Abstract:
Fig trees (Ficus spp.) are pollinated by tiny wasps that enter their enclosed inflorescences (syconia). The wasp larvae also consume some fig ovules, which negatively affects seed production. Within syconia, pollinator larvae mature mostly in the inner ovules whereas seeds develop mostly in outer ovules—a stratification pattern that enables mutualism persistence. Pollinators may prefer inner ovules because they provide enemy-free space from externally ovipositing parasitic wasps. In some Australasian Ficus, this results in spatial segregation of pollinator and parasite offspring within syconia, with parasites occurring in shorter ovules than pollinators. Australian figs lack non-pollinating fig wasps (NPFW) that enter syconia to oviposit, but these occur in Africa and Asia, and may affect mutualist reproduction via parasitism or seed predation. We studied the African fig, F. burkei, and found a similar general spatial pattern of pollinators and NPFWs within syconia as in Australasian figs. However, larvae of the NPFW Philocaenus barbarus, which enters syconia, occurred in inner ovules. Philocaenus barbarus reduced pollinator abundance but not seed production, because its larvae replaced pollinators in their favoured inner ovules. Our data support a widespread role for NPFWs in contributing to factors preventing host overexploitation in fig-pollinator mutualisms. 1. Introduction Mutualisms are reciprocally beneficial interspecific interactions [1, 2], and a well-known system is that between fig trees (Ficus spp.) and their agaonid wasp pollinators [3–6]. In return for pollination, the wasps gall some fig ovules, which are then eaten by the larvae. About half (300+) of Ficus species are monoecious, where both male flowers and ovules are present in the same syconium (enclosed inflorescence or “fig”). Within monoecious syconia, ovules are highly variable in length [7–10]. Long (inner) ovules have short styles and mature near the centre of the syconium, whereas short (outer), long-styled ovules mature nearer the outer wall (see Figure 1). Female pollinating wasps (foundresses) lay their eggs by inserting their ovipositors down the flower styles. At maturation, wasp galls are clustered at the syconium’s centre [4, 6, 9–13] with seeds at the outer wall. This spatial stratification of pollinating wasps and seeds enables mutualism stability, although the mechanisms preventing the wasps from galling all ovules are unclear. Figure 1: Variation in style and pedicel length in female flowers of monoecious Ficus (adapted from Dunn et al. [ 13]). Mechanisms proposed to

Abstract:
Mutualisms are interspecific interactions in which both players benefit. Explaining their maintenance is problematic, because cheaters should outcompete cooperative conspecifics, leading to mutualism instability. Monoecious figs (Ficus) are pollinated by host-specific wasps (Agaonidae), whose larvae gall ovules in their “fruits” (syconia). Female pollinating wasps oviposit directly into Ficus ovules from inside the receptive syconium. Across Ficus species, there is a widely documented segregation of pollinator galls in inner ovules and seeds in outer ovules. This pattern suggests that wasps avoid, or are prevented from ovipositing into, outer ovules, and this results in mutualism stability. However, the mechanisms preventing wasps from exploiting outer ovules remain unknown. We report that in Ficus rubiginosa, offspring in outer ovules are vulnerable to attack by parasitic wasps that oviposit from outside the syconium. Parasitism risk decreases towards the centre of the syconium, where inner ovules provide enemy-free space for pollinator offspring. We suggest that the resulting gradient in offspring viability is likely to contribute to selection on pollinators to avoid outer ovules, and by forcing wasps to focus on a subset of ovules, reduces their galling rates. This previously unidentified mechanism may therefore contribute to mutualism persistence independent of additional factors that invoke plant defences against pollinator oviposition, or physiological constraints on pollinators that prevent oviposition in all available ovules.

Abstract:
Mutualisms are interspecific interactions in which both players benefit. Explaining their maintenance is problematic, because cheaters should outcompete cooperative conspecifics, leading to mutualism instability. Monoecious figs (Ficus) are pollinated by host-specific wasps (Agaonidae), whose larvae gall ovules in their “fruits” (syconia). Female pollinating wasps oviposit directly into Ficus ovules from inside the receptive syconium. Across Ficus species, there is a widely documented segregation of pollinator galls in inner ovules and seeds in outer ovules. This pattern suggests that wasps avoid, or are prevented from ovipositing into, outer ovules, and this results in mutualism stability. However, the mechanisms preventing wasps from exploiting outer ovules remain unknown. We report that in Ficus rubiginosa, offspring in outer ovules are vulnerable to attack by parasitic wasps that oviposit from outside the syconium. Parasitism risk decreases towards the centre of the syconium, where inner ovules provide enemy-free space for pollinator offspring. We suggest that the resulting gradient in offspring viability is likely to contribute to selection on pollinators to avoid outer ovules, and by forcing wasps to focus on a subset of ovules, reduces their galling rates. This previously unidentified mechanism may therefore contribute to mutualism persistence independent of additional factors that invoke plant defences against pollinator oviposition, or physiological constraints on pollinators that prevent oviposition in all available ovules.

Abstract:
Fig trees are pollinated by fig wasps, which also oviposit in female flowers. The wasp larvae gall and eat developing seeds. Although fig trees benefit from allowing wasps to oviposit, because the wasp offspring disperse pollen, figs must prevent wasps from ovipositing in all flowers, or seed production would cease, and the mutualism would go extinct. In Ficus racemosa, we find that syconia (‘figs’) that have few foundresses (ovipositing wasps) are underexploited in the summer (few seeds, few galls, many empty ovules) and are overexploited in the winter (few seeds, many galls, few empty ovules). Conversely, syconia with many foundresses produce intermediate numbers of galls and seeds, regardless of season. We use experiments to explain these patterns, and thus, to explain how this mutualism is maintained. In the hot summer, wasps suffer short lifespans and therefore fail to oviposit in many flowers. In contrast, cooler temperatures in the winter permit longer wasp lifespans, which in turn allows most flowers to be exploited by the wasps. However, even in winter, only in syconia that happen to have few foundresses are most flowers turned into galls. In syconia with higher numbers of foundresses, interference competition reduces foundress lifespans, which reduces the proportion of flowers that are galled. We further show that syconia encourage the entry of multiple foundresses by delaying ostiole closure. Taken together, these factors allow fig trees to reduce galling in the wasp-benign winter and boost galling (and pollination) in the wasp-stressing summer. Interference competition has been shown to reduce virulence in pathogenic bacteria. Our results show that interference also maintains cooperation in a classic, cooperative symbiosis, thus linking theories of virulence and mutualism. More generally, our results reveal how frequency-dependent population regulation can occur in the fig-wasp mutualism, and how a host species can ‘set the rules of the game’ to ensure mutualistic behavior in its symbionts.

Abstract:
We give a survey of the basic statistical ideas underlying the definition of entropy in information theory and their connections with the entropy in the theory of dynamical systems and in statistical mechanics.

Abstract:
aspirin has always remained an enigmatic drug. not only does it present with new benefits for treating an ever-expanding list of apparently unrelated diseases at an astounding rate but also because aspirin enhances our understanding of the nature of these diseases processe. originally, the beneficial effects of aspirin were shown to stem from its inhibition of cyclooxygenase-derived prostaglandins, fatty acid metabolites that modulate host defense. however, in addition to inhibiting cyclooxygenase activity aspirin can also inhibit pro-inflammatory signaling pathways, gene expression and other factors distinct from eicosanoid biosynthesis that drive inflammation as well as enhance the synthesis of endogenous protective anti-inflammatory factors. its true mechanism of action in anti-inflammation remains unclear. here the data from a series of recent experiments proposing that one of aspirin's predominant roles in inflammation is the induction of nitric oxide, which potently inhibits leukocyte/endothelium interaction during acute inflammation, will be discussed. it will be argued that this nitric oxide-inducing effects are exclusive to aspirin due to its unique ability, among the family of traditional anti-inflammatory drugs, to acetylate the active site of inducible cyclooxygenase and generate a family of lipid mediators called the epi-lipoxins that are increasingly being shown to have profound roles in a range of host defense responses.

Abstract:
Let $\Omega$ be a connected open subset of $\Ri^d$. We analyze $L_1$-uniqueness of real second-order partial differential operators $H=-\sum^d_{k,l=1}\partial_k\,c_{kl}\,\partial_l$ and $K=H+\sum^d_{k=1}c_k\,\partial_k+c_0$ on $\Omega$ where $c_{kl}=c_{lk}\in W^{1,\infty}_{\rm loc}( \Omega), c_k\in L_{\infty,{\rm loc}}(\Omega)$, $c_0\in L_{2,{\rm loc}}(\Omega)$ and $C(x)=(c_{kl}(x))>0$ for all $x\in\Omega$. Boundedness properties of the coefficients are expressed indirectly in terms of the balls $B(r)$ associated with the Riemannian metric $C^{-1}$ and their Lebesgue measure $|B(r)|$. \noindent\hspace{10mm}First we establish that if the balls $B(r)$ are bounded, the T\"acklind condition $\int^\infty_Rdr\,r(\log|B(r)|)^{-1}=\infty$ is satisfied for all large $R$ and $H$ is Markov unique then $H$ is $L_1$-unique. If, in addition, $C(x)\geq \kappa\, (c^{T}\!\otimes\, c)(x)$ for some $\kappa>0$ and almost all $x\in\Omega$, $\divv c\in L_{\infty,{\rm loc}}(\Omega)$ is upper semi-bounded and $c_0$ is lower semi-bounded then $K$ is also $L_1$-unique. \noindent\hspace{10mm}Secondly, if the $c_{kl}$ extend continuously to functions which are locally bounded on $\partial\Omega$ and if the balls $B(r)$ are bounded we characterize Markov uniqueness of $H$ in terms of local capacity estimates and boundary capacity estimates. For example, $H$ is Markov unique if and only if for each bounded subset $A$ of $\overline\Omega$ there exist $\eta_n \in C_c^\infty(\Omega)$ satisfying $\lim_{n\to\infty} \|\one_A\Gamma(\eta_n)\|_1 = 0$, where $\Gamma(\eta_n)=\sum^d_{k,l=1}c_{kl}\,(\partial_k\eta_n)\,(\partial_l\eta_n)$, and $\lim_{n\to\infty}\|\one_A (\one_\Omega-\eta_n )\, \varphi\|_2 = 0$ for each $\varphi \in L_2(\Omega)$ or if and only if $\capp(\partial\Omega)=0$.

Abstract:
Let $h$ be a quadratic form with domain $W_0^{1,2}(\Ri^d)$ given by \[ h(\varphi)=\sum^d_{i,j=1}(\partial_i\varphi,c_{ij}\,\partial_j\varphi) \] where $c_{ij}=c_{ji}$ are real-valued, locally bounded, measurable functions and $C=(c_{ij})\geq 0 $. If $C$ is strongly elliptic, i.e.\ if there exist $\lambda, \mu>0$ such that $\lambda\,I\geq C\geq \mu \,I>0$, then $h$ is closable, the closure determines a positive self-adjoint operator $H$ on $L_2(\Ri^d)$ which generates a submarkovian semigroup $S$ with a positive distributional kernel~$K$ and the kernel satisfies Gaussian upper and lower bounds. Moreover, $S$ is conservative, i.e.\ $S_t\one=\one$ for all $t>0$. Our aim is to examine converse statements. First we establish that $C$ is strongly elliptic if and only if $h$ is closable, the semigroup $S$ is conservative and $K$ satisfies Gaussian bounds. Secondly, we prove that if the coefficients are such that a Tikhonov growth condition is satisfied then $S$ is conservative. Thus in this case strong ellipticity of $C$ is equivalent to closability of $h$ together with Gaussian bounds on $K$. Finally we consider coefficients $c_{ij}\in W^{1,\infty}_{\rm loc}(\Ri^d)$. It follows that $h$ is closable and a growth condition of the T\"acklind type is sufficient to establish the equivalence of strong ellipticity of $C$ and Gaussian bounds on $K$.