From organism to population: the role of life-history theory

The role of life-history theory in population and evolutionary analyses is outlined. In both cases general life histories can be analysed, but simpler life histories need fewer parameters for their description. The simplest case, of semelparous (breed-once-then-die) organisms, needs only three parameters: somatic growth rate, mortality rate and fecundity. This case is analysed in detail. If fecundity is fixed, population growth rate can be calculated direct from mortality rate and somatic growth rate, and isoclines on which population growth rate is constant can be drawn in a ”state space” with axes for mortality rate and somatic growth rate. In this space density-dependence is likely to result in a population trajectory from low density, when mortality rate is low and somatic growth rate is high and the population increases (positive population growth rate) to high density, after which the process reverses to return to low density. Possible effects of pollution on this system are discussed. The state-space approach allows direct population analysis of the twin effects of pollution and density on population growth rate. Evolutionary analysis uses related methods to identify likely evolutionary outcomes when an organism's genetic options are subject to trade-offs. The trade-off considered here is between somatic growth rate and mortality rate. Such a trade-off could arise because of an energy allocation trade-off if resources spent on personal defence (reducing mortality rate) are not available for somatic growth rate. The evolutionary implications of pollution acting on such a trade-off are outlined

The Optimum Growth Rate for Population Reconsidered

This article gives exact general conditions for the existence of an interior optimum growth rate for population in the neoclassical two-generations-overlapping model. In an economy where high (low) growth rates of population lead to a growth path which is efficient (inefficient) there always exists an interior optimum growth rate for population. In all other cases there exists no interior optimum. The Serendipity Theorem, however, does in general not hold in an economy with government debt. Moreover, the growth rate for population which leads an economy with debt to a golden rule allocation can never be optimal.

Population Growth Rate, Life Expectancy and Pension Program Improvement in China

Applying an overlapping-generations model with lifetime uncertainty, we examine in this paper China’s partially funded public pension system. The findings show that the individual contribution rate does not affect the capital-labor ratio but the firm contribution rate does. The optimal firm contribution rate depends on the capital share of income, social discount factor, survival probability, and population growth rate. The simulation results indicate that the optimal firm contribution rate rises with China’s life expectancy but, surprisingly, falls with the population growth rate. We demonstrate that the optimal firm contribution rate should be cut when the effect of falling population growth rate is greater than that of rising life expectancy and that the rate is much more sensitive to the population growth rate than to life expectancy. This paper also solves the optimal interval to cope with China’s population aging peak in the 2030s.Public Pension; Population Growth Rate; Life Expectancy

Uncertainty and economic growth in a stochastic R&D model

The paper examines an R&D model with uncertainty from the population growth, which is a stochastic cooperative Lotka-Volterra system, and obtains a suciently condition for the existence of the globally positive solution. The long-run growth rate of the economic system is ultimately bounded in mean and fluctuation of its growth will not be faster than the polynomial growth. When uncertainty of the population growth, in comparison with its expectation, is suciently large, the growth rate of the technological progress andthe capital accumulation will converge to zero. Inversely, when uncertainty of the population growth is suciently small or its expected growth rate is suciently high, the economic growth rate will not decay faster than the polyno-mial speed. The paper explicitly computes the sample average of the growth rates of both the technology and the capital accumulation in time and compares them with their counterparts in the corresponding deterministic model

The Consequences of Increased Population Growth for Climate Change

This paper examines the impact of population growth on global climate change. The author employs the Global Change Assessment Model (GCAM) to estimate the effects of population growth on the change global average temperature by 2100. Observing that a larger population supports a larger economy, which translates in close proportion into additional releases of carbon dioxide (CO2), the paper notes that global temperature should in any year be nearly linear in relation to the rate of growth when the rate of population growth is constant.The paper finds that that an additional 1 percentage point of population growth through the end of the century would coincide with about an additional 2 degrees Fahrenheit in average global temperatures. Over time, the temperature change is greater and becomes increasingly sensitive to population growth

Semi-endogenous growth when population is decreasing

The paper analyzes the effect of a negative population growth rate on per capita income growth using a simple model of semi-endogenous growth. It is shown that there is a non-monotonous relationship between population growth rates and long-run per capita income growth rates. Compared to the case of positive population growth the dynamics are richer and depend on the rate of depreciation. Semi-endogenous growth becomes partly endogenous.negative population growth, semi-endogenous growth

Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates

The population growth rate, or intrinsic rate of increase, measures the potential rate of growth of a population with specified and fixed vital rates.The sensitivity of population growth rate to changes in the vital rates can be written in terms of the stable stage or age distribution and the reproductive value distribution. If the vital rate measures the rate of production of one type of individual by another, then the sensitivity of growth rate is proportional to the reproductive value of the destination type and the representation in the stable stage distribution of the source type. This formal relationship exists in three forms: one limited to age-classified populations, a second that applies to stage- or age-classified populations, and a third that uses matrix calculus. Each uses a different set of formal demographic techniques; together they provide a relationship that beautifully cuts across different types of demographic models.matrix population models, population growth, senescence, sensitivity

MODELLING NIGERIA POPULATION GROWTH RATE

Thomas Robert Malthus Theory of population highlighted the potential dangers of over population. He stated that while the populations of the world wouldincrease in geometric proportions, the food resources available for them would increase in arithmetic proportions. This study was carried out to find the trend, fit a model and forecast for the population growth rate of Nigeria.The data were based on the population growth rate of Nigeria from 1982 to 2012 obtained from World Bank Data (data.worldbank.org). Both time and autocorrelation plots were used to assess the Stationarity of the data. Dickey-Fuller test was used to test for the unit root. Ljung box test was used to check for the fit of the fitted model. Time plot showed that the random fluctuations of the data are not constant over time. There was an initial decrease in the trend of the growth rate from 1983 to 1985 and an increase in 1986 which was constant till 1989 and then slight fluctuations from 1990 to 2004 and a general increase in trend from 2005 to 2012. There was a slow decay in the correlogram of the ACF and this implied that the process is non stationary. The series was stationary after second differencing, Dickey-Fuller = -4.7162, Lag order = 0, p-value = 0.01 at a= 0.05. The p-value (0.01) and concluded that there is no unit root i.e the series is stationary having d=2. Correlogram and partial correlogram for the second-order differenced data showed that the ACF at lag 1 and lag 5 exceed the significant bounds and the partial correlogram tailed off at lag 2.The identified order for the ARIMA(p,d,q) model was ARIMA(2,2,1). The estimate of AR1 co-efficient =1.5803 is observed to be statistically significant but the estimated value does not conforms strictly to the bounds of the stationary parameter hence was excluded from the model. =-0.9273 is observed to be statistically significant and conformed strictly to the bounds of the stationary parameter , hence was maintained in the model. The estimate of MA1 co-efficient = - 0.1337 was observed to be statistically significant conformed strictly to the bounds of the parameter invertibility. For ARIMA (2, 2, 0) the estimate of AR1 co-efficient =1.5430 was observed to be statistically significant and not conformed strictly to the bounds of the parameter stationary, hence excluded from the model. The estimate of AR 2 co-efficient=-0.9000 is observed to be statistically significant and conformed strictly to the bounds of the parameter stationary, hence retained in the model. The ARIMA (2, 2, 0) is considered the best model. It has the smallest AIC. The Ljung test showed that residuals are random and  implies that the model is fit enough for the data. The forecast Arima function gives us a forecast of the Population Growth Rate in the next thirty eight (38) years, as well as 80% and 95% prediction intervals for those predictions i.e up to 2050

Stochastic population growth in spatially heterogeneous environments

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study the following model for population abundances in $n$ patches: the conditional law of $X_{t+dt}$ given $X_t=x$ is such that when $dt$ is small the conditional mean of $X_{t+dt}^i-X_t^i$ is approximately $[x^i\mu_i+\sum_j(x^j D_{ji}-x^i D_{ij})]dt$, where $X_t^i$ and $\mu_i$ are the abundance and per capita growth rate in the $i$-th patch respectivly, and $D_{ij}$ is the dispersal rate from the $i$-th to the $j$-th patch, and the conditional covariance of $X_{t+dt}^i-X_t^i$ and $X_{t+dt}^j-X_t^j$ is approximately $x^i x^j \sigma_{ij}dt$. We show for such a spatially extended population that if $S_t=(X_t^1+...+X_t^n)$ is the total population abundance, then $Y_t=X_t/S_t$, the vector of patch proportions, converges in law to a random vector $Y_\infty$ as $t\to\infty$, and the stochastic growth rate $\lim_{t\to\infty}t^{-1}\log S_t$ equals the space-time average per-capita growth rate \sum_i\mu_i\E[Y_\infty^i] experienced by the population minus half of the space-time average temporal variation \E[\sum_{i,j}\sigma_{ij}Y_\infty^i Y_\infty^j] experienced by the population. We derive analytic results for the law of $Y_\infty$, find which choice of the dispersal mechanism $D$ produces an optimal stochastic growth rate for a freely dispersing population, and investigate the effect on the stochastic growth rate of constraints on dispersal rates. Our results provide fundamental insights into "ideal free" movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology.Comment: 47 pages, 4 figure