Landscapes

This chapter begins by discussing fitness landscape, an idea first introduced by evolutionary geneticist Sewall Wright and later extended by several other authors. The fitness landscape is defined in terms of some particular traits that are implicit in the virus particle phenotype and are usually described in terms of replication rate or infectivity. The landscape appears in most textbook plots as a multi-peaked surface. Local maxima represent optimal fitness values, which can be reached through mutation from a subset of lower-fitness neighbors. Given an initial condition defined by a quasi-species distribution localized somewhere in the sequence space, the population will evolve by exploring nearest positions through mutation. The remainder of the chapter deals with symmetric competition, epistasis in RNA viruses, experimental virus landscapes, the survival of the flattest effect, and virus robustness.

Patterns of size variation over time in ponderosa pine stands established at different initial densities

We used six metrics of size and growth variation (standard deviation (SD), coefficient of variation (CV), skewness coefficient (S), Gini coefficient (G), Lorenz asymmetry coefficient (LAC), and growth dominance coefficient (GD)) to describe changes in two long-term ponderosa pine (Pinus ponderosa Douglas ex P. Lawson & C. Lawson) initial spacing trials in Oregon and Washington, USA. Trends were examined over a 35-year time period and across a range of initial stand densities (from 154 to 2470 trees·ha−1) for four measures of tree size: diameter at breast height (dbh, 1.37 m), basal area (BA), height, and volume. Unlike many previous studies of size variation in monospecific stands, our results suggest that variation declined or remained relatively stable for all treatments at both study areas. This suggests that these stands are experiencing size symmetric competition for belowground resources. We found that a combination of metrics is necessary to provide a complete picture of size variability and differentiation in developing stands. We recommend using the CV or G, as there were clear trends with increasing density for all size variables. If the objective of the assessment was to track changes in absolute size within an individual stand, we would recommend using the SD, as there were consistent trends with time for all size variables. S, LAC, and GD may be less suited for comparing differentiation during the early stages of stand development because of a lack of clear trends with stand density and time.

A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability

The object of this paper is to study the stability behaviours of the deterministic and stochastic versions of a two-species symmetric competition model. The logistic parameters of the competitive species are perturbed by colored noises or Ornstein-Uhlenbeck processes due to random environment. The Fokker-Planck equation has been used to obtain probability density functions. Here, we have also discussed the relationship between stability behaviours of this model in a deterministic environment and the corresponding model in a stochastic environment.

Size-symmetric versus size-asymmetric competition and growth partitioning among trees in forest stands along an ecological gradient in central Europe

Current individual tree growth models rarely consider the mode of tree competition, which can be size-asymmetric when growth is limited by light or size-symmetric when belowground resources are scarce. Even with the same competition index, growth reactions may vary considerably due to a prevailing resource limitation, as the dominant trees in a stand benefit disproportionately more on light-limited sites. To scrutinize and model the relationship between mode of competition and site conditions, 34 long-term experiments with 120 plots dating back to 1871 were used. The data cover the dominating tree species in central Europe along a broad range of ecological conditions. For Norway spruce ( Picea abies (L.) Karst.), Scots pine ( Pinus sylvestris L.), and sessile oak ( Quercus petrea (Matt.) Liebl.), stronger light competition can be shown on fertile sites compared with sites with poorer conditions. Based on these findings, we constructed an enhanced version of a classic potential modifier growth model. Simulations for archetypical stands yield a transition from size-asymmetric to size-symmetric competition along the gradient from fertile to poor sites that is not covered by traditional models. It was concluded that by integrating the interaction between competition and site quality, individual tree models become more site sensitive, a prerequisite for their application under fluctuating environmental conditions.

Changes in structural inequality in Norway spruce stands on peatland sites after water-level drawdown

Size structural dynamics of naturally established Norway spruce (Picea abies (L.) Karst.) stands growing on peatlands drained for forestry were investigated. The study was based on modelling of diameter at breast height (DBH) distributions of repeatedly measured stands in southern Finland. The Weibull function was used to parameterize the DBH distributions and mixed linear models were constructed to characterize the impacts of different ecological factors on stand dynamics. Initially, the positive skewness of the DBH distributions increased after drainage as a result of increases in stem numbers and a reduction in mean diameters. Simultaneously, the size inequality among trees increased. These changes were due to regeneration and (or) ingrowth and indicated only little competition from the larger trees. Subsequently, the DBH distributions changed from positively skewed to normal and finally to negatively skewed resulting from tree growth and a reduction in the number of small DBH trees. This indicated increased asymmetric intertree competition. Size inequality did not change during this later stage in stand development, suggesting a concurrent component of symmetric competition. Thinnings had little impact on DBH distribution trends. The observed stand dynamics allow the allocation of growth resources to the desired crop component by appropriate silvicultural treatments.

ADVERTISING IN A COMPETITIVE PRODUCT LINE

In many markets, competing but differentiated firms offer a product line in order to target each product to a different type of customer. Under competition, firms, while trying to target different products to different segments, are also interested in "stealing" customers from the competitors and, in particular, customers from the most profitable segments. How should a profit-maximising firm allocate the advertising budget along a competitive product line? Devel oping a closed-loop time-variant Nash equilibrium strategy for a multi-player multi-product advertising game, we find the determinants of the optimal advertising budget allocation in a product line in an oligopoly growing market. Moreover, for a symmetric competition in a fixed market, we derive an analytic feedback time-variant Nash equilibrium strategy. Marketing implications regarding the firm's strategic orientation in product preference advertising spending, as well as comparison to rivals' spending, are discussed. Finally, we show that using a single-product advertising game instead of a multi-product advertising game, leads to over-advertising.