Metaphysiological and evolutionary dynamics of populations exploiting constant and interactive resources:R?K selection revisited

It doesn't always pay to be fit: success landscapes

Landscapes play an important role in many areas of biology, in which biological lives are deeply entangled. Here we discuss a form of landscape in evolutionary biology which takes into account (1) initial growth rates, (2) mutation rates, (3) resource consumption by organisms, and (4) cyclic changes in the resources with time. The long-term equilibrium number of surviving organisms as a function of these four parameters forms what we call a success landscape, a landscape we would claim is qualitatively different from fitness landscapes which commonly do not include mutations or resource consumption/changes in mapping genomes to the final number of survivors. Although our analysis is purely theoretical, we believe the results have possibly strong connections to how we might treat diseases such as cancer in the future with a deeper understanding of the interplay between resource degradation, mutation, and uncontrolled cell growth.

Disease transmission and introgression can explain the long-lasting contact zone of modern humans and Neanderthals

Neanderthals and modern humans both occupied the Levant for tens of thousands of years prior to the spread of modern humans into the rest of Eurasia and their replacement of the Neanderthals. That the inter-species boundary remained geographically localized for so long is a puzzle, particularly in light of the rapidity of its subsequent movement. Here, we propose that infectious-disease dynamics can explain the localization and persistence of the inter-species boundary. We further propose, and support with dynamical-systems models, that introgression-based transmission of alleles related to the immune system would have gradually diminished this barrier to pervasive inter-species interaction, leading to the eventual release of the inter-species boundary from its geographic localization. Asymmetries between the species in the characteristics of their associated ‘pathogen packages’ could have generated feedback that allowed modern humans to overcome disease burden earlier than Neanderthals, giving them an advantage in their subsequent spread into Eurasia.

Modern humans and Neanderthals coexisted in the Levant for tens of thousands of years before modern humans spread and replaced Neanderthals. Here, Greenbaum et al. develop a model showing that transmission of disease and genes can explain the maintenance and then collapse of this contact zone.

Extending r/K selection with a maternal risk-management model that classifies animal species into divergent natural selection categories

Reproduction is a defining process of biological systems. Every generation, across all species, breeding females repopulate ecosystems with offspring. r/K selection was the first theory to classify animal species by linking the rates with which breeding females repopulated ecosystems, to the stability of ecosystems. Here, I introduce a species classification scheme that extends the reach of r-K selection and CSR selection by linking breeder investments in offspring quantity, quality, and diversity to specific natural selection pressures. The species classification scheme is predicated on the assumption that high rates of predation favor breeders that invest more in offspring quantity than quality; and that spatiotemporal scarcity favors breeders that investment more in offspring quality than quantity. I present equations that convert the species classification scheme into a maternal risk-management model. Thereafter, using the equations, I classify eighty-seven animal species into the model's natural selection categories. Species of reptiles, fish, and marine invertebrates clustered in the predation selection category. Species of birds and mammals clustered in the scarcity selection category. Several species of apex predators clustered in the weak selection category. Several species of social insects and social mammals clustered in the convergent selection category. In summary, by acknowledging breeding females as the individuals upon which natural selection acts to repopulate ecosystems with offspring, the proposed maternal risk-management model offers a testable, theoretical framework for the field of ecology.

Making ecological models adequate

Critical evaluation of the adequacy of ecological models is urgently needed to enhance their utility in developing theory and enabling environmental managers and policymakers to make informed decisions. Poorly supported management can have detrimental, costly or irreversible impacts on the environment and society. Here, we examine common issues in ecological modelling and suggest criteria for improving modelling frameworks. An appropriate level of process description is crucial to constructing the best possible model, given the available data and understanding of ecological structures. Model details unsupported by data typically lead to over parameterisation and poor model performance. Conversely, a lack of mechanistic details may limit a model's ability to predict ecological systems' responses to management. Ecological studies that employ models should follow a set of model adequacy assessment protocols that include: asking a series of critical questions regarding state and control variable selection, the determinacy of data, and the sensitivity and validity of analyses. We also need to improve model elaboration, refinement and coarse graining procedures to better understand the relevancy and adequacy of our models and the role they play in advancing theory, improving hind and forecasting, and enabling problem solving and management.

PREY ADAPTATION AS A CAUSE OF PREDATOR-PREY CYCLES

We analyze simple models of predator-prey systems in which there is adaptive change in a trait of the prey that determines the rate at which it is captured by searching predators. Two models of adaptive change are explored: (1) change within a single reproducing prey population that has genetic variation for vulnerability to capture by the predator; and (2) direct competition between two independently reproducing prey populations that differ in their vulnerability. When an individual predator's consumption increases at a decreasing rate with prey availability, prey adaptation via either of these mechanisms may produce sustained cycles in both species' population densities and in the prey's mean trait value. Sufficiently rapid adaptive change (e.g., behavioral adaptation or evolution of traits with a large additive genetic variance), or sufficiently low predator birth and death rates will produce sustained cycles or chaos, even when the predator-prey dynamics with fixed prey capture rates would have been stable. Adaptive dynamics can also stabilize a system that would exhibit limit cycles if traits were fixed at their equilibrium values. When evolution fails to stabilize inherently unstable population interactions, selection decreases the prey's escape ability, which further destabilizes population dynamics. When the predator has a linear functional response, evolution of prey vulnerability always promotes stability. The relevance of these results to observed predator-prey cycles is discussed.

Computational Population Biology: Linking the inner and outer worlds of organisms

Computationally complex systems models are needed to advance research and implement policy in theoretical and applied population biology. Difference and differential equations used to build lumped dynamic models (LDMs) may have the advantage of clarity, but are limited in their inability to include fine-scale spatial information and individual-specific physical, physiological, immunological, neural and behavioral states. Current formulations of agent-based models (ABMs) are too idiosyncratic and freewheeling to provide a general, coherent framework for dynamically linking the inner and outer worlds of organisms. Here I propose principles for a general, modular, hierarchically scalable, framework for building computational population models (CPMs) designed to treat the inner world of individual agents as complex dynamical systems that take information from their spatially detailed outer worlds to drive the dynamic inner worlds of these agents, simulate their ecology and the evolutionary pathways of their progeny. All the modeling elements are in place, although improvements in software technology will be helpful; but most of all we need a cultural shift in the way population biologists communicate and share model components and the models themselves, fit, test, refute, and refine models, to make the progress needed to meet the ecosystems management challenges posed by global change biology.

A Biomass Flow Approach to Population Models and Food Webs

The dominant differential equation paradigm for modeling the population dynamics of species interacting in the framework of a food web retains at its core the basic prey-predator and competition models formulation by Alfred J. Lotka (1880-1945) and Vito Volterra (1860-1940) nearly nine decades ago. This paradigm lacks a trophic-level-independent formulation of population growth leading to ambiguities in how to treat populations that are simultaneously both prey and predator. Also, this paradigm does not fundamentally include inertial (i.e. change resisting) processes needed to account for the response of populations to fluctuating resource environments. Here I present an approach that corrects both these deficits and provides a unified framework for accounting for biomass transformation in food webs that include both live and dead components of all species in the system. This biomass transformation formulation (BTW) allows for a unified treatment of webs that include consumers of both live and dead material-both carnivores and carcasivores, herbivores and detritivores-and incorporates scavengers, parasites, and other neglected food web consumption categories in a coherent manner. I trace how BTW is an outgrowth of the metaphysiological growth modeling paradigm and I provide a general compact formulation of BTW in terms of a three-variable differential equation formulation for each species in the food web: viz. live biomass, dead biomass, and a food-intake-related measure called deficit-stress. I then illustrate the application of this new paradigm to provide insights into two-species competition in variable environments and discuss application of BTW to food webs that incorporate parasites and pathogens.

Accommodating environmental variation in population models: metaphysiological biomass loss accounting

1. There is a pressing need for population models that can reliably predict responses to changing environmental conditions and diagnose the causes of variation in abundance in space as well as through time. In this 'how to' article, it is outlined how standard population models can be modified to accommodate environmental variation in a heuristically conducive way. This approach is based on metaphysiological modelling concepts linking populations within food web contexts and underlying behaviour governing resource selection. Using population biomass as the currency, population changes can be considered at fine temporal scales taking into account seasonal variation. Density feedbacks are generated through the seasonal depression of resources even in the absence of interference competition. 2. Examples described include (i) metaphysiological modifications of Lotka-Volterra equations for coupled consumer-resource dynamics, accommodating seasonal variation in resource quality as well as availability, resource-dependent mortality and additive predation, (ii) spatial variation in habitat suitability evident from the population abundance attained, taking into account resource heterogeneity and consumer choice using empirical data, (iii) accommodating population structure through the variable sensitivity of life-history stages to resource deficiencies, affecting susceptibility to oscillatory dynamics and (iv) expansion of density-dependent equations to accommodate various biomass losses reducing population growth rate below its potential, including reductions in reproductive outputs. Supporting computational code and parameter values are provided. 3. The essential features of metaphysiological population models include (i) the biomass currency enabling within-year dynamics to be represented appropriately, (ii) distinguishing various processes reducing population growth below its potential, (iii) structural consistency in the representation of interacting populations and (iv) capacity to accommodate environmental variation in space as well as through time. Biomass dynamics provide a common currency linking behavioural, population and food web ecology. 4. Metaphysiological biomass loss accounting provides a conceptual framework more conducive for projecting and interpreting the population consequences of climatic shifts and human transformations of habitats than standard modelling approaches.

Consumer-resource dynamics: quantity, quality, and allocation

BACKGROUND

The dominant paradigm for modeling the complexities of interacting populations and food webs is a system of coupled ordinary differential equations in which the state of each species, population, or functional trophic group is represented by an aggregated numbers-density or biomass-density variable. Here, using the metaphysiological approach to model consumer-resource interactions, we formulate a two-state paradigm that represents each population or group in a food web in terms of both its quantity and quality.

METHODOLOGY AND PRINCIPAL FINDINGS

The formulation includes an allocation function controlling the relative proportion of extracted resources to increasing quantity versus elevating quality. Since lower quality individuals senescence more rapidly than higher quality individuals, an optimal allocation proportion exists and we derive an expression for how this proportion depends on population parameters that determine the senescence rate, the per-capita mortality rate, and the effects of these rates on the dynamics of the quality variable. We demonstrate that oscillations do not arise in our model from quantity-quality interactions alone, but require consumer-resource interactions across trophic levels that can be stabilized through judicious resource allocation strategies. Analysis and simulations provide compelling arguments for the necessity of populations to evolve quality-related dynamics in the form of maternal effects, storage or other appropriate structures. They also indicate that resource allocation switching between investments in abundance versus quality provide a powerful mechanism for promoting the stability of consumer-resource interactions in seasonally forcing environments.

CONCLUSIONS/SIGNIFICANCE

Our simulations show that physiological inefficiencies associated with this switching can be favored by selection due to the diminished exposure of inefficient consumers to strong oscillations associated with the well-known paradox of enrichment. Also our results demonstrate how allocation switching can explain observed growth patterns in experimental microbial cultures and discuss how our formulation can address questions that cannot be answered using the quantity-only paradigms that currently predominate.

Biomass transformation webs provide a unified approach to consumer-resource modelling

An approach to modelling food web biomass flows among live and dead compartments within and among species is formulated using metaphysiological principles that characterise population growth in terms of basal metabolism, feeding, senescence and exploitation. This leads to a unified approach to modelling interactions among plants, herbivores, carnivores, scavengers, parasites and their resources. Also, dichotomising sessile miners from mobile gatherers of resources, with relevance to feeding and starvation time scales, suggests a new classification scheme involving 10 primary categories of consumer types. These types, in various combinations, rigorously distinguish scavenger from parasite, herbivory from phytophagy and detritivore from decomposer. Application of the approach to particular consumer-resource interactions is demonstrated, culminating in the construction of an anthrax-centred food web model, with parameters applicable to Etosha National Park, Namibia, where deaths of elephants and zebra from the bacterial pathogen, Bacillus anthracis, provide significant subsidies to jackals, vultures and other scavengers.

Disease and the dynamics of food webs

What models and statistical tools can best help us assess how ecosystems respond to the impact of multiple factors, such as disease, predation, fire, and rain?

Correlative coherence analysis: variation from intrinsic and extrinsic sources in competing populations

The concept of the correlation between two signals is generalized to the correlative coherence of a set of n signals by introducing a Shannon-Weaver-type measure of the entropy of the normalized eigenvalues of the n-dimensional correlation matrix associated with the set of signals. Properties of this measure are stated for canonical cases. The measure is then used to evaluate which subsets of a particular set of n signals are more or less coherent. This set of signals comprises extrinsic, stochastic resource inputs and the population trajectories obtained from simulations of a discrete time model of competing biological populations driven by these resource inputs. The analysis reveals that, at low levels of competition, the correlative coherence of the combined system of intrinsic population and extrinsic resource variables is relatively low, but increases with increasing variation in the resources. Further, at intermediate and high competition levels, the correlative coherence depends more strongly on competition than entrainment of stochasticity in the extrinsic resource variables. Density dependence has the effect of amplifying variation in noise only when this variation is relatively large. Also, chaotic systems appear to be entrained by sufficiently noisy environmental inputs.

The impact of consumer-resource cycles on the coexistence of competing consumers

This article seeks to determine the extent to which endogenous consumer-resource cycles can contribute to the coexistence of competing consumer species. It begins with a numerical analysis of a simple model proposed by Armstrong and McGehee. This model has a single resource and two consumers, one with a linear functional response and one with a saturating response. Coexistence of the two consumer species can occur when the species with a saturating response generates population cycles of the resource, and also has a lower resource requirement for zero population growth. Coexistence can be achieved over a wide range of relative efficiencies of the two consumers provided that the functional response of the saturating consumer reaches its half-saturation value when the resource population is a small fraction of its carrying capacity. In this case, the range of efficiencies allowing coexistence is comparable to that when two competitors have stable dynamics and a high degree of resource partitioning. A variety of modifications of this basic model are analyzed to investigate the consequences for coexistence of different resource growth equations, different functional and numerical response shapes, and other factors. Large differences in functional response shape appear to be the most important factor in producing robust coexistence via resource cycles. If the unstable species has a concave numerical response, this greatly expands the conditions allowing coexistence. If the stable consumer species has a convex (accelerating) functional and/or numerical response, the range of conditions allowing coexistence is also expanded. We argue that large between-species differences in functional response form can often be produced by between-consumer differences in the adaptive adjustments of foraging effort to food density. Consumer-resource cycles can also expand the conditions allowing coexistence when there is resource partitioning, but do so primarily when resource partitioning is relatively slight; this makes the ease of coexistence relatively independent of consumer similarity.

Population-level consequences of antipredator behavior: a metaphysiological model based on the functional ecology of the leaf-eared mouse

We present a predator-prey metaphysiological model, based on the available behavioral and physiological information of the sigmodontine rodent Phyllotis darwini. The model is focused on the population-level consequences of the antipredator behavior, performed by the rodent population, which is assumed to be an inducible response of predation avoidance. The decrease in vulnerability is explicitly considered to have two associated costs: a decreasing foraging success and an increasing metabolic loss. The model analysis was carried out on a reduced form of the system by means of numerical and analytical tools. We evaluated the stability properties of equilibrium points in the phase plane, and carried out bifurcation analyses of rodent equilibrium density under varying conditions of three relevant parameters. The bifurcation parameters chosen represent predator avoidance effectiveness (A), foraging cost of antipredator behavior (C(1)'), and activity-metabolism cost (C(4)'). Our analysis suggests that the trade-offs involved in antipredator behavior plays a fundamental role in the stability properties of the system. Under conditions of high foraging cost, stability decreases as antipredator effectiveness increases. Under the complementary scenario (not considering the highest foraging costs), the equilibria are either stable when both costs are low, or unstable when both costs are higher, independent of antipredator effectiveness. No evidence of stabilizing effects of antipredator behavior was found.

Evolutionary Stable Strategies and Trade-Offs in Generalized Beverton and Holt Growth Models

A generalized Beverton-Holt model is considered in which a parameter gamma characterizes the onset of density dependence. An evolutionary stable strategy analysis of this parameter, reported in Getz (1996), is developed further here, using invasion exponents and the strategy dynamics of Vincent et al. (1993). The parameter gamma is also allowed to be density dependent, and it is shown that the most successful strategies of this type are those for which gamma is large for low densities and close to its minimum for high densities. A biological interpretation is given in the context of mobile females depositing their relatively sessile young on patches of resource, namely, females should overdisperse their young on resources when adult densities are high and underdisperse them when these densities are low. Finally the per capita growth rate parameter is also allowed to depend on gamma. It is shown that this dependence provides a mechanism by which periodic or chaotic attractor dynamics could evolve towards equilibrium attractor dynamics. Copyright 1998 Academic Press.