem.

Size and molecular flexibility affect the binding of ellagitannins to bovine serum albumin

Binding to bovine serum albumin of monomeric (vescalagin and pedunculagin) and dimeric ellagitannins (roburin A, oenothein B, and gemin A) was investigated by isothermal titration calorimetry and fluorescence spectroscopy, which indicated two types of binding sites. Stronger and more specific sites exhibited affinity constants, K1, of 104–106 M–1 and stoichiometries, n1, of 2–13 and dominated at low tannin concentrations. Weaker and less-specific binding sites had K2 constants of 103–105 M–1 and stoichiometries, n2, of 16–30 and dominated at higher tannin concentrations. Binding to stronger sites appeared to be dependent on tannin flexibility and the presence of free galloyl groups. Positive entropies for all but gemin A indicated that hydrophobic interactions dominated during complexation. This was supported by an exponential relationship between the affinity, K1, and the modeled hydrophobic accessible surface area and by a linear relationship between K1 and the Stern–Volmer quenching constant, KSV.

Advanced source apportionment of size-resolved trace elements at multiple sites in London during winter

Trace element measurements in PM10–2.5, PM2.5–1.0 and PM1.0–0.3 aerosol were performed with 2 h time resolution at kerbside, urban background and rural sites during the ClearfLo winter 2012 campaign in London. The environment-dependent variability of emissions was characterized using the Multilinear Engine implementation of the positive matrix factorization model, conducted on data sets comprising all three sites but segregated by size. Combining the sites enabled separation of sources with high temporal covariance but significant spatial variability. Separation of sizes improved source resolution by preventing sources occurring in only a single size fraction from having too small a contribution for the model to resolve. Anchor profiles were retrieved internally by analysing data subsets, and these profiles were used in the analyses of the complete data sets of all sites for enhanced source apportionment. A total of nine different factors were resolved (notable elements in brackets): in PM10–2.5, brake wear (Cu, Zr, Sb, Ba), other traffic-related (Fe), resuspended dust (Si, Ca), sea/road salt (Cl), aged sea salt (Na, Mg) and industrial (Cr, Ni); in PM2.5–1.0, brake wear, other traffic-related, resuspended dust, sea/road salt, aged sea salt and S-rich (S); and in PM1.0–0.3, traffic-related (Fe, Cu, Zr, Sb, Ba), resuspended dust, sea/road salt, aged sea salt, reacted Cl (Cl), S-rich and solid fuel (K, Pb). Human activities enhance the kerb-to-rural concentration gradients of coarse aged sea salt, typically considered to have a natural source, by 1.7–2.2. These site-dependent concentration differences reflect the effect of local resuspension processes in London. The anthropogenically influenced factors traffic (brake wear and other traffic-related processes), dust and sea/road salt provide further kerb-to-rural concentration enhancements by direct source emissions by a factor of 3.5–12.7. The traffic and dust factors are mainly emitted in PM10–2.5 and show strong diurnal variations with concentrations up to 4 times higher during rush hour than during night-time. Regionally influenced S-rich and solid fuel factors, occurring primarily in PM1.0–0.3, have negligible resuspension influences, and concentrations are similar throughout the day and across the regions.