Facilitation and competition interact with seed dormancy to affect population dynamics in annual plants

Seed dormancy increases population size via bet-hedging and by limiting negative interactions (e.g., competition) among individuals. On the other hand, individuals also interact positively (e.g., facilitation), and in some systems, facilitation among juveniles precedes competition among adults in the same generation. Nevertheless, studies of the benefits of seed dormancy typically ignore facilitation. Using a population growth model, we ask how the facilitation–competition balance interacts with seed dormancy rate to affect population dynamics in constant and variable environments. Facilitation increases the growth rate and equilibrium size (in both constant and variable environments) and reduces the extinction rate of populations (in a variable environment), and a higher rate of seed dormancy allows populations with facilitation to reach larger sizes. However, the combined benefits of facilitation and a high dormancy rate only occur in large populations. In small populations, weak facilitation does not affect the growth rate, but does induce a weak demographic Allee effect (where population growth decreases with decreasing population size). Our results suggest that facilitation within populations can interact with bet-hedging traits (such as dormancy) or other traits that mediate density to affect population dynamics. Further, by ensuring survival but limiting reproduction, ontogenetic switches from facilitation to competition may enable populations to persist but limit their maximum size in variable environments. Such intrinsic regulation of populations could then contribute to the maintenance of similar species within communities.     

The dynamics of density dependent population models

Summary The dynamics of density-dependent population models can be extraordinarily complex as numerous authors have displayed in numerical simulations. Here we commence a theoretical analysis of the mathematical mechanisms underlying this complexity from the viewpoint of modern dynamical systems theory. After discussing the chaotic behavior of one-dimensional difference equations we proceed to illustrate the general theory on a density-dependent Leslie model with two age classes. The pattern of bifurcations away from the equilibrium point is investigated and the existence of a strange attractor is demonstrated — i.e. an attracting limit set which is neither an equilibrium nor a limit cycle. Near the strange attractor the system exhibits essentially random behavior. An approach to the statistical analysis of the dynamics in the chaotic regime is suggested. We then generalize our conclusions to higher dimensions and continuous models (e.g. the nonlinear von Foerster equation).Supported by NSF Grant No. BMS 74-21240.     

Aerial seed bank dynamics and seedling emergence patterns in two annual Mediterranean Asteraceae

Question: We explored the functional significance of seasonal aerial seed banks in two coexisting, heterocarpic annual Asteraceae with dormant (Chrysanthemum coronarium) and non‐dormant (Anacyclus radiatus) achenes. We hypothesised that the plant achene pool is a significant component of total seed reserves, and that within‐season seedling emergence timing is shaped by achene release patterns. Location: SW Spain. Methods: In an observational study, we established temporal achene release patterns. We also quantified the aerial and soil achene pools throughout the release season, and assessed seedling emergence timing. Sowing experiments were used to explore the influence of achene release dynamics on emergence timing, and to establish achene morph‐specific patterns of between‐year distribution of germination. Results: Achene release extended from late spring to late autumn (Chrysanthemum), or from early autumn to early winter (Anacyclus). Within species, achene morphs differed in release timing. Only in Chrysanthemum, a small achene fraction seemed to persist in the soil, and between‐year germination distribution differed among morphs. In coexisting populations, the Anacyclus plant achene pool was an order of magnitude higher than the soil pool throughout the release season, whereas in Chrysanthemum both pools were of the same magnitude during autumn. Within‐year seedling emergence was significantly staggered beneath parent plants compared with the pattern resulting solely from the germination response in soil, with the exception of Chrysanthemum in one of the two study years. Conclusions: Results suggest that seasonal aerial seed banks are effective within‐season, risk‐reducing traits in ruderal Mediterranean habitats characteristic of the study species.     

The impact of litter and annual plants on recruitment from the seed bank of a lacustrine wetland

In an experimental marsh complex, 2 years of high water (1 m above normal) killed most of the emergent vegetation. During 1983, the first year of a 2-year drawdown, immediately following this period of high water, field experiments involving the removal of fallen emergent, filamentous algal and mixed (algal and emergent) litter were established at 6, 4 and 7 sites, respectively. All three indicated that the removal of litter significantly increased the number of species and the number of individuals of a species recruited from the seed bank. During 1984, the number of species and number of individuals in the removal treatment at emergent- and mixed-litter sites was again significantly higher than in the controls, but there was no longer a difference at algal litter sites.The addition of a mat of Typha litter in June 1983, at five sites that were free of litter, reduced seedling recruitment from the seed bank almost completely in both 1983 and 1984.The removal of 1982-standing litter, from sites at higher elevations that were invaded by Typha or Phragmites during the high water period, also increased the number of species and the number of individuals of a species compared with the controls in 1983.Removal of seedlings of the mudflat annual, Atriplex patula L., increased the number of grass shoots significantly in both 1983 and 1984. Grasses in the seedling removal treatment were also taller and flowered in 1983, the first year of the drawdown.     

A population dynamics model for annual plants subject to inbreeding depression

Summary We present a population dynamics model for annual plants subject to density dependent competition and a decline in mean individual fitness with inbreeding. An analysis of this model provides three distinct sets of parameter values that define the relative influence of inbreeding depression and density on population growth. First, a population with a relatively high finite rate of increase and a relatively small environmental carrying capacity can persist in spite of low levels of inbreeding depression. These types of population may occur during a bottleneck event that is caused by pure predation (or collecting) pressure rather than loss of habitat. Second, there can exist a minimum viable population size when the finite rate of increase is relatively low and the population is also affected by density: the growth or decline of the population will depend on the initial population size. Third, when the population is small enough to be simultaneously effected by density and by inbreeding depression, there can be no viable population.     

Uncoupling the effects of seed predation and seed dispersal by granivorous ants on plant population dynamics

Secondary seed dispersal is an important plant-animal interaction, which is central to understanding plant population and community dynamics. Very little information is still available on the effects of dispersal on plant demography and, particularly, for ant-seed dispersal interactions. As many other interactions, seed dispersal by animals involves costs (seed predation) and benefits (seed dispersal), the balance of which determines the outcome of the interaction. Separate quantification of each of them is essential in order to understand the effects of this interaction. To address this issue, we have successfully separated and analyzed the costs and benefits of seed dispersal by seed-harvesting ants on the plant population dynamics of three shrub species with different traits. To that aim a stochastic, spatially-explicit individually-based simulation model has been implemented based on actual data sets. The results from our simulation model agree with theoretical models of plant response dependent on seed dispersal, for one plant species, and ant-mediated seed predation, for another one. In these cases, model predictions were close to the observed values at field. Nonetheless, these ecological processes did not affect in anyway a third species, for which the model predictions were far from the observed values. This indicates that the balance between costs and benefits associated to secondary seed dispersal is clearly related to specific traits. This study is one of the first works that analyze tradeoffs of secondary seed dispersal on plant population dynamics, by disentangling the effects of related costs and benefits. We suggest analyzing the effects of interactions on population dynamics as opposed to merely analyzing the partners and their interaction strength.     

The effective size of annual plant populations: the interaction of a seed bank with fluctuating population size in maintaining genetic variation

Many annual plant populations undergo dramatic fluctuations in size. Such fluctuations can result in the loss of genetic variability. Here I formalize the potential for a seed bank to buffer against such genetic loss. The average time to seed germination (T) defines the generation time of "annuals" with a seed bank, and assuming random seed germination, I show that, under otherwise ideal conditions, a population's effective size (Ne) equals NT, where N is the number of adult plants. This result supports the general principle that lengthening the prereproductive period increases Ne. When adult numbers vary, Ne at any time depends on N and on the numbers contributing to the seed bank in previous seasons. Averaging these effects over time gives Ne approximately Nh + (T - 1)Na, where Nh and Na are the harmonic and arithmetic means of the adult population. Thus if T > 1, Ne is determined primarily by Na. Simulations showed that until fluctuations in N are large (>25x) this relationship is accurate. I extended the theory to incorporate a selfing rate (S) and reproductive variance (I) through seed production (k), outcrossed pollen (m), and variation in selfing rate: Ne = NT(1 -S/2)/(1 + I) = NT/[1 + FIS)(1 + I)]. Reproductive variance (I) equals [Ik(1 + S)2 + IM(1 - S)2 + 2(1 - S2)Ikm = S2IS(1 + Ik)]/4, , where Ij is the standardized variance (Vj/j2) of factor j and Ikm is the standardized covariance between k and m. These results are applicable to other organisms with a similar life history, such as freshwater crustaceans with diapausing eggs (e.g., tadpole shrimp, clam shrimp, and fairy shrimp) and other semelparous species with discrete breeding seasons and a variable maturation time (e.g., Pacific salmon).     

濒危植物明党参种子散布和种子库动态研究

对伞形科濒危植物明党参（Changium smyrnioides)的种子生产、散布和种子库动态进行了研究。明党参平均每株产生完好种子132粒,86.36%来自顶生花序,不同生境中个体产生的种子千粒重有差异;其平均1.06m高的花葶在种子散布过程中易倒伏,使种子远离母株;种子散布格局为聚集型;种子库密度随时间逐渐下降。明党参种子产量和不同时期种子库密度均低于同科非濒危植物峨参（Anthriscus sylvestris),2个种的种子库均为非持续型;明党参具有低种子数、大粒种子、种子散布远离母株以减少种内竞争的K对策,在受到人类大量采挖和生境干扰后种群不容易迅速恢复;而峨参采取高种子数、小粒种子、种子近母株密集分布和产生无性系的r对策,种群受干扰后易恢复。     

Consumers limit the abundance and dynamics of a perennial shrub with a seed bank

For nearly 30 years, ecologists have argued that predators of seeds and seedlings seldom have population-level effects on plants with persistent seed banks and density-dependent seedling survival. We parameterized stage-based population models that incorporated density dependence and seed dormancy with data from a 5.5-year experiment that quantified how granivorous mice and herbivorous voles influence bush lupine (Lupinus arboreus) demography. We asked how seed dormancy and density-dependent seedling survival mediate the impacts of these consumers in dune and grassland habitats. In dune habitat, mice reduced analytical lambda (the intrinsic rate of population growth) by 39%, the equilibrium number of aboveground plants by 90%, and the seed bank by 98%; voles had minimal effects. In adjacent grasslands, mice had minimal effects, but seedling herbivory by voles reduced analytical lambda by 15% and reduced both the equilibrium number of aboveground plants and dormant seeds by 63%. A bootstrap analysis demonstrated that these consumer effects were robust to parameter uncertainty. Our results demonstrate that the quantitative strengths of seed dormancy and density-dependent seedling survival--not their mere existence--critically mediate consumer effects. This study suggests that plant population dynamics and distribution may be more strongly influenced by consumers of seeds and seedlings than is currently recognized.     

A model of Calluna population dynamics; the effects of varying seed and vegetative regeneration

Regeneration of Calluna vulgaris in heathlands occurs from both seed and layering, although the relative importance of these two strategies appears to vary. A population model based on transitions between growth phases has been devised and parameter values obtained from published and original work. The effects of differing amounts of seed and vegetative regeneration on the population changes were then tested.The model predicts that a population with a relatively high occurrence of layering will tend towards a steady state, with little temporal variation in population density and cover. Conversely, low layering capacity increases temporal variation with little effect on mean cover. Increased seed regeneration on the other hand, increases both the amplitude of temporal variation in population density, and the frequency of cycles, whereas low seed regeneration results in a stable age distribution at less than 100% cover.     

Indirect interactions between browsers and seed predators affect the seed bank dynamics of a chaparral shrub

Interactions between herbivores and seed predators may have long-term consequences for plant populations that rely on persistent seed banks for recovery after unpredictable fires. We assessed the effects of browsing by deer and seed predation by rodents, ants and birds on the densities of seeds entering the seed bank of Ceanothus cuneatus var. rigidus, a maritime chaparral shrub in coastal California. Ceanothus produced many more seeds when protected from browsers in long-term experimental exclosures than did browsed plants, but the seed densities in the soil beneath browsed and unbrowsed Ceanothus were the same at the start of an intensive one-year study. The density of seeds in the soil initially increased in both treatments following summer seed drop: while densities returned to pre-drop levels within a few weeks under browsed plants, soil seed densities remained high for 5–8 months beneath unbrowsed plants. Rodent abundance (especially deer mice) was higher near unbrowsed plants than >30 m away, and rodents removed Ceanothus seeds from dishes in the experimental plots. At least in the short term, rodent density and rates of seed removal were inversely related to the intensity of browsing. Our data have management implications for maintaining viable Ceanothus populations by regulating the intensity of browsing and the timing, intensity and frequency of fires.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

Vegetation and seed bank dynamics in a tidal freshwater marsh

Questions: What are the feedbacks among the seed bank, parent vegetation, and landscape structure that control plant species turnover in space and time in a tidal freshwater marsh? How can these feedbacks be used to better understand marsh community dynamics and to establish restoration practices that seek to restore vegetation diversity of this important and widely distributed ecosystem? Location: Potomac River, Virginia, United States (15 km south of Washington, DC). Methods: We sampled the seed bank and standing vegetation in a tidal freshwater marsh and explored similarities between seed bank and vegetation composition through space and time. We then investigated marsh surface elevation, distance to nearest tidal channels, and life history of component species as potential explanations for the observed vegetation patterns. Results: The composition of individual plots changed considerably from year to year; however, the composition at broader spatial (whole marsh) and temporal (4 years) scales was relatively stable. Species composition of the seed bank was dissimilar to both the previous and current year's standing vegetation, and similarity to standing vegetation was particularly low in plots dominated by annual species. Landscape structure and life history characteristics of individual species best explained the spatiotemporal variability in marsh vegetation. Conclusions: Restoration designs should be landscape‐dependent and explicitly incorporate spatially structured elements such as elevation gradients to maximize community diversity in reconstructed tidal freshwater marshes. Optimal designs include areas of high seed input, areas of high species turnover, as well as other areas of greater stability.     

Stability of an age specific population with density dependent fertility

A nonlinear version of the Lotka-Sharpe model of population growth is considered in which the age specific fertility is a function of the population size. The stability of an equilibrium population distribution is investigated with respect to both global and local perturbations. Sufficient conditions for such stability are presented, as are estimates for the rate of return of the population to the equilibrium configuration. Particular attention is paid to those situations in which the age dependent stability criteria coincide with those of age independent models.     

Effects of density dependent sex allocation on the dynamics of a simultaneous hermaphroditic population: Modelling and analysis

In this work we present a mathematical model describing the dynamics of a population where sex allocation remains flexible throughout adult life and so can be adjusted to current environmental conditions. We consider that the fractions of immature individuals acquiring male and female sexual roles are density dependent through nonlinear functions of a weighted total population size. The main goal of this work is to understand the role of life-history parameters on the stabilization or destabilization of the population dynamics.The model turns out to be a nonlinear discrete model which is analysed by studying the existence of fixed points as well as their stability conditions in terms of model parameters. The existence of more complex asymptotic behaviours of system solutions is shown by means of numerical simulations.Females have larger fertility rate than males. On the other hand, increasing population density favours immature individuals adopting the male role. A positive equilibrium of the system exists whenever fertility and survival rates of one of the sexual roles, if shared by all adults, allow population growing while the opposite happens with the other sexual role. In terms of the female inherent net reproductive number, η_F, it is shown that the positive equilibria are stable when η_F is larger and closed to 1 while for larger values of η_F a certain asymptotic assumption on the investment rate in the female function implies that the population density is permanent. Depending on the other parameters values, the asymptotic behaviour of solutions becomes more complex, even chaotic. In this setting the stabilization/destabilization effects of the abruptness rate in density dependence, of the survival rates and of the competition coefficients are analysed.