Population dynamics in variable environments. II. Correlated environments,sensitivity analysis and dynamics

Mean and mean square number are studied for age-structured populations with serially correlated temporally fluctuating vital rates. Results are that (1) Moments of population number can be used effectively to analyse growth rates of the coefficient of variation and an approximate median population number. (2) Analytical approximations to the growth rates of moments reveal dynamic consequences of covarying phenotypic traits and of temporal correlation along environmental sequences. (3) Dynamic properties can be explicitly related to the static sensitivity of an average vital rate matrix. (4) The use of (1), (2) and (3) allows an extension of many applications of static vital rate theory to dynamics with fluctuating rates.     

Primitivity and convergence to stability

An exact expression for the index of primitivity g of a Leslie matrix is obtained, which applies also to time-varying matrices which share an incidence matrix. Elapsed time (not time intervals) to primitivity is shown to depend only weakly on the discretization scheme used. A lower bound for speed of convergence to the stable (fixed or time-dependent as appropriate) state is given which depends sensitively on g.     

Population dynamics in variable environments. IV. Weak ergodicity in the Lotka equation

The Hilbert projective metric is applied to the continuous-time Lotka equation in demography to establish weak ergodicity: populations with the same time-varying fecundity and mortality schedules ultimately have the same age composition. The analysis displays clearly the dynamic content of Lotka's equation and identifies a contraction operator which forces convergence of birth sequences over time. The relationship between primitivity in the discrete (Leslie) and continuous (Lotka) demographic models is made clear.     

Cycles in nonlinear age-structured models. I. Renewal equations

A variety of density-dependent population models can be described by nonlinear renewal equations. This paper develops analytical tools for such models to study the sustained population cycles which arise by bifurcation. The results obtained describe explicitly the direction of bifurcation, and the period, form, and dynamic stability of sustained cycles. The results are illustrated by application to a cohort-controlled model of human populations which has been proposed as a formalization of the Easterlin effect.     

Revisiting the use of Iprodione and Trichoderma in the integrated management of onion white rot

The biocontrol properties of Trichoderma species are well documented, but their effectiveness in antagonism of the problematic Sclerotium cepivorum, the causal agent of white rot in Allium species, appears limited with reports of significant control only relating to deliberately-mutated strains of Trichoderma. Our previous studies have indicated the possibility of using selected naturally-occurring strains of the antagonist in the suppression of other diseases; now in vitro and controlled environment in vivo studies have indicated that a degree of control of Onion White Rot is possible, and that the selected antagonist strains can be used in integrated treatments with Iprodione to good effect. The possible value of such treatments is considered in light of other approaches to the suppression of this continuing problem.     

Linking demographic responses and life history tactics from longitudinal data in mammals

In stochastic environments, a change in a demographic parameter can influence the population growth rate directly or via a resulting impact on age structure. Stochastic elasticity of the long‐run stochastic growth rate λ_s to a demographic parameter offers a suitable way to measure the overall demographic response because it includes both the direct effect of changing the demographic parameter and its indirect effect through changes in the age structure. From 25 mammalian populations with contrasting life histories, we investigated how pace of life and population growth rate influence the demographic responses (measured as the relative contributions of the direct and indirect components of stochastic elasticity on λ_s). We found that in short‐lived species, the change in population structure resulting from an increase in yearling survival leads to an additional increase in λ_s, whereas in long‐lived species, the same change in population structure leads to a decrease. Short‐lived species thus display a boom‐bust life history strategy contrary to long‐lived species, for which the long lifespan dampens the demographic consequences of changing age structure. Irrespective of the species’ life history strategy, the change in population age structure resulting from an increase in adult survival leads to an additional increase in λ_s due to an increase of the proportion of mature individuals in the population. On the contrary, a change in population age structure resulting from an increase of reproductive performance leads to a decrease in λ_s that is due to the increase of the proportion of immature individuals in the population. Our comparative analysis of stochastic elasticity patterns in mammals shows the existence of different demographic responses to changes in age structure between short‐ and long‐lived species, which improves our understanding of population dynamics in variable environments in relation to the species‐specific pace of life.     

A spatiotemporal characterization of the effect of p53 phosphorylation on its interaction with MDM2

The interaction of p53 and MDM2 is modulated by the phosphorylation of p53. This mechanism is key to activating p53, yet its molecular determinants are not fully understood. To study the spatiotemporal characteristics of this molecular process we carried out Brownian dynamics simulations of the interactions of the MDM2 protein with a p53 peptide in its wild type state and when phosphorylated at Thr18 (pThr18) and Ser20 (pSer20). We found that p53 phosphorylation results in concerted changes in the topology of the interaction landscape in the diffusively bound encounter complex domain. These changes hinder phosphorylated p53 peptides from binding to MDM2 well before reaching the binding site. The underlying mechanism appears to involve shift of the peptide away from the vicinity of the MDM2 protein, peptide reorientation, and reduction in peptide residence time relative to wild-type p53 peptide. pThr18 and pSr20 p53 peptides experience reduction in residence times by factors of 13.6 and 37.5 respectively relative to the wild-type p53 peptide, indicating a greater role for Ser20 phosphorylation in abrogating p53 MDM2 interactions. These detailed insights into the effect of phosphorylation on molecular interactions are not available from conventional experimental and theoretical approaches and open up new avenues that incorporate molecular interaction dynamics, for stabilizing p53 against MDM2, which is a major focus of anticancer drug lead development.     

Risky Business: Temporal and Spatial Variation in Preindustrial Dryland Agriculture

Traditional dryland agriculture in the Pacific island was often labor-intensive and risky, yet settlement and farming in dry areas played an important role in the development of Polynesian societies. We investigate how temporal and spatial climatic fluctuations shape variation in agricultural production across dryland landscapes. We use a model that couples plant growth, climate, and soil organic matter dynamics, together with data from Kohala, Hawai'i, to understand how temperature, rainfall, nitrogen availability, and cropping activity interact to determine yield dynamics through time and space. Due to these interactions, the statistical characterization of rainfall alone is a poor characterization of agricultural yield. Using a simple linear model of human population dynamics, we show that the observed yield variation can affect long-term population growth substantially. Our approach to analyzing spatial and temporal fluctuations in food supply, and to interpreting the population consequences of these fluctuations, provides a quantitative evaluation of agricultural risk and human carrying capacity in dry regions.     

Stage dynamics, period survival, and mortality plateaus

Mortality plateaus at advanced ages have been found in many species, but their biological causes remain unclear. Here, we exploit age-from-stage methods for organisms with stage-structured demography to study cohort dynamics, obtaining age patterns of mortality by weighting one-period stage-specific survivals by expected age-specific stage structure. Cohort dynamics behave as a killed Markov process. Using as examples two African grasses, one pine tree, a temperate forest perennial herb, and a subtropical shrub in a hurricane-driven forest, we illustrate diverse patterns that may emerge. Age-specific mortality always reaches a plateau at advanced ages, but the plateau may be reached rapidly or slowly, and the trajectory may follow positive or negative senescence along the way. In variable environments, birth state influences mortality at early but not late ages, although its effect on the level of survivorship persists. A new parameter micro omega summarizes the risk of mortality averaged over the entire lifetime in a variable environment. Recent aging models for humans that employ nonobservable abstract states of "vitality" are also known to produce diverse trajectories and similar asymptotic behavior. We discuss connections, contrasts, and implications of our results to these models for the study of aging.     

The dynamics of a quantitative trait in an age-structured population living in a variable environment

Time series of rapid phenotypic change have been documented in age-structured populations living in the wild. Researchers are often interested in identifying the processes responsible for such change. We derive an equation to exactly decompose change in the mean value of a phenotypic trait into contributions from fluctuations in the demographic structure and age-specific viability selection, fertility selection, phenotypic plasticity, and differences between offspring and parental trait values. We treat fitness as a sum of its components rather than as a scalar and explicitly consider age structure by focusing on short time steps, which are appropriate for describing phenotypic change in species with overlapping generations. We apply the method to examine stasis in birth weight in a well-characterized population of red deer. Stasis is achieved because positive viability selection for an increase in birth weight is countered by parents producing offspring that are, on average, smaller than they were at birth. This is one of many ways in which equilibria in the mean value of a phenotypic trait can be maintained. The age-structured Price equation we derive has the potential to provide considerable insight into the processes generating now frequently reported cases of rapid phenotypic change.