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We establish necessary conditions for the existence of solutions to a class of semilinear hyperbolic problems on complete noncompact Riemannian manifolds, extending some nonexistence results for the wave operator with power nonlinearity on the whole Euclidean space. A general weight function depending on spacetime is allowed in front of the power nonlinearity.

We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $M\times \mathbb R_+$, where $M$ is a complete noncompact Riemannian manifold. Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the direction along which infinity is approached. Moreover, the large-time behavior of such solutions is studied. We consider also elliptic equations on $M$ with similar conditions at infinity.

We describe the main reproductive characteristics (laying date, egg size, hatchling mass, and breeding success), chick growth, and patterns of provisioning in Lesser Noddies (Anous tenuirostris) on Aride Island, Seychelles, 1995–2002. The bulk of the population laid eggs between late May and late June in most years. Both hatching and fledging success varied significantly between years, with fledging success (2–92%) more variable than hatching success (28–91%). Productivity of less than 0.10 chicks per breeding pair occurred in 25% of the years. In 2001, egg volume did not differ significantly between hatched and unhatched eggs. Chick mass at hatching was significantly correlated with an egg volume index, but there were no correlations between egg size and either hatching date or linear growth rate. Around 40% of the Lesser Noddy chicks were fed at dusk. Chicks aged 0–5 and 6–10 days received significantly less food than older chicks. There was evidence of daily and stochastic variation in the foraging success of individual birds. Comparing similar studies, chicks of Lesser Noddies and Sooty Terns (Sterna fuscata) appeared more resistant to fluctuating food supplies than those of Roseate Terns (Sterna dougallii), indicating that, in tropical seas, slow growth and foraging farther offshore are more advantageous than faster growth and inshore feeding. Datas de Postura, Alimentação dos Filhotes e Sucesso Reprodutivo de Anous tenuirostris na Ilha de Aride, Seychelles Resumo. Neste estudo descrevemos as principais características da biologia reprodutiva (datas de postura, tamanho dos ovos, peso dos filhotes ao nascerem e sucesso reprodutivo), crescimento e padrões de alimentação dos filhotes em Tinhosa-de-barrete, Anous tenuirostris, na ilha de Aride, Seychelles, 1995–2002. Na maioria dos anos a postura ocorreu entre o fim de Maio e o fim de Junho. O sucesso de eclosão e o sucesso de sobrevivência das crias variaram significativamente entre anos, apresentando o sucesso de sobrevivência (2–92%) uma maior variação do que o sucesso de eclosão (28–91%). Uma produtividade inferior a 0,10 crias por casal reprodutor ocorreu em 25% dos anos. Em 2001, o volume dos ovos que eclodiram não diferiu significativamente do volume dos ovos que não eclodiram. O peso dos filhotes ao nascerem apresentou uma correlação significativa com o índice de volume dos ovos, mas não se obtiveram correlações entre o tamanho dos ovos e, a data de eclosão e a taxa de crescimento linear dos filhotes. Cerca de 40% dos filhotes de Tinhosa-de-barrete foram alimentados ao anoitecer. Os filhotes com idades entre 0–5 e 6–10 dias receberam significativamente menos alimento do que os filhotes mais velhos. Foram observadas variações diárias e estocásticas no sucesso de alimentação dos indivíduos. A comparação do presente estudo com estudos semelhantes, sugere que as crias de A. tenuirostris e de Sterna fuscata sejam mais resistentes a flutuações na disponibilidade de alimento do que as crias de Sterna dougallii. Isto indica que, em mares tropicais, uma menor taxa de crescimento e uma alimentação em zonas pelágicas são estratégias mais vantajosas do que uma taxa de crescimento rápida e alimentação em zonas costeiras.

Many demographic studies on long-lived seabirds have focused on the estimation of adult survival, but much less is known about survival during the early years of life, especially in tropical species. We report analyses of a capture-recapture dataset of 685 roseate terns ringed as fledglings and adults between 1998 and 2005 on Aride Island, Seychelles, and recaptured/resighted at the same colony site over a 5 yr (2002 to 2006) period. A multistate model was used to estimate survival for different age classes, including juvenile (first-year) birds returning as non-breeding prospectors. The effect of infestation by parasites (ticks) on survival was also examined. Overall, the estimated return of first-year individuals to the natal colony was very variable, ranging from 2 to 22%. Conditioned on survival, the probability of returning from Age 2 yr onwards increased to 70%. Survival rates were best modeled as time-specific, with estimates varying from 0.02 to 1.00 (mean 0.69) in first-year birds with a marked negative effect of tick infestation. In older birds (minimum age of 2 yr), the annual estimates fell between 0.69 and 0.86 (mean 0.77). Using a components of variance approach for estimation of year-to-year variation, we found high temporal variability for first-year individuals (coefficient of variation [CV] = 65 %) compared to much less variation in the survival rate of older birds (CV = 9 %). These findings agree with the life-history prediction that demographic rates of juveniles are usually lower and more variable than those of older individuals. Our results are also consistent with the predicted negative effect of tick parasitism on juvenile survival. Compared with data from other roseate tern populations, survival over the first 2 yr (Age 0 to 2 yr) was 18 to 40 % higher in this study, suggesting that a high 'young' survival rate may be an important demographic trait in this tropical population to compensate for the low annual reproductive success. Our data show that estimating survival of young individuals may be crucial to elucidating the demographic tactics of seabirds.

We assessed the influence of inter-annual changes in primary productivity and local, regional and large scale ocean indices on the breeding parameters of roseate terns Sterna dougallii on Aride Island, Seychelles, western Indian Ocean. Productivity (chicks per breeding pair), timing of breeding and clutch and egg sizes were monitored annually for 8 yr and correlated with local ocean productivity (denoted by Sea-viewing Wide Field-of -view Sensor, SeaWiFS, estimates of chlorophyll concentration, CC), sea surface temperature and indices recording the status of the Indian Ocean Dipole and of El Nino. The rate of increase in CC between mean laying date and CC peak value was positively related to roseate tern productivity and mean clutch size over the 1998 to 2005 study period. Colony productivity seemed also to be influenced by the Multivariate El Nino Index. In most years, the breeding phenology of roseate terns corresponded to the local increase in CC around Aride, and failure to adjust timing of reproduction to the timing of the phytopankton bloom decreased the probability of breeding success. This is the first study showing that a tropical seabird species is sensitive to inter-annual variations in the intensity and timing of the phytoplankton bloom, which should be connected to annual variations in the availability of its main fish prey (juvenile goatfishes). Overall, these patterns indicate that the reproduction of this top marine predator is dictated by the temporal variability in oceanographic conditions. We suggest that CC data available over the world's oceans may be a useful tool to develop models predicting the fate of colonies of inshore feeding seabirds when other, more conventional, monitoring methods cannot be used.