Modeling temporal dynamics of genetic diversity in stage-structured plant populations with reference to demographic genetic structure.

Predicting temporal dynamics of genetic diversity is important for assessing long-term population persistence. In stage-structured populations, especially in perennial plant species, genetic diversity is often compared among life history stages, such as seedlings, juveniles, and flowerings, using neutral genetic markers. The comparison among stages is sometimes referred to as demographic genetic structure, which has been regarded as a proxy of potential genetic changes because individuals in mature stages will die and be replaced by those in more immature stages over the course of time. However, due to the lack of theoretical examination, the basic property of the stage-wise genetic diversity remained unclear. We developed a matrix model which was made up of difference equations of the probability of non-identical-by-descent of each life history stage at a neutral locus to describe the dynamics and the inter-stage differences of genetic diversity in stage-structured plant populations. Based on the model, we formulated demographic genetic structure as well as the annual change rate of the probability of non-identical-by-descent (denoted as η). We checked if theoretical expectations on demographic genetic structure and η obtained from our model agreed with computational results of stochastic simulation using randomly generated 3,000 life histories. We then examined the relationships of demographic genetic structure with effective population size Ne, which is the determinants of diversity loss per generation time. Theoretical expectations on η and demographic genetic structure fitted well to the results of stochastic simulation, supporting the validity of our model. Demographic genetic structure varied independently of Ne and η, while having a strong correlation with stable stage distribution: genetic diversity was lower in stages with fewer individuals. Our results indicate that demographic genetic structure strongly reflects stable stage distribution, rather than temporal genetic dynamics, and that inferring future genetic diversity solely from demographic genetic structure would be misleading. Instead of demographic genetic structure, we propose η as an useful tool to predict genetic diversity at the same time scale as population dynamics (i.e., per year), facilitating evaluation on population viability from a genetic point of view.

Sensitivity analysis on the declining population in Japan: Effects of prefecture-specific fertility and interregional migration.

Japan has been facing a population decline since 2010 due to low birth rates, interregional migration, and regional traits. In this study, we modeled the demographic dynamics of Japan using a transition matrix model. Then, from the mathematical structure of the model, we quantitatively evaluated the domestic factors of population decline. To achieve this, we constructed a multi-regional Leslie matrix model and developed a method for representing the reproductive value and stable age distribution using matrix entries. Our method enabled us to interpret the mathematical indices using the genealogies of the migration history of individuals and their ancestors. Furthermore, by combining our method with sensitivity analysis, we analyzed the effect of region-specific fertility rates and interregional migration rates on the population decline in Japan. We found that the sensitivity of the population growth rate to the migration rate from urban areas with large populations to prefectures with high fertility rates was greatest for people aged under 30. In addition, compared to other areas, the fertility rates of urban areas exhibited higher sensitivity for people aged over 30. Because this feature is robust in comparison with those in 2010 and 2015, it can be said to be a unique structure in Japan in recent years. We also established a method to represent the reproductive value and stable age distribution in an irreducible non-negative matrix population model by using the matrix entries. Furthermore, we show the effects of fertility and migration rates numerically in urban and non-urban areas on the population growth rates for each age group in a society with a declining population.

Effects of environmental change and early-life stochasticity on Pacific bluefin tuna population growth.

Species conservation and fisheries management require approaches that relate environmental conditions to population-level dynamics, especially because environmental conditions shift due to climate change. We combined an individual-level physiological model and a conceptually simple matrix population model to develop a novel tool that relates environmental change to population dynamics, and used this tool to analyze effects of environmental changes and early-life stochasticity on Pacific bluefin tuna (PBT) population growth. We found that (i) currently, PBT population experiences a positive growth rate, (ii) somewhat surprisingly, stochasticity in early life survival increases this growth rate, (iii) sexual maturation age strongly depends on food and temperature, (iv) current fishing pressure, though high, is tolerable as long as the environment is such that PBT mature in less than 9 years of age (maturation age of up to 10 is possible in some environments), (v) PBT population growth rate is much more susceptible to changes in juvenile survival than changes in total reproductive output or adult survival. These results suggest that, to be effective, fishing regulations need to (i) focus on smaller tuna (i.e., juveniles and young adults), and (ii) mitigate adverse effects of climate change by taking into the account how future environments may affect the population growth.

Stability and bifurcation analysis of a ratio-dependent community dynamics model on Batesian mimicry.

Batesian mimicry is the similarity of coloration and patterns in an unpalatable species (the "model-species") and a palatable species (the "mimic-species"). The resemblance is advantageous for the mimic-species because the mimic-species can deceive predators and avoid predation. While Batesian mimicry is an important subject in ecology as a general phenomenon in nature, previous theoretical studies focus mainly on the evolution of mimicry and the predator learning process. In these mathematical models, the population sizes of the model- and mimic-species are not considered explicitly or are assumed to be constant, but this is not plausible in model-mimic community dynamics. Thus, the model-mimic community has been paid relatively less attention; However, to elucidate problems on Batesian mimicry, it is essential to understand the fundamental characteristics of the model-mimic community dynamics. Here, we construct a basic model-mimic community dynamics model, obtain the existence and stability conditions of its equilibria, and conduct the bifurcation analysis and numerical calculation. The results show that the instability of the model-only population is predicted, and this is consistent with the typical pattern of geographical distribution in Batesian mimicry in the field. We propose three new hypotheses to explain the typical pattern of geographical distribution. Furthermore, we reveal an irreversibility regarding the model-mimic coexistence that is important for the conservation of the model- and mimic-species.

Mechanism underlying the negative effect of prostate volume on the outcome of extensive transperineal ultrasound-guided template prostate biopsy.

Previous studies have indicated a possible relationship between increased prostate volume (PV) and decreased biopsy yield, although the mechanism involved is unclear. We evaluated 1650 patients who underwent template biopsy. The distribution of 993 cancer lesions in 302 prostatectomy specimens was compared with the biopsy data to determine whether each lesion was detected. A receiver operating characteristic (ROC) model was used to determine the diagnostic accuracy of prostate-specific antigen (PSA) and related markers. A medical record number (MRN) was used as a negative control. The cancer positive rate did not change as PSA increased in patients with PV ≥50 mL (P = 0.466), although it increased as PSA increased in patients with PV<50 mL (P = 0.001). The detection rate of cancer lesions decreased as the diameter of the lesions decreased (P = 0.018), but remained unchanged with respect to PV. The diameters of the maximum lesions in patients with PV ≥ 50 mL were significantly smaller than those in patients with PV<50 mL (P = 0.003). In patients with PV ≥ 50 mL, the areas under the ROC curves for PSA-related markers did not differ significantly from that for MRN, although they were significantly greater than that for MRN in patients with PV<50 mL (P < 0.001). These results suggest that an increase in PV is associated with a decrease in size and detectability of cancer lesions resulting in a decrease in biopsy yield. Loss of diagnostic accuracy of markers in patients with PV ≥ 50 mL indicates a decrease in serum levels of PSA produced by prostate cancer, which suggests growth inhibition of the cancer.

The analysis of an effect of seed propagation on defense strategy against pathogen transmission within clonal plant population using lattice model.

Many clonal plants have two breeding systems, vegetative and seed propagation. In vegetative propagation, plants reproduce genetically identical offspring that have lower mortality rates. By contrast, the seed propagated offspring has higher mortality rate, however, the seed propagation acts an important role in maintaining the genetic diversity and reproduce widely. According to the experimental studies, the balance between the breeding systems, vegetative and seed propagation, is determined by several functions, such as resource allocation. The infection and spread of systemic pathogen also affect the optimal balance of the breeding systems. Thus, we examine the effect of invasion of systemic pathogen on the optimal balance of the breeding systems of clonal plant using lattice model in two cases, single population and mixed population. In the analysis, the equilibrium and its local stability were derived using approximation method and numerical simulation in single population. Additionally, two situations were assumed in mixed population, infected and uninfected populations, and the efficacy of seed propagation on the suppression of epidemic infections was examined by comparing the results in the two situations. As a result, seed propagation is an effective defensive behavior against systemic pathogens. In the single population, the plants increase their population by increasing the proportion of seed propagation when the epidemic pathogen has highly infective. In mixed population, the increasing proportion of seed propagation is the optimal breeding strategy to defend against the spread of a systemic pathogen.

Pathogen Propagation Model with Superinfection in Vegetatively Propagated Plants on Lattice Space.

Many clonal plants have two reproductive patterns, seed propagation and vegetative propagation. By vegetative propagation, plants reproduce the genetically identical offspring with a low mortality, because resources are supplied from the other individuals through interconnected ramets at vegetative-propagated offspring. However, the ramets transport not only resources but also systemic pathogen. Pathogens evolve to establish and spread widely within the plant population. The superinfection, which is defined as the ability that an established pathogen spreads widely by infecting to already-infected individuals with other strains of a pathogen, is important to the evolution of pathogens. We examine the dynamics of plant reproduction and pathogen propagation considering spatial structure and the effect of superinfection on genetic diversity of pathogen by analysis of several models, 1-strain and multiple-strain models, on two-dimensional square lattice. In the analysis of 1-strain model, we derive equilibrium value by mean-field approximation and pair approximation, and its local stability by Routh-Hurwitz stability criterion. In the multiple-strain models, we analyze the dynamics by numerical simulation of mean-field approximation, pair approximation and Monte Carlo simulation. Through the analyses, we show the effect of parameter values to dynamics of models, such as transition of dominant strain of pathogen, competition between plants and pathogens and density of individuals. As a result, (i) The strain with intermediate cost becomes dominant when both superinfection rate and growth rate are low. (ii) The competition between plants and pathogens occurs in the phase of coexistence of various strains by pair approximation and Monte Carlo simulation. (iii) Too high growth rate leads to the decrease of plant population in all models. (iv) Pathogens are easy to maintain their genetic diversity with low superinfection rate. However, if they do not superinfect, the maintenance becomes difficult. (v) When growth rate of plant is low, individuals are very influenced by distant individuals.

Species extinction thresholds in the face of spatially correlated periodic disturbance.

The spatial correlation of disturbance is gaining attention in landscape ecology, but knowledge is still lacking on how species traits determine extinction thresholds under spatially correlated disturbance regimes. Here we develop a pair approximation model to explore species extinction risk in a lattice-structured landscape subject to aggregated periodic disturbance. Increasing disturbance extent and frequency accelerated population extinction irrespective of whether dispersal was local or global. Spatial correlation of disturbance likewise increased species extinction risk, but only for local dispersers. This indicates that models based on randomly simulated disturbances (e.g., mean-field or non-spatial models) may underestimate real extinction rates. Compared to local dispersal, species with global dispersal tolerated more severe disturbance, suggesting that the spatial correlation of disturbance favors long-range dispersal from an evolutionary perspective. Following disturbance, intraspecific competition greatly enhanced the extinction risk of distance-limited dispersers, while it surprisingly did not influence the extinction thresholds of global dispersers, apart from decreasing population density to some degree. As species respond differently to disturbance regimes with different spatiotemporal properties, different regimes may accommodate different species.

A general method for calculating the optimal leaf longevity from the viewpoint of carbon economy.

According to the viewpoint of the optimal strategy theory, a tree is expected to shed its leaves when they no longer contribute to maximisation of net carbon gain. Several theoretical models have been proposed in which a tree was assumed to strategically shed an old deteriorated leaf to develop a new leaf. We mathematically refined an index used in a previous theoretical model [Kikuzawa (Am Nat 138:1250-1263, 1991)] so that the index is exactly proportional to a tree's lifelong net carbon gain. We also incorporated a tree's strategy that determines the timing of leaf expansion, and examined three kinds of strategies. Specifically, we assumed that a new leaf is expanded (1) immediately after shedding of an old leaf, (2) only at the beginning of spring, or (3) immediately after shedding of an old leaf if the shedding occurs during a non-winter season and at the beginning of spring otherwise. We derived a measure of optimal leaf longevity maximising the value of an appropriate index reflecting total net carbon gain and show that use of this index yielded results that are qualitatively consistent with empirical records. The model predicted that expanding a new leaf at the beginning of spring than immediately after shedding usually yields higher carbon gain, and combined strategy of the immediate replacement and the spring flushing earned the highest gain. In addition, our numerical analyses suggested that multiple flushing seen in a few species of subtropical zones can be explained in terms of carbon economy.

Ecological conditions favoring budding in colonial organisms under environmental disturbance.

Dispersal is a topic of great interest in ecology. Many organisms adopt one of two distinct dispersal tactics at reproduction: the production of small offspring that can disperse over long distances (such as seeds and spawned eggs), or budding. The latter is observed in some colonial organisms, such as clonal plants, corals and ants, in which (super)organisms split their body into components of relatively large size that disperse to a short distance. Contrary to the common dispersal viewpoint, short-dispersal colonial organisms often flourish even in environments with frequent disturbances. In this paper, we investigate the conditions that favor budding over long-distance dispersal of small offspring, focusing on the life history of the colony growth and the colony division ratio. These conditions are the relatively high mortality of very small colonies, logistic growth, the ability of dispersers to peacefully seek and settle unoccupied spaces, and small spatial scale of environmental disturbance. If these conditions hold, budding is advantageous even when environmental disturbance is frequent. These results suggest that the demography or life history of the colony underlies the behaviors of the colonial organisms.

Hot temperatures can force delayed mosquito outbreaks via sequential changes in Aedes aegypti demographic parameters in autocorrelated environments.

Aedes aegypti L. (Diptera: Culicidae) is a common pantropical urban mosquito, vector of dengue, Yellow Fever and chikungunya viruses. Studies have shown Ae. aegypti abundance to be associated with environmental fluctuations, revealing patterns such as the occurrence of delayed mosquito outbreaks, i.e., sudden extraordinary increases in mosquito abundance following transient extreme high temperatures. Here, we use a two-stage (larvae and adults) matrix model to propose a mechanism for environmental signal canalization into demographic parameters of Ae. aegypti that could explain delayed high temperature induced mosquito outbreaks. We performed model simulations using parameters estimated from a weekly time series from Thailand, assuming either independent or autocorrelated environments. For autocorrelated environments, we found that long delays in the association between the onset of "hot" environments and mosquito outbreaks (10 weeks, as observed in Thailand) can be generated when "hot" environments sequentially trigger a larval survival decrease and over-compensatory fecundity increase, which lasts for the whole "hot" period, in conjunction with a larval survival increase followed by a fecundity decrease when the environment returns to "normal". This result was not observed for independent environments. Finally, we discuss our results implications for prospective entomological research and vector management under changing environments.

Optimal life schedule with stochastic growth in age-size structured models: theory and an application.

Reproduction timing is one of the most important factors for the life history because it is closely related to subsistence of species. On the other hand, ecological demographers recently noted the effects of environmental stochasticity on the population dynamics by using linear demographic models because stochasticity reduces the population growth rate. Linear demographic models are generally composed of reproduction timing, several life history traits and stochasticity. The stochasticity is generated by twofold stochasticity, that is, internal and external stochasticities. In transition matrix models, the internal stochasticity gives a species a set of transition probabilities to other states, whereas the external stochasticity annually variegates the value of these transition probabilities. If the population vector has only the internal stochasticity, it satisfies a partial differential equation, in which it is described by a stochasticity in body-size growth rate. In this paper, we focus on the stochasticity which affects the body-size growth rate under r-selection. We construct a mathematical model of stochastic life history of each individual by using a stochastic differential equation, and analyze the relationship between optimal life schedule and the population dynamics by finding Euler-Lotka equation. Then, we use the formalism of path-integral expression to the population dynamics and show that the expression is consistent with other expressions in linear demographic models. Finally, we apply our method to a simple example, and obtain a characteristic of the stochasticity which has not only negative effect on the fitness but also positive effect from our model.

Floral sex ratio strategy in wind-pollinated monoecious species subject to wind-pollination efficiency and competitive sharing among male flowers as a game.

To explain the floral sex ratio strategy in wind-pollinated monoecious species, we developed four models with special reference to wind-pollination efficiency (WPE) and competitive sharing among male flowers (CSM). WPE is a function that follows a Poisson distribution and explains the frequency of seeds fertilized by an individual via wind-pollination, whereas CSM is defined by the sharing of female flowers among male flowers within the local breeding population. We argued the applicability of the results to the actual tendencies observed in wind-pollinated monoecious species and found that a game model with WPE and CSM was the most applicable. The model predicted that individuals should change their gender expression in the following order: female phase (female flowers only), male phase (male flowers only), and constant male phase (individuals constantly allocate reproductive resources to male flowers, and remaining resources to female flowers), with increasing reproductive resources. However, the trend is likely to be influenced by the variation in the reproductive investment among individuals and the degree of WPE. Thus, large variation and low pollination efficiency enable three phases to co-occur within a population. Actual trends in real populations correspond to our prediction.

Elasticity analysis of density-dependent matrix population models: the invasion exponent and its substitutes.

In density-independent models, the population growth rate lambda measures population performance, and the perturbation analysis of lambda (its sensitivity and elasticity) plays an important role in demography. In density-dependent models, the invasion exponent lambdaI replaces lambda as a measure of population performance. The perturbation analysis of lambdaI reveals the effects of environmental changes and management actions, gives the direction and intensity of density-dependent natural selection on life history traits, and permits calculation of the sampling variance of the invasion exponent. Because density-dependent models require more data than density-independent models, it is tempting to look for substitutes for the invasion exponent, the sensitivity and elasticity of which can be calculated from a density-independent model. Here we examine the accuracy of two such substitutes: the dominant eigenvalue of the projection matrix evaluated at equilibrium (An) and the dominant eigenvalue of the matrix averaged over the attractor (A). Using a two-stage model that represents a wide range of life history types, we find that the elasticities of An or A often agree to within less than 5% error with those of the invasion exponent, even when population dynamics are chaotic. The exceptions are for semelparous life histories, especially when density-dependence affects fertility. This suggests that the elasticity analysis of density-independent models near equilibrium, or averaged over the attractor, provides useful information about the elasticity of the invasion exponent in density-dependent models.