Seasonality in the reproductive phenology ofFicus: Its evolution and consequences

Summary Ficus can only reproduce if they are pollinated by mutualistic wasps that breed within the figs. Pollen-loaded wasps enter the figs when the female flowers are receptive. Several weeks later, their offspring load pollen within the fig and then emerge. As individual trees typically produce crops of synchronous figs at long intervals, the shortlived wasps have to move to another, receptive, tree. The wasp population can only survive, and hence the fig population reproduce, if there are trees fruiting all over the year. When only few trees are present within a population gaps in the flowering sequence may lead to the extinction of the local pollinator population. Two models are presented. One investigates the number of trees necessary in order to sustain a local pollinator population when the tree population has a seasonal pattern of fruiting. The second model investigates how such a seasonal pattern may evolve within a fig population as a result of individual selection on the trees. It is shown that pollinator populations are fragilized under seasonal conditions. Hence, the breeding system ofFicus limits their expansion into highly seasonal habitats. Seasonal habitats may also lead to seasonal adjustment of male versus female investments and to the evolution of dioecy.     

Structure and function of the fig

Summary An overview is given of the functional anatomy of the fig. The fig is the site of pollination and oviposition, it produces wasps, seeds and pollen, and it is the unit of dispersal. Therefore the fig acts as both a flower and a fruit. When a flower is both fertilized and receives a wasp egg, it eventually produces a wasp. Fertilization in flowers that do not recieve a wasp egg initiates seed production. Wide variation exists in the structural features of figs among different subgenera and sections. Monoecious species and gynodioecious species have different strategies for maintaining the symbiosis with the pollinating fig wasps. Monoecious species produce wasps and seeds in a single fig type and show imperfect heterostyly. Gynodioecious species have specialized figs for wasp and for seed production and are characterized by perfect heterostyly.     

Population biology of figs: Applications for conservation

Summary The flowering phenology typical of at least monoecious figs-intra-tree synchrony and inter-tree asynchrony-poses problems for persistence of the pollinator population, and hence of the fig population itself, when fig population size is small. Establishment and maintenance of a population of the short-lived, species-specific wasp pollinator require that the fig population include a critical minimum number of trees (critical population size: CPS). Below CPS, temporal gaps between flowering trees occur that are unbridgeable by the pollinator, leading to its local extinction. This has implications for conservation in two contexts: human-aided invasions of introduced fig/wasp pairs, in which initial populations of figs and/or wasps may be small, and the persistence of figs and wasps in fragmented forest, in which initially large populations may be drastically reduced. Long-distance range extension by fig/wasp pairs is problematical for two reasons: 1) the fig species must first attain CPS, most likely through repeated seed dispersal events, before the wasp can establish; and 2) long-distance transit should be difficult for the tiny, short-lived wasp pollinators. I review the biology of natural and human-aided range extension by figs and fig wasps, and show that in human-aided range extensions these two difficult steps are circumvented. Once introduced into an area where hosts are abundant, fig wasps should readily establish from a small number of initial colonists, since they mate before dispersal and are highly tolerant of inbreeding. They are thus less subject than many insects to the genetic and demographic hazards of small population size. Of 5–6 fig/wasp pairs that have performed human-aided long-distance range extensions, one Asian pair,Ficus microcarpa and its pollinatorParapristina verticillata, is established in numerous areas in the northern neotropics, and the plant may become a serious weed. In tropical forests, figs may provide keystone resources for frugivores, providing fruit during seasons when other resources are scarce. Figs pose difficult problems for conservation biology, since minimum viable populations appear to be large, and since many species of tropical rainforests occur at low densities. This means that minimum areas required for persistence of a fig population- and for those of other species that would be affected were figs to be removed from the system-may often be large.     

Ecological and evolutionary dynamics of fig communities

Summary I review the status of five topics in fig research: pollen-vector versus seed production, flowering phenology and wasp population dynamics, monoecy versus dioecy, parasite pressure, and fig wasp behavior. I raise several new questions based on recent research on two components of fig reproduction: pollen-donation (male) and seed-production (female) success. I focus on how these two components of reproductive success depend on the flowering phenology of the figs and the population dynamics of the pollinator wasps.     

Selection and estimation of component models for seasonal time series

We present a method for investigating the evolution of trend and seasonality in an observed time series. A general model is fitted to a residual spectrum, using components to represent the seasonality. We show graphically how well the fitted spectrum captures the evidence for evolving seasonality associated with the different seasonal frequencies. We apply the method to model two time series and illustrate the resulting forecasts and seasonal adjustment for one series. Copyright © 2000 John Wiley & Sons, Ltd.     

Seasonal prediction of European cereal prices: good forecasts using bad models?

Because of their natural adherence to the climate and pronounced seasonal cycles, prices of field crops constitute an interesting field for exploring seasonal time series models. We consider quarterly prices of two major cereals: barley and wheat. Using traditional in‐sample fit and moving‐window techniques, we investigate whether seasonality is deterministic or unit‐root stochastic and whether seasonal cycles have converged over time. We find that seasonal cycles in the data are mainly deterministic and that evidence on common cycles across countries differs for the two commodities. Out‐of‐sample prediction experiments, however, yield a ranking with respect to accuracy that does not match the statistical in‐sample evidence. Parametric bootstrap experiments establish that the observed mismatch is indeed an inherent and systematic feature. Copyright © 2008 John Wiley & Sons, Ltd.     

Seasonality in large-scale macroeconometric models

Macroeconomic indicators are typically appraised in seasonally adjusted form, and forecasts are often presented in a similar way (as annual changes, for example). Moreover, the quarterly macroeconomic models used in forecasting are commonly estimated from seasonally adjusted data. Nevertheless, these models can generate forecasts with seasonal patterns, and this paper assesses the cause and cure of this phenomenon. It is found that forecast seasonality is induced by seasonality in the various inputs: exogenous variables, residual adjustments, the dynamic specification of certain equations, and annual changes in policy variables. Series changing annually but observed quarterly are termed ‘intercalated series’, and are simple examples of periodic processes. Forecast seasonality can be removed by appropriate adjustment of all these inputs. Models containing explicit future expectations variables solved in a model-consistent manner are also considered: numerical sensitivity to the terminal quarter may result from terminal conditions that require adjustment when seasonality is present.     

Seasonal heteroscedasticity and trends

This paper discusses the possibility of accommodating features such as seasonal heteroscedasticity and trends in a seasonal model. The former takes place when one or more seasonal effects are more variable than others and it is quite pervasive in hydrology, although interesting examples are found in economics, where it has recently been shown to characterize the output of the manufacturing series; seasonal trends occur when the seasonal effect shows a systematic tendency to increase or decrease its amplitude over the years. We consider different models of seasonality available in the literature and we argue that the Harrison and Stevens seasonal model enhances the flexibility that is necessary to capture effects associated to particular seasons. The resulting seasonally heteroscedastic model provides an explanation for the periodicity in the series alternative to that provided by the literature on periodic integration. © 1998 John Wiley & Sons, Ltd.     

A class of periodic trend models for seasonal time series

Trend and seasonality are the most prominent features of economic time series that are observed at the subannual frequency. Modeling these components serves a variety of analytical purposes, including seasonal adjustment and forecasting. In this paper we introduce unobserved components models for which both the trend and seasonal components arise from systematically sampling a multivariate transition equation, according to which each season evolves as a random walk with a drift. By modeling the disturbance covariance matrix we can encompass traditional models for seasonal time series, like the basic structural model, and can formulate more elaborate ones, dealing with season specific features, such as seasonal heterogeneity and correlation, along with the different role of the nonstationary cycles defined at the fundamental and the harmonic frequencies in determining the shape of the seasonal pattern.     

Heterochromatin characterization and distribution in the chromosomes of two populations ofIdotea baltica basteri Audouin, 1826 (Isopoda,Valvifera)

Two mediterranean populations ofIdotea baltica basteri from Messina and Naples showed a set of chromosomes composed by 58 all-biarmed chromosomes. The heterochromatin was located in the pericentromeric region of the chromosomes, and its composition appeared heterogeneous. In fact, not all the homologs showed heterochromatin resistant to digestion with three restriction enzymes (Alu I, Hae III and Sau 3A). Moreover, the two populations showed polymorphism in a band of G+C-rich telomeric heterochromatin, which was present only in the population from Messina. It is hypothesized that chromosomal polymorphism might reflect the geographical isolation of the two populations. It is also suggested that a process of diversification is taking place.     

Tourism in the Canary Islands: forecasting using several seasonal time series models

This paper deals with the analysis of the number of tourists travelling to the Canary Islands by means of using different seasonal statistical models. Deterministic and stochastic seasonality is considered. For the latter case, we employ seasonal unit roots and seasonally fractionally integrated models. As a final approach, we also employ a model with possibly different orders of integration at zero and the seasonal frequencies. All these models are compared in terms of their forecasting ability in an out‐of‐sample experiment. The results in the paper show that a simple deterministic model with seasonal dummy variables and AR(1) disturbances produce better results than other approaches based on seasonal fractional and integer differentiation over short horizons. However, increasing the time horizon, the results cannot distinguish between the model based on seasonal dummies and another using fractional integration at zero and the seasonal frequencies. Copyright © 2008 John Wiley & Sons, Ltd.     

Generalised Estimators for Seasonal Forecasting by Combining Grouping with Shrinkage Approaches

In this paper, generalised estimators are proposed to estimate seasonal indices for certain forms of additive and mixed seasonality. The estimators combine one of two group seasonal indices methods—Dalhart's group method and Withycombe's group method—with a shrinkage method in different ways. Optimal shrinkage parameters are derived to maximise the performance of the estimators. Then, the generalised estimators, with the optimal shrinkage parameters, are evaluated based on forecasting accuracy. Moreover, the effects of three factors are examined, namely, the length of data history, variance of random components and the number of series. Finally, a simulation experiment is conducted to support the evaluation. Copyright © 2011 John Wiley & Sons, Ltd.     

Seasonality in human sleep

The timing of sleep and sleep EEG parameters in 10 healthy male subjects were investigated in four seasons under controlled conditions. The phase of nocturnal sleep was delayed about one and a half hours in winter as compared to that in summer. The duration of stage 4 sleep decreased and REM sleep increased significantly in winter compared with summer. The seasonality in the timing of sleep can be explained by photoperiodic time cues, but the changes in sleep EEG parameters are diffucult to explain in terms of photoperiod.     

Seasonality in human sleep.

The timing of sleep and sleep EEG parameters in 10 healthy male subjects were investigated in four seasons under controlled conditions. The phase of nocturnal sleep was delayed about one and a half hours in winter as compared to that in summer. The duration of stage 4 sleep decreased and REM sleep increased significantly in winter compared with summer. The seasonality in the timing of sleep can be explained by photoperiodic time cues, but the changes in sleep EEG parameters are difficult to explain in terms of photoperiod.     

Modelling the daily banknotes in circulation in the context of the liquidity management of the European Central Bank

The main focus of this paper is to model the daily series of banknotes in circulation. The series of banknotes in circulation displays very marked seasonal patterns. To the best of our knowledge the empirical performance of two competing approaches to model seasonality in daily time series, namely the ARIMA‐based approach and the Structural Time Series approach, has never been put to the test. The application presented in this paper provides valid intuition on the merits of each approach. The forecasting performance of the models is also assessed in the context of their impact on the liquidity management of the Eurosystem. Copyright © 2008 John Wiley & Sons, Ltd.     

Phenology of fruit and leaf production by ‘strangler’ figs on Barro Colorado Island,Panamá

Summary Fruit and leaf initiation by 26 trees representing five stranglerFicus species in the subgenusUrostigma were monitored for 5–8 years in a seasonal lowland forest of central Panamá. Individual trees of each species initiated fruit in synchronized crops. High variation in the number of crops, intervals between crops and dates of crop initiation indicate that these species, like species in the subgenusPharmacosycea, initiate fruit crops the year around. Nevertheless, mean crop initiation dates for four of five species fell within the four-month dry season. Similarly, all species produced new leaf flushes throughout the year, however, mean leaf flush dates of all species fell within the first three months of the dry season.     

Ontogenetic changes in isozyme patterns during seed germination of self-pollinatedSecale species

Summary Six isozymatic systems have been studied comparatively during the first week of germination of seeds of self-pollinatedSecale species (S. silvestre Host. andS. vavilovii Gross.). Isozymatic systems do not change at all, or reach their definitive adult plant pattern early during germination.Acknowledgements. This work was carried out at the Dpto. de Genética, Univ. Complutense, Madrid and supported by grants from the C.A.I.C.Y.T. (1789-82) and the P.F.P.I.     

The chatfield-prothero case study: Another look

The Chatfield-Prothero case study in time series, ‘Sales of a company X’, is analysed from a perspective different to that of the authors. More accurate forecasting performance for these data is obtained by adopting the following two tactics: (1) shifting from a problem in transformation of the original series to one of seasonality adjustment; (2) assuming a mixed seasonality type model in contrast to employing a multiplicative assumption.     

(S)-(+)-4,4,4-Trifluoro-3-(indole-3-)butyric acid,a novel fluorinated plant growth regulator

Racemic 4,4,4-trifluoro-3-(indole-3-)butyric acid (TFIBA) has been synthesized and shown to inhibitAvena coleoptile elongation. (S)-(+)-TFIBA (fig. 1), which was prepared by an enzymatic method and markedly promotes root growth of Chinese cabbage, lettuce and rice plants, is a novel fluorinated plant growth regulator. Activity of the (S)-(+)-enantiomer of TFIBA was 10-fold greater than that of the (R)-(–)-enantiomer in the first two plant species and 5-fold greater in rice.     

Estimating and forecasting the long‐memory parameter in the presence of periodicity

We consider one parametric and five semiparametric approaches to estimate D in SARFIMA (0, D, 0)_s processes, that is, when the process is a fractionally integrated ARMA model with seasonality s. We also consider h‐step‐ahead forecasting for these processes. We present the proof of some features of this model and also a study based on a Monte Carlo simulation for different sample sizes and different seasonal periods. We compare the different estimation procedures analyzing the bias, the mean squared error values, and the confidence intervals for the estimators. We also consider three different methods to choose the total number of regressors in the regression analysis for the semiparametric class of estimation procedures. We apply the methodology to the Nile River flow monthly data, and also to a simulated seasonal fractionally integrated time series. Copyright © 2007 John Wiley & Sons, Ltd.