EFFECTS OF AGE AND SIZE ON LIFE HISTORIES AND POPULATION GROWTH OF RHODODENDRON MAXIMUM SHOOTS

Age- and size-specific shoot life histories were studied with population censuses in June 1984 and June 1985 in an evergreen understory shrub. Rhododendron maximum. Most shoots (65%) survived without branching or flowering, and lesser numbers branched (2%), flowered (20%), or died (23%) during the year between censuses. The probabilities of surviving, branching, flowering or dying were both age- and size-dependent. Small, young shoots increased in leaf area. Flowering occurred most prominently in 3- to 6-year old shoots that had exceeded a leaf area of 200 cm², and the rate of flowering increased proportionately with size above this threshold. Branching normally occurred in the year following flowering. The age and size distributions of the population shifted significantly between years, indicating a nonequilibrium population. The survival schedule was Deevey Type I, indicating a high degree of “parental care” of young shoots. Age- and age + size-based demographic models predicted a rapid decline of the shoot population over a decade, while a size-based model predicted a much slower decline in shoot numbers. A sensitivity analysis of the models showed that overall shoot population growth was positively influenced by branching shoots and shoots that added leaf area, and negatively influenced by shoots that lost leaf area, died, or flowered. The role of shoot life histories in determining individual plant fitness and ecological dominance is discussed.     

Variation in flowering size and age of a facultative biennial, Aster kantoensis (Compositae), in response to nutrient availability

Although the flowering of facultative biennials is size-dependent, flowering size varies markedly within a single population as well as among populations. In this study, 15 half-sib families of the facultative biennial Aster kantoensis were grown from seeds at three nutrient levels (low, medium, and high). A significant nutrient × family interaction effect was found for bolting size, and among-family variation in bolting size increased with decreasing nutrient level. Growth from bolting to flowering tended to be greatest at the high nutrient level. Such responses of bolting size and growth from bolting to flowering resulted in an increase in flowering size at the high nutrient level and a significant variation in its reaction norm among families. For flowering age, there was a significant interaction of nutrient × family, and its among-family variation increased with decreasing nutrient levels, as was the case with bolting size. These results indicate that genetic variation in phenotypic plasticity of bolting size with nutrient availability was one cause of the variation in flowering size and age in the A. kantoensis population on the floodplain with the spatially heterogeneous nutrient availability. Moreover, responses of growth from bolting to flowering to nutrient availability could enhance the variation in flowering size.     

Shoot growth dynamics and size-dependent shoot fate of a clonal plant,Festuca rubra, in a mountain grassland

The relation of the within-season and between-season patterns of shoot growth were compared in a clonal grass with long-lived shoots,Festuca rubra, in a mown mountain grassland. The growth rate of shoot length from spring to summer in a year was almost constant for each shoot irrespective of spring shoot length each year. The annual shoot growth rate from spring to spring was negatively correlated with the shoot length in the first spring. Shoots of different length and age therefore tended to converge over time to a population of identical shoot size, suggesting an equalizing effect of growth pattern on size structure. Shoot size (shoot length and number of leaves) influenced the fates of shoots. Larger shoots showed an increased incidence of both flowering and formation of intravaginal daughter shoots and a decreased incidence of death in the subsequent time period. The fates of shoots were independent of their age. Although the negatively size-dependent springto-spring annual shoot growth rate acted to decrease shoot size variation, the remaining variation within the shoot population was still sufficient to generate different fates of shoots. These fates were not related to the previous life history of individual shoots. There was a significantly positive effect of the shoot size at initiation on its life expectancy. This was mainly attributable to the positively size-dependent survival rate of shoots in the early stage (<1 year old) of shoot life history. Later on (> 1 year old), shoot size had little effect on the survival rate of shoots. Once small young shoots have survived this early stage (< 1 year old) in life history, they can grow vigorously, little affected by competition regardless of shoot size, and converge to a stable size structure of shoots of similar size. Only shoot size in the early stage ( < 1 year old) of life history is important for the persistence of a shoot population.     

Stochastic stable population growth in integral projection models: theory and application

Stochastic matrix projection models are widely used to model age- or stage-structured populations with vital rates that fluctuate randomly over time. Practical applications of these models rest on qualitative properties such as the existence of a long term population growth rate, asymptotic log-normality of total population size, and weak ergodicity of population structure. We show here that these properties are shared by a general stochastic integral projection model, by using results in (Eveson in D. Phil. Thesis, University of Sussex, 1991, Eveson in Proc. Lond. Math. Soc. 70, 411-440, 1993) to extend the approach in (Lange and Holmes in J. Appl. Prob. 18, 325-344, 1981). Integral projection models allow individuals to be cross-classified by multiple attributes, either discrete or continuous, and allow the classification to change during the life cycle. These features are present in plant populations with size and age as important predictors of individual fate, populations with a persistent bank of dormant seeds or eggs, and animal species with complex life cycles. We also present a case-study based on a 6-year field study of the Illyrian thistle, Onopordum illyricum, to demonstrate how easily a stochastic integral model can be parameterized from field data and then applied using familiar matrix software and methods. Thistle demography is affected by multiple traits (size, age and a latent "quality" variable), which would be difficult to accommodate in a classical matrix model. We use the model to explore the evolution of size- and age-dependent flowering using an evolutionarily stable strategy (ESS) approach. We find close agreement between the observed flowering behavior and the predicted ESS from the stochastic model, whereas the ESS predicted from a deterministic version of the model is very different from observed flowering behavior. These results strongly suggest that the flowering strategy in O. illyricum is an adaptation to random between-year variation in vital rates.     

Convergence of two-locus gamete frequencies in random mating age-structured populations

We study two models describing infinite random mating age-structured populations. Under model I, the number of matings at any time is proportional to the number of mature females at that time, and the fecundity of a mating is assumed to be a product of factors that depend upon the ages of the mates, but not upon sex. Under model II, individuals can mate only with others of the same age group, and the number of matings of individuals of an age group is, at any time, proportional to the number of females of that age group. If model II holds, or the special case of model I in which the fecundity of all matings is the same, it is possible to show that, in the long run, allele frequencies converge and the gametic disequilibrium approaches zero at a geometric rate. A heuristic argument and a numerical example suggest that these things are also more generally true for model I. A good approximation to the time that it takes to reduce the gametic disequilibrium by a fraction equal to the recombination rate turns out to be the measure of the generation interval in Leslie's theory of population growth.     

Flowering Frequency and Plant Performance and their Relation to Age in the Perennial Orchid Spiranthes spiralis (L.) Chevall.

Abstract: Long-term demographic data have been analyzed to establish possible costs of flowering in the terrestrial orchid Spiranthes spiralis (L.) Chevall. in The Netherlands. Costs of flowering can be expressed as individual plant performance and flowering frequency in relation to the generative or vegetative status in the following year. Flowering in individuals of S. spiralis in a given year (t) is followed by a non-flowering phase in the next growing season (t + 1) in more than 80 % of the plants. The decline in flowering frequency is not a result of the age structure of the population involved because individual plants do not show signs of senescence after 10 - 15 years of aerial presence as an autotrophic plant. Rosettes have a smaller leaf area in the year of flowering (t), compared to the previous (t - 1) and following year (t + 1), due to the allocation of the limited underground resources to both flowering stalk and rosette at the beginning of its growing season. Generative reproduction in S. spiralis has a significant negative impact on both flowering frequency in subsequent years and on rosette size in the year of flowering. The flowering frequency and rosette size in relation to the life history, characterized by the yearly replacement of the underground tuber, is discussed. Better understanding of the life-history strategy, including costs of reproduction, may contribute to the creation of sustainable environmental conditions for growth of S. spiralis, e.g., optimal conditions for photosynthesis during the aboveground stage of the tiny wintergreen rosettes.     

Dynamics of an age‐structured population drawn from a random numbers table

I constructed age‐structured populations by drawing numbers from a random numbers table, the constraints being that within a cohort each number be smaller than the preceding number (indicating that some individuals died between one year and the next) and that the first two‐digit number following 00 or 01 ending one cohort’s life be the number born into the next cohort. Populations constructed in this way showed prolonged existence with total population numbers fluctuating about a mean size and with long‐term growth rate (r) ≈ 0. The populations’ birth rates and growth rates and the females’ per capita fecundity decreased significantly with population size, whereas the death rates showed no significant relationship to population size. These results indicate that age‐structured populations can persist for long periods of time with long‐term growth rates of zero in the absence of negative‐feedback loops between a population’s present or prior density and its birth rate, growth rate, and fecundity, contrary to the assumption of density‐dependent regulation hypotheses. Thus, a long‐term growth rate of zero found in natural populations need not indicate that a population’s numbers are regulated by density‐dependent factors.     

松嫩平原碱化草甸星星草种群分蘖株延长生殖生长的表型可塑性调节

在松嫩平原碱化草甸,采用大样本随机取样的方法,研究了不同时间到达抽穗初期、抽穗期、开花期和乳熟期的星星草种群生殖分蘖株数量性状的可塑性及其调节规律.结果表明：除在开花期存在一定的波动外,在每5 d的时间里,随着生殖生长时间的延长, 星星草种群在抽穗初期、抽穗期和乳熟期的生殖分蘖株高、分蘖株生物量、花序长和花序生物量均依次显著增加.各生育期的星星草种群生殖分蘖株高与花序生物量呈显著正相关,而与生殖分配呈显著负相关.随着生殖生长时间的延长,抽穗初期、开花期和乳熟期的星星草花序生物量随着分蘖株高增加,其幂函数的增长速率均呈增大趋势.生殖生长时间延长10 d,其抽穗初期和抽穗期的生殖分配直线下降速率分别降低了43.2%和44.31%;延长5 d,乳熟期的下降速率降低了130%.表明星星草种群分蘖株生殖生长的表型可塑性调节遵循着一定的规律.     

Environmental Uncertainty and Variable Diapause

We analyze a stage-structured model of a population that displays variable diapause in a randomly varying environment. The ruggedness of the environment is measured by the extent of random variation in per-capita reproductive success. We show how variable diapause and environmental characteristics affect the population′s stochastic growth rate. In rugged unpredictable environments, phenotypes that show some tendency to diapause are found to have a higher growth rate than nondiapausing phenotypes. In harsh rugged environments, some tendency to diapause may be all that permits population persistence. Positive serial autocorrelation causes the optimal diapause fraction to decrease, while negative autocorrelation causes that fraction to increase. The structured model behaves very differently from a scalar model for large diapause fractions even in uncorrelated environments, and in many cases predicts a broad optimum. The difference between models is due to the extreme variability of stage structure in populations subject to even small variability when diapause tendency is high.     

Growth and flowering history of Xanthorrhoea johnsonii Lee (Liliaceae) in Toohey Forest Queensland

The settlement of Australia by European man has been a major ecological factor in the history of the vegetation. A reconstruction of one aspect of this influence is given, based on estimations of the growth rate and flowering history of a population of Xanthorrhoea johnsonii .
The age structure of four parts of the existing population within the campus of Griffith University, Brisbane was examined. The mean growth rate, based on counts of leaf production and the number of leaf scars per unit length of the caudexes, was estimated to be 0.88 (s.d. 0.17) cm year^-1. The flowering history was reconstructed from the numbers and positions of flower scars recorded after removal of the leaf bases from 264 individuals. Flowering potential appears to increase up to about 50 years of age and is then relatively stable. Flower production gradually increased from 1820 to 1967 and then fell sharply. Since 1840 there is a strong correlation between the number of residences established within 3 km of the site and the number of flowers produced. The number of plants flowering is known to increase as a result of fire, and we therefore suggest that increasing numbers of accidental or deliberate fires started by settlers and later inhabitants may have caused the increase in flowering.     

Impact of climate change factors on the clonal sedge Carex bigelown: implications for population growth and vegetative spread

Hypothesized life-cycle responses to climate change for the arctic, clonal perennial Carex bigelown are constructed using a range of earlier observations and experiments together with new information from monitoring and an environmental perturbation study These data suggest, that under current climate change scenarios, increases in CO₂, temperature and nutrient availability would promote growth in a qualitatively similar way The evidence suggests that both tiller size and daughter tiller production will increase, and be shifted towards production of phalanx tillers which have a greater propensity for flowering Furthermore, age at tillering as well as tiller life span may decrease, whereas survival of younger age classes might be higher Mathematical models using experimental data incorporating these hypotheses were used to a) integrate the various responses and to calculate the order of magnitude of changes in population growth rate (γ). and b) to explore the implications of responses in individual demographic parameters for population growth rate The models suggest that population growth rate following climate change might increase significantly, but not un-realistically so. with the younger, larger, guerilla ullers being the most important tiller categones in contributing to X The rate of vegetative spread is calculated to more than double, while cyclical trends in flowering and populauon growth are predicted to decrease substantially     

Evolution in the real world: stochastic variation and the determinants of fitness in Carlina vulgaris

Empirical studies of life histories often ignore stochastic variation, despite theoretical demonstrations of its potential impact on life-history evolution. Here we use a novel approach to explore the effects of stochastic variation on life-history evolution and estimate the selection pressures operating on the monocarpic perennial Carlina vulgaris, in which flowering may be delayed by up to eight years. The approach is novel in that we use modern theoretical techniques to estimate selection pressures and the fitness landscape from a fully parameterised individual-based model. These approaches take into account temporal variation in demographic rates and density dependence. Analysis of 16 years' data revealed significant temporal variation in growth, mortality, and recruitment in our study population. Flowering was strongly size dependent and, unusually for such a species, also age dependent. Individual-based models of the flowering strategy, parameterized using field data, consistently underestimated the size at flowering, when temporal variation in demographic rates was ignored. In contrast, models that incorporated temporal variation in growth, mortality, and recruitment predicted sizes at flowering not significantly different from those observed in the field. Temporal variation in mortality, which had the largest effect on the flowering strategy, selected for increased size at flowering. An analytical approximation is presented to explain this result, extending the "1-year look-ahead criterion" presented in Rees et al. (2000). A fitness landscape generated by following the fate of rare mutant invaders with a broad range of alternative flowering strategies demonstrated that the observed parameters were adaptive. However, the fitness landscape reveals that approximately equal fitness is achieved by a broad range of strategies, providing a mechanism for the maintenance of genetic variation. To understand how the different parameters that defined our models determine the fitness of rare mutants, we numerically estimated the elasticities and sensitivities of mutant fitness. This demonstrated strong selection on a number of the parameters. Elasticities and sensitivities estimated in constant and random environments were significantly positively correlated, and both were negatively related to the standard error of the parameter. This last result is surprising and, we argue, reflects the genetic and phenotypic responses to selection.     

Tiller dynamics and assimilate partitioning in Lolium perenne with particular reference to flowering

The fate of 100 seedling plants of Lolium perenne L. was studied over a period of 2 years in a field plot. The birth and death of tillers and the production of inflorescences was followed, and the components of seed yield were recorded in detail in the first year. The pattern of distribution of ¹⁴CO₂ assimilated by the main shoot was examined at monthly intervals and during the first flowering season the distribution of ¹⁴C-assimilate from individual leaves and from the inflorescence was also studied. The capacity of individual tillers to assimilate ¹⁴CO₂ prior to flowering and the re-distribution of previously accumulated assimilate during seed growth were also assessed. Plants died at a more or less constant rate with time and only 54 survived to the end of the 2–yr period. First year mortality was associated with severe grazing or cutting but in the second year the death of ungrazed plants was observed. There was great variability in the production of tillers by surviving plants. In both years the number of live tillers per plant increased from July to the end of April with particularly rapid tillering in March and April establishing the maximum value for each year. There was a similar phase of rapid tillering after flowering in July. The number of live tillers per plant declined by 50% during stem elongation and inflorescence emergence and the majority of dead tillers were young secondary (in the first year) and tertiary (in the second year) tillers with a mean age of 40 days. Such tillers had poor assimilatory capacity prior to the onset of death and were not supplied with assimilate from the main shoot. Most of the plants surviving at the end of the experiment flowered in both years and one quarter of the maximum number of live tillers per plant recorded in April of each year produced inflorescences. The earlier a tiller was produced the greater was its chance of flowering and the greater its production of seed. The greater weight of seed produced was associated with the development of more seed-bearing florets per spikelet. There was relatively little export of “C-assimilate from the flowering main shoot, and the lower internodes formed the major sink for post-anthesis assimilate. The growth of seeds appeared to be relatively independent of the leaves for current assimilate. There was some evidence that assimilate accumulated in lower internodes was remobilised and utilised in the growth of seeds and new tillers. Overall, the results confirm the view that the grass plant is a dynamic population of short-lived tillers and indicate that increasing competition for assimilate at flowering exerts a major influence on the production and survival of tillers.     

Population growth rates: issues and an application

Current issues in population dynamics are discussed in the context of The Royal Society Discussion Meeting 'Population growth rate: determining factors and role in population regulation'. In particular, different views on the centrality of population growth rates to the study of population dynamics and the role of experiments and theory are explored. Major themes emerging include the role of modern statistical techniques in bringing together experimental and theoretical studies, the importance of long-term experimentation and the need for ecology to have model systems, and the value of population growth rate as a means of understanding and predicting population change. The last point is illustrated by the application of a recently introduced technique, integral projection modelling, to study the population growth rate of a monocarpic perennial plant, its elasticities to different life-history components and the evolution of an evolutionarily stable strategy size at flowering.     

Population dynamics of the perennial Plantago media in semi‐natural grasslands

Abstract. In this study we investigated population dynamics of a perennial forb, Plantago media, in semi‐natural grasslands in southeastern Sweden. Plantago media is a rather common inhabitant of grasslands in this region, but it has been shown to experience dispersal limitations both among managed grassland sites and at potential dispersal routes along road verges. The demography of P. media was studied in 22 permanent plots at two sites over five years. A seed sowing experiment was also performed at each site. The life‐cycle of P. media includes seedlings, juveniles, small vegetative rosettes, large vegetative rosettes and flowering rosettes. The population growth rates (λ‐values) were negative for both populations, with one exception: the first year transition matrix at one site. The projected life span for individuals surviving from seedlings to flowering rosettes varied between 19.6 yr and 227.8 yr. Elasticity analysis showed that remaining in the large rosette stages, both vegetative and flowering, was the most important factor influencing population growth rate. LTRE analysis gave similar results, indicating that spatial and temporal variation have similar effects on the population growth rate. The expected time to extinction in populations with an initial size of between 100 and 1000 individuals varied between 60 and 200 yr. The seed sowing experiment showed that seedling emergence was enhanced by both seed addition and disturbance, suggesting that recruitment is limited by seed and microsite availability. Recruitment was not found to have much impact on population growth rate. However, long‐term population maintenance may depend on occasional small‐scale disturbances that enhance pulses of recruitment. Fragmented landscape is likely to effect plant populations including rare and endangered species as well as more common species which have limited dispersal mechanisms.     

黑长臂猿栖息地旱冬瓜和潺槁木姜子种群分布格局和动态

旱冬瓜（Alnus nepalensis）和潺槁木姜子（Litsea glutinosa）是云南省无量山黑长臂猿（Nomascus concolor）栖息地中的两种常见乔木.利用最近邻体法和Heygi单木竞争指数模型,对两个种群的分布格局和竞争情况进行分析.结果表明,旱冬瓜在不同生长阶段均呈现随机分布,而伴生的潺槁木姜子种群则呈现随机分布 聚集分布 均匀分布的变化趋势.种间竞争和物种自身生物学特性对两个种群的分布格局具有显著影响.旱冬瓜种群的龄级结构为衰退型,潺槁木姜子种群则为成长型.     

Optimal individual growth and reproduction in perennial species with indeterminate growth

Summary A model predicting optimal timing of growth and reproduction in perennial species with indeterminate growth living in a seasonal environment, is presented. According to the model, the optimal fraction of growing season devoted to growth decreases with increasing individual age and size, which leads to S-shaped growth curves. Winter mortality seems to be a crucial factor affecting the timing of growth and reproduction, under the same function describing the dependence of growth rate and reproductive rate on body size. When winter mortality is heavy, it is often optimal to start reproducing in the first year, and to devote a large proportion of the subsequent years to reproduction, thus leading to small adult body sizes.The model has been applied to two species of mollusc and one species of fish. The model predictions fit well to the field data for these three species.