On our best behavior: optimality models in human behavioral ecology

This paper discusses problems associated with the use of optimality models in human behavioral ecology. Optimality models are used in both human and non-human animal behavioral ecology to test hypotheses about the conditions generating and maintaining behavioral strategies in populations via natural selection. The way optimality models are currently used in behavioral ecology faces significant problems, which are exacerbated by employing the so-called ‘phenotypic gambit’: that is, the bet that the psychological and inheritance mechanisms responsible for behavioral strategies will be straightforward. I argue that each of several different possible ways we might interpret how optimality models are being used for humans face similar and additional problems. I suggest some ways in which human behavioral ecologists might adjust how they employ optimality models; in particular, I urge the abandonment of the phenotypic gambit in the human case.     

Connecting behavioural biologists and psychologists: Clarifying distinctions and suggestions for further work

This article is a reply to the commentaries on our target article, which relates our group's work on simple heuristics to biological research on rules of thumb. Several commentators contrasted both these approaches with behaviour analysis, in which the patterns of behaviour investigated in the laboratory are claimed to be near-universal attributes, rather than specific to particular appropriate environments. We question this universality. For instance, learning phenomena such Pavlovian or operant conditioning have mostly been studied only in a few generalist species that learn easily; in many natural situations the environment hinders learning as an adaptive strategy. Other supposedly general phenomena such as impulsiveness and matching are outcome models, which several different models of simple cognitive processes might explain. We clarify some confusions about optimisation, optima and optimality modelling. Lastly, we say a little more about how heuristics might be selected, learnt and tuned to suit the current environment.     

Can optimality models and an ‘optimality research program’ help us understand some plant–fungal relationships?

In this paper we suggest that the field of fungal ecology may benefit from the use of optimality models in the context of an ‘optimality research program’ (ORP). An ORP is a research program in the sense of modern philosopher of science Lakatos' [1978. The Methodology of Scientific Research Programmes: philosophical papers, vol. 1. Cambridge University Press, Cambridge] seminal work. An optimality research program has a lengthy history and record of success in the field of behavioural ecology, but has been seldom employed in fungal ecology. We discuss the ORP and provide some examples of how optimality models may be useful in fungal ecology. We suggest that such an approach may benefit experimental fungal ecologists by: providing a framework for organizing knowledge; generating hypotheses; helping in the planning of experiments; aiding in the interpretation of results; and directing the next steps of an experimental research program. We illustrate these benefits by sketching out how an ORP might be used to answer some fundamental questions about the interactions between host plants and arbuscular mycorrhizal fungi.     

Optimality principles for model-based prediction of human gait

Although humans have a large repertoire of potential movements, gait patterns tend to be stereotypical and appear to be selected according to optimality principles such as minimal energy. When applied to dynamic musculoskeletal models such optimality principles might be used to predict how a patient's gait adapts to mechanical interventions such as prosthetic devices or surgery. In this paper we study the effects of different performance criteria on predicted gait patterns using a 2D musculoskeletal model. The associated optimal control problem for a family of different cost functions was solved utilizing the direct collocation method. It was found that fatigue-like cost functions produced realistic gait, with stance phase knee flexion, as opposed to energy-related cost functions which avoided knee flexion during the stance phase. We conclude that fatigue minimization may be one of the primary optimality principles governing human gait.     

Optimality modeling in a suboptimal world

The fate of optimality modeling is typically linked to that of adaptationism: the two are thought to stand or fall together (Gould and Lewontin, Proc Relig Soc Lond 205:581–598, 1979; Orzack and Sober, Am Nat 143(3):361–380, 1994). I argue here that this is mistaken. The debate over adaptationism has tended to focus on one particular use of optimality models, which I refer to here as their strong use. The strong use of an optimality model involves the claim that selection is the only important influence on the evolutionary outcome in question and is thus linked to adaptationism. However, biologists seldom intend this strong use of optimality models. One common alternative that I term the weak use simply involves the claim that an optimality model accurately represents the role of selection in bringing about the outcome. This and other weaker uses of optimality models insulate the optimality approach from criticisms of adaptationism, and they account for the prominence of optimality modeling (broadly construed) in population biology. The centrality of these uses of optimality models ensures a continuing role for the optimality approach, regardless of the fate of adaptationism.

DIFFUSION POTENTIALS IN MODELS AND IN LIVING CELLS

The behavior of guaiacol resembles that of certain protoplasmic surfaces to such an extent that it can be advantageously used in models designed to imitate certain aspects of protoplasmic behavior. In these models the electrical potentials appear to consist of diffusion potentials and this may be true of certain living cells. In dealing with models we determine ionic mobilities and use these to predict potentials. In studying living cells we measure potentials and from these calculate ionic mobilities. The question arises, how far is this method justified. To test this we have treated guaiacol like a living cell, measuring potentials and from these estimating ionic mobilities. The results Justify the use of this method. This is of interest because the method is most useful in studying protoplasmic activity. In its extended form it enables us to follow changes in mobilities and in partition coefficients due to applied reagents and to metabolism.     

Predicting resource utilization: the utility of optimal foraging models

Predicting how predation changes communities is an important challenge for ecologists. One view assumes that predictions can be made in terms of behavioural phenomena. Static optimality methods have been used to devise models of prey choice and are thought to have performed well. Two examples from the literature show that models of diet choice have either been applied without first testing them at the individual level, or have been tested in a way that does not fulfil all their assumptions. A discussion of the nature of mathematical models shows why it is dangerous to translate theories into natural language and how important it is to appreciate the limitations on the mathematical functions describing behaviour. A final section discusses behavioural phenomena such as satiation and learning, which are likely to limit the predictive capacities of static optimization models. It is likely that dynamic models are the way forward although they may be harder to apply at the ecological level.     

Information processing limits on generating neuroanatomy: global optimization of rat olfactory cortex and amygdala

A pattern of widespread connection optimization in the nervous system has become evident: deployment of some neural interconnections attains optimality, sometimes without detectable limits. New results for optimization of layout of connected areas of rat olfactory cortex and of rat amygdala are reported here. One larger question concerns mechanisms—how such minimization is attained. A next question is why a nervous system would optimize rather than just moderately satisfice. A morphogenic proposal that relates these questions is that the means of organizing neural wiring happens also to yield optimization. Some neuroanatomy is generated via “saving wire,” and this optimizing is via simple physical processes rather than DNA-mediated mechanisms. Such “non-genomic nativism” is thereby a path around fundamental limitations on generating brains, some of the most complex structures in the known universe.     

The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements.     

Designing and analyzing clinical trials with composite outcomes: consideration of possible treatment differences between the individual outcomes

When the individual outcomes within a composite outcome appear to have different treatment effects, either in magnitude or direction, researchers may question the validity or appropriateness of using this composite outcome as a basis for measuring overall treatment effect in a randomized controlled trial. The question remains as to how to distinguish random variation in estimated treatment effects from important heterogeneity within a composite outcome. This paper suggests there may be some utility in directly testing the assumption of homogeneity of treatment effect across the individual outcomes within a composite outcome. We describe a treatment heterogeneity test for composite outcomes based on a class of models used for the analysis of correlated data arising from the measurement of multiple outcomes for the same individuals. Such a test may be useful in planning a trial with a primary composite outcome and at trial end with final analysis and presentation. We demonstrate how to determine the statistical power to detect composite outcome treatment heterogeneity using the POISE Trial data. Then we describe how this test may be incorporated into a presentation of trial results with composite outcomes. We conclude that it may be informative for trialists to assess the consistency of treatment effects across the individual outcomes within a composite outcome using a formalized methodology and the suggested test represents one option.     

The power of a single representation: morphological tone and allomorphy

This paper investigates the question of how much work phonology can do in accounting for apparently suppletive but phonologically predictable allomorphy. Two case studies of surface alternations in the domain of morphological tone are discussed and monorepresentational optimality theoretic analyses are proposed that predict the apparent suppletive allomorphies from a single underlying representation for the morphemes in question.     

Ecologists should not use statistical significance tests to interpret simulation model results

Simulation models are widely used to represent the dynamics of ecological systems. A common question with such models is how changes to a parameter value or functional form in the model alter the results. Some authors have chosen to answer that question using frequentist statistical hypothesis tests (e.g. ANOVA). This is inappropriate for two reasons. First, p‐values are determined by statistical power (i.e. replication), which can be arbitrarily high in a simulation context, producing minuscule p‐values regardless of the effect size. Second, the null hypothesis of no difference between treatments (e.g. parameter values) is known a priori to be false, invalidating the premise of the test. Use of p‐values is troublesome (rather than simply irrelevant) because small p‐values lend a false sense of importance to observed differences. We argue that modelers should abandon this practice and focus on evaluating the magnitude of differences between simulations. Synthesis Researchers analyzing field or lab data often test ecological hypotheses using frequentist statistics (t‐tests, ANOVA, etc.) that focus on p‐values. Field and lab data usually have limited sample sizes, and p‐values are valuable for quantifying the probability of making incorrect inferences in that situation. However, modern ecologists increasingly rely on simulation models to address complex questions, and those who were trained in frequentist statistics often apply the hypothesis‐testing approach inappropriately to their simulation results. Our paper explains why p‐values are not informative for interpreting simulation models, and suggests better ways to evaluate the ecological significance of model results.     

Evolutionary optimality applied to Drosophila experiments: hypothesis of constrained reproductive efficiency

The general purpose of the paper is to test evolutionary optimality theories with experimental data on reproduction, energy consumption, and longevity in a particular Drosophila genotype. We describe the resource allocation in Drosophila females in terms of the oxygen consumption rates devoted to reproduction and to maintenance. The maximum ratio of the component spent on reproduction to the total rate of oxygen consumption, which can be realized by the female reproductive machinery, is called metabolic reproductive efficiency (MRE). We regard MRE as an evolutionary constraint. We demonstrate that MRE may be evaluated for a particular Drosophila phenotype given the fecundity pattern, the age-related pattern of oxygen consumption rate, and the longevity. We use a homeostatic model of aging to simulate a life history of a representative female fly, which describes the control strain in the long-term experiments with the Wayne State Drosophila genotype. We evaluate the theoretically optimal trade-offs in this genotype. Then we apply the Van Noordwijk-de Jong resource acquisition and allocation model, Kirkwood's disposable soma theory. and the Partridge-Barton optimality approach to test if the experimentally observed trade-offs may be regarded as close to the theoretically optimal ones. We demonstrate that the two approaches by Partridge-Barton and Kirkwood allow a positive answer to the question, whereas the Van Noordwijk-de Jong approach may be used to illustrate the optimality. We discuss the prospects of applying the proposed technique to various Drosophila experiments, in particular those including manipulations affecting fecundity.     

Optimal allocation between nutrient uptake and growth in a microbial trichome

 A microbial trichome grows by assimilating nutrients from its environment, and converting these into catalytic macro-molecular machinery. This machinery may be divided into assimilatory machinery and proliferative machinery. The former type is involved in nutrient uptake, whereas the latter type enables the trichome to grow. The cells in the trichome are faced with an allocation problem: given the availability of nutrients in the environment, how many macro-molecular building blocks should be allocated to the synthesis of assimilatory machinery, and how many to the synthesis of proliferative machinery? We answer this question for a particular model, which is a generalization of the Droop quota model. We formulate a two-dimensional non-linear optimal control problem, corresponding to this model. An optimal allocation regime with a singular segment is derived, based on Pontryagin’s maximum principle. We give a direct proof of optimality. We discuss how actual biological cells might implement this optimal regime. Received: 16 December 1996 / Revised version: 14 September 1997     

Bayesian flux balance analysis applied to a skeletal muscle metabolic model

In this article, the steady state condition for the multi-compartment models for cellular metabolism is considered. The problem is to estimate the reaction and transport fluxes, as well as the concentrations in venous blood when the stoichiometry and bound constraints for the fluxes and the concentrations are given. The problem has been addressed previously by a number of authors, and optimization-based approaches as well as extreme pathway analysis have been proposed. These approaches are briefly discussed here. The main emphasis of this work is a Bayesian statistical approach to the flux balance analysis (FBA). We show how the bound constraints and optimality conditions such as maximizing the oxidative phosphorylation flux can be incorporated into the model in the Bayesian framework by proper construction of the prior densities. We propose an effective Markov chain Monte Carlo (MCMC) scheme to explore the posterior densities, and compare the results with those obtained via the previously studied linear programming (LP) approach. The proposed methodology, which is applied here to a two-compartment model for skeletal muscle metabolism, can be extended to more complex models.     

Prospects and challenges for parametric models in historical biogeographical inference

In historical biogeography, phylogenetic trees have long been used as tools for addressing a wide range of inference problems, from explaining common distribution patterns of species to reconstructing ancestral geographic ranges on branches of the tree of life. However, the potential utility of phylogenies for this purpose has yet to be fully realized, due in part to a lack of explicit conceptual links between processes underlying the evolution of geographic ranges and processes of phylogenetic tree growth. We suggest that statistical approaches that use parametric models to forge such links will stimulate integration and propel hypothesis-driven biogeographical inquiry in new directions. We highlight here two such approaches and describe how they represent early steps towards a more general framework for model-based historical biogeography that is based on likelihood as an optimality criterion, rather than having the traditional reliance on parsimony. The development of this framework will not be without significant challenges, particularly in balancing model complexity with statistical power, and these will be most apparent in studies of regions with many component areas and complex geological histories, such as the Mediterranean Basin.     

Optimality models of phage life history and parallels in disease evolution

Optimality models constitute one of the simplest approaches to understanding phenotypic evolution. Yet they have shortcomings that are not easily evaluated in most organisms. Most importantly, the genetic basis of phenotype evolution is almost never understood, and phenotypic selection experiments are rarely possible. Both limitations can be overcome with bacteriophages. However, phages have such elementary life histories that few phenotypes seem appropriate for optimality approaches. Here we develop optimality models of two phage life history traits, lysis time and host range. The lysis time models show that the optimum is less sensitive to differences in host density than suggested by earlier analytical work. Host range evolution is approached from the perspective of whether the virus should avoid particular hosts, and the results match optimal foraging theory: there is an optimal "diet" in which host types are either strictly included or excluded, depending on their infection qualities. Experimental tests of both models are feasible, and phages provide concrete illustrations of many ways that optimality models can guide understanding and explanation. Phage genetic systems already support the perspective that lysis time and host range can evolve readily and evolve without greatly affecting other traits, one of the main tenets of optimality theory. The models can be extended to more general properties of infection, such as the evolution of virulence and tissue tropism.     

A coefficient of determination (R2) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R²) or the adjusted R² are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance‐covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.     

On the Use of Enterprise Models

This paper presents the results of a field study designed to determine how enterprise models are used. The paper begins with an introduction to enterprise models then provides an overview of the survey method used. No known empirical studies have been conducted to determine how enterprise models actually are used by industry. The research is designed to answer this question. A screening sample and complete web-based survey of 72 enterprise modelers was conducted. The primary research question of this survey was on the use of enterprise models, with particular focus on the three dimensions of living models: scope, enactment, and dynamicity. Half the respondents claim that their enterprise models were of their entire division, multiple divisions, and even multiple enterprises. It is encouraging to see that enterprise models are used on such a wide scope. The enactment of the enterprise models was not as large as was expected. Of the respondents, 75% claimed that their models did not receive information from the enterprise more frequently than quarterly. The same was true for how often the models provided information to the enterprise. Seventy-five percent did not update their models more than five times (although, 32% did update the model three to five times). Finally, additional areas of research are proposed.