A graphical analysis of life history evolution in biennial plants

Graphical analysis was done on the lfie history evolution of biennials (or monocarpic perennials). The age of seed production (x), the probability of surviving to agex [l(x)], and the number of seeds produced at agex[b(x)] determine the ultimate rate of population increase (r). The ages whenr=max andr=0 define the optimal and critical age for seed production, respectively, which depend on the shape and combination of thel(x) andb(x) curves. The otpimal age of seed production appears only for the convex function of the natural logarithm of the net reproductive rate [R ₀(x)], while the critical age appears irrespective of the shape of theR ₀(x) curves. The effects of environmental change on the optimal and critical ages are, analyzed, with the conclusion that in an environment imposing higher mortality or lower fecundity, delayed reproduction is favored. Age- and size-dependent productions of seeds have different effects on the variation ofr in a changing environment.     

Stochastic prey-predator relationships: A random evolution approach

The formalism and results of the theory of random evolutions are used to establish and investigate a model for two randomly interacting populations. The asymptotic stability of the expected solution is studied and contrasted to that of the associated deterministic system.     

Exploratory path analysis with applications in ecology and evolution

In this article, I first describe some recent developments in the identification of the structure of dependencies among variables in multivariate data relevant to exploratory path analysis. I then introduce a bootstrap modification of one important method (the SGS algorithm) that is designed to improve error rates of exploratory path analysis in the small data sets that are typical of studies in ecology and evolution. Monte Carlo results indicate that this modified technique can find path models that are close to the true model even in very small data sets. The bootstrapped SGS algorithm is then applied to a previously published data set involving attributes affecting seed dispersal in St. Lucie's cherry.     

Energy and biological evolution—III. Theoretical ecology and macromolecular self-organization

We show that the elementary models of biochemical evolutionary processes are the bases for the study of open ecological systems and macromolecular self-organisation. We deduce a biochemical analogue for the basic closed phytoplankton-zooplankton food chain. The perturbation of the Michaelis-Menten mechanism which determines the nutrient-dependent growth rate of the phytoplankton species leads to higher catastrophes for the nutrient equilibrium manifold. The umbilic models are generalizations of the equations of organization of Eigen. Work supported by an Associateship of The International Centre for Theoretical Physics, P.O. Box 586, Miramare, 34100 Trieste, Italy.     

A qualitative method for analysis of prey-predator systems under enrichment

A new qualitative method of analysis suitable for dynamic systems of the prey-predator type is presented. An application of the method to a specific ecosystem is given and the model's behaviour under conditions of enrichment is examined. It is shown that the existence of limit cycle oscillations, as well as the location of these cycles, can be positively established. The critical value of enrichment at which globally stable oscillations occur is found using the method, and the results are shown to be in agreement with those of previous research.     

Phylogenetic analysis of the ecology and evolution of mammalian sleep

The amount of time asleep varies greatly in mammals, from 3 h in the donkey to 20 h in the armadillo. Previous comparative studies have suggested several functional explanations for interspecific variation in both the total time spent asleep and in rapid-eye movement (REM) or "quiet" (non-REM) sleep. In support of specific functional benefits of sleep, these studies reported correlations between time in specific sleep states (NREM or REM) and brain size, metabolic rate, and developmental variables. Here we show that estimates of sleep duration are significantly influenced by the laboratory conditions under which data are collected and that, when analyses are limited to data collected under more standardized procedures, traditional functional explanations for interspecific variation in sleep durations are no longer supported. Specifically, we find that basal metabolic rate correlates negatively rather than positively with sleep quotas, and that neither adult nor neonatal brain mass correlates positively with REM or NREM sleep times. These results contradict hypotheses that invoke energy conservation, cognition, and development as drivers of sleep variation. Instead, the negative correlations of both sleep states with basal metabolic rate and diet are consistent with trade-offs between sleep and foraging time. In terms of predation risk, both REM and NREM sleep quotas are reduced when animals sleep in more exposed sites, whereas species that sleep socially sleep less. Together with the fact that REM and NREM sleep quotas correlate strongly with each other, these results suggest that variation in sleep primarily reflects ecological constraints acting on total sleep time, rather than the independent responses of each sleep state to specific selection pressures. We propose that, within this ecological framework, interspecific variation in sleep duration might be compensated by variation in the physiological intensity of sleep.     

Inference in ecology and evolution

Most ecologists and evolutionary biologists continue to rely heavily on null hypothesis significance testing, rather than on recently advocated alternatives, for inference. Here, we briefly review null hypothesis significance testing and its major alternatives. We identify major objectives of statistical analysis and suggest which analytical approaches are appropriate for each. Any well designed study can improve our understanding of biological systems, regardless of the inferential approach used. Nevertheless, an awareness of available techniques and their pitfalls could guide better approaches to data collection and broaden the range of questions that can be addressed. Although we should reduce our reliance on significance testing, it retains an important role in statistical education and is likely to remain fundamental to the falsification of scientific hypotheses.     

Oscillations in a size-structured prey-predator model

This article introduces a predator–prey model with the prey structured by body size, based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the one-species physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator–prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka–Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey’s population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining with prey population size. We find that predation, even size-non-specific linear predation can destabilize a stable prey-only equilibrium, if reproduction is size specific and limited to individuals of large enough size. Furthermore, we show that size-specific predation can also destabilize the predator–prey equilibrium in the PDE model. We surmise that size-specific predation allows for temporary prey escape which is responsible for destabilization in the predator–prey dynamics.     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.     

The behavioral ecology of threshold evolution in a polyphenic beetle

Facultative expression of alternative male morphologies is thoughtto allow individual males to select the phenotype with the highestfitness gain given their competitive status relative to othermales with which they compete for females. Choice of, or switchingbetween, morphs commonly relies on developmental threshold responses.Evolutionary changes in developmental threshold responses arethought to provide an important avenue for phenotypic diversificationand the evolution of morphological and behavioral novelties.However, the extent to which alternative male phenotypes andtheir underlying threshold responses actually evolve in naturalpopulations is unclear. Likewise, the ecological factors thatshape the evolution of threshold responses in natural populationsare unexplored for most organisms, as are the consequences ofsuch modifications for patterns of morphological diversity.I examined the ecological basis of rapid threshold evolutionin exotic populations of the horn-polyphenic dung beetle Onthophagustaurus. Male O. taurus vary continuously in body size as a functionof larval feeding conditions. Only males that exceed a criticalthreshold body size develop a pair of long horns on their heads,whereas males below this threshold remain hornless. Populationsin two exotic ranges of this species, the eastern United Statesand western Australia, have diverged in the mean threshold bodysize, which has resulted in the evolution of highly divergentand novel horn length–body size allometries in these populations.Populations in a third and previously unstudied exotic rangeof O. taurus in eastern Australia exhibit threshold body sizesroughly intermediate between the eastern U.S. and western Australianpopulations. I tested three hypothesis to explain how differencesin ecological and demographic factors can drive allometric divergencesbetween populations, using data derived from comparative, standardizedsampling of a large number of populations in each exotic range.Results suggest that differences in the intensity of both intra-and interspecific competition have contributed to the evolutionof divergent thresholds in these populations. My results donot support the hypothesis that shifts in threshold body sizesto larger body sizes are a consequence of increases in the meanbody size of competing males. I discuss my results in the contextof Onthophagus mating systems and the evolutionary implicationsof threshold evolution.     

Network thinking in ecology and evolution

Although pairwise interactions have always had a key role in ecology and evolutionary biology, the recent increase in the amount and availability of biological data has placed a new focus on the complex networks embedded in biological systems. The increased availability of computational tools to store and retrieve biological data has facilitated wide access to these data, not just by biologists but also by specialists from the social sciences, computer science, physics and mathematics. This fusion of interests has led to a burst of research on the properties and consequences of network structure in biological systems. Although traditional measures of network structure and function have started us off on the right foot, an important next step is to create biologically realistic models of network formation, evolution, and function. Here, we review recent applications of network thinking to the evolution of networks at the gene and protein level and to the dynamics and stability of communities. These studies have provided new insights into the organization and function of biological systems by applying existing techniques of network analysis. The current challenge is to recognize the commonalities in evolutionary and ecological applications of network thinking to create a predictive science of biological networks.