The effects of background mortality on optimal reproduction in a seasonal environment

We consider optimal annual routines of reproductive behaviour in a seasonal environment. In our model the condition of the organism is adversely affected by hard work, but can recover during easy periods. Our analysis concentrates on the effects of background mortality (i.e., mortality that cannot be avoided) on the optimal strategy and how often an organism following this strategy breeds. In particular, we are concerned with whether reproduction occurs at specific times of year (entrained to the annual cycle), and if so then how many reproductive bouts occur per year. We find that an increase in background mortality can have various effects. If the animal is entrained to the annual cycle and has one breeding attempt per year, then breeding tends to occur earlier and there may be two breeding attempts per season. Another possible outcome is that breeding is no longer entrained. If the animal is entrained but sometimes skips reproduction so that it does not breed every year, then an increase in mortality may make it more likely that the animal breeds every year. We show that as background mortality increases the resultant increase in the frequency of breeding contributes to the increase in annual mortality. We also explore the effects of mortality on the timing of reproduction within a year, highlighting the tension between the interests of the parent and that of the young.     

Climate change and the optimal arrival of migratory birds

Recent climate change has sparked an interest in the timing of biological events, which is a general problem in life-history evolution. Reproduction in many organisms breeding in seasonal environments, e.g. migratory birds, is dependent on the exploitation of a short but rich food supply. If the seasonal timing of the food peak advances owing to climate change, then one would expect the bird to track those changes, hence, initiate migration and breeding earlier. However, when there is competition for territories and a risk of pre-breeding mortality, the optimal response to a shifting food distribution is no longer obvious. We develop a theoretical model to study how the optimal arrival time depends on the mean and variance of the food distribution, the degree of competition for territories and the risk of mortality. In general, the optimal shift in arrival date should never be as extreme as the shift in food peak date. Our results also show that we should expect the high variation of trends in arrival date observed among migratory birds, even if migration and information about climate change were unconstrained.     

Assessing predation risk: optimal behaviour and rules of thumb

We look at a simple model in which an animal makes behavioural decisions over time in an environment in which all parameters are known to the animal except predation risk. In the model there is a trade-off between gaining information about predation risk and anti-predator behaviour. All predator attacks lead to death for the prey, so that the prey learns about predation risk by virtue of the fact that it is still alive. We show that it is not usually optimal to behave as if the current unbiased estimate of the predation risk is its true value. We consider two different ways to model reproduction; in the first scenario the animal reproduces throughout its life until it dies, and in the second scenario expected reproductive success depends on the level of energy reserves the animal has gained by some point in time. For both of these scenarios we find results on the form of the optimal strategy and give numerical examples which compare optimal behaviour with behaviour under simple rules of thumb. The numerical examples suggest that the value of the optimal strategy over the rules of thumb is greatest when there is little current information about predation risk, learning is not too costly in terms of predation, and it is energetically advantageous to learn about predation. We find that for the model and parameters investigated, a very simple rule of thumb such as 'use the best constant control' performs well.     

A lifetime perspective on foraging and mortality

Food intake carries many potential risks which may impair an animal's reproductive success not only in the current breeding cycle, but also for the rest of its lifetime. We examine the lifetime trade-off between the costs and benefits of food intake by presenting a simple animal foraging model, where each unit of food eaten carries with it a risk of mortality. We show that the optimal food intake rate over an animal's lifetime, for both semelparous and iteroparous animals, is not maximal. Instead, animals are required to strike a balance between the immediate reproductive benefits of gathering food and the future reproductive costs incurred by the food's mortality risk. This balance depends upon the lifespan of the animal as well as the nature of the risk. Different mortality risks are compared and it is shown that a mortality risk per unit time spent foraging is not, in general, equivalent to a mortality risk per unit of food consumed. The results suggest that a mortality risk per unit of food consumed, such as that presented by the presence of a toxin or of a parasite in the diet, has important consequences for feeding behaviour and is a possible factor involved in food intake regulation.     

``Two' Many Optimalities

In evolutionary biology, a trait is said to be optimal if it maximizes the fitness of the organism, that is, if the trait allows the organism to survive and reproduce better than any other competing trait would. In engineering, a design is said to be optimal if it complies with its functional requirements as well as possible. Cognitive science is both a biological and engineering discipline and hence it uses both notions of optimality. Unfortunately, the lack of a clear methodological stance on this tissue has made it common for researchers to conflate these two kinds of optimality. In this paper, I argue that a strict distinction must kept in order to avoid inaccurate assumptions.     

Anti-predation behaviour during bird migration; the benefit of studying multiple behavioural dimensions

Predation and predation risk have recently been shown to have profound effects on bird migration, but we still know relatively little about how birds respond to predation risk en route and how this is translated into fundamental aspects of optimal migration. Here, we make the case that to understand the fitness consequences of foraging and anti-predation behaviour en route we cannot rely on single behaviour relationships but must take many aspects of behaviour into account, because of predation risk compensation. We show this in a case study of fat and vigilant birds feeding close to cover, which emphasises the importance and potential of predation risk compensation. Another reason for taking many aspects of behaviour into account is that different behaviours need not contribute equally to individual fitness. Birds faced with an increased predation risk during migration can compensate for increased predation risk in different ways. This implies that the adaptive value of a behavioural trait can still be ambiguous even if a survival cost can be correlated with particular behaviour where all other things are equal (e.g. in an experiment). That is because in natural systems there may frequently be many other ways for animals to compensate, because all other things are never equal, so that the particular behaviour can actually be of little consequence to individual fitness. In conclusion, when studying foraging decisions and anti-predation behaviour during stopover potential compensatory mechanisms should be incorporated. This knowledge is also critical for improving future models of optimal migration.     

Estimating Root Longevity at Sites with Long Periods of Low Root Mortality

Minirhizotron technique is capable of providing median root longevity. The use of the median longevity might overestimate root longevity if the distribution of survival times is very skewed or irregular, as is the case at sites where root mortality is very low during the long winter. In this paper we illustrate the case theoretically and compare that with field observation in northern Sweden to show an alternative procedure for such sites. Hypothetical root cohorts were constructed to investigate and show some technical problems with estimating median root longevity at a Swedish northern site where root mortality is very low during long winter time (8 months), and to investigate whether these problems could be overcome by discarding winter time from the survival analysis and include only the growing season in which the roots are at risk of mortality. Authentic root data, gathered in a minirhizotron study at such a site, were analysed on a whole year basis and on season basis. By analysing longevity based only on the season when there is a risk for root death, the median longevity became a more reliable estimate of the true mean longevity. When this method was applied to root data from northern Sweden, the estimated root longevity in different treatments became between 17% lower and 8% higher compared to the longevity estimated on a whole year basis.We conclude that the reliability of the median longevity as an estimate of the true mean longevity can be increased by basing the survival analysis only on the parts of the year when fine roots are at risk of mortality at sites with long winter and low root mortality.     

Ways to test stochastic dynamic programming models empirically

Stochastic dynamic programming (SDP) models are widely used to predict optimal behavioural and life history strategies. We discuss a diversity of ways to test SDP models empirically, taking as our main illustration a model of the daily singing routine of birds. One approach to verification is to quantify model parameters, but most SDP models are schematic. Because predictions are therefore qualitative, testing several predictions is desirable. How state determines behaviour (the policy) is a central prediction that should be examined directly if both state and behaviour are measurable. Complementary predictions concern how behaviour and state change through time, but information is discarded by considering behaviour rather than state, by looking only at average state rather than its distribution, and by not following individuals. We identify the various circumstances in which an individual's state/behaviour at one time is correlated with its state/behaviour at a later time. When there are several state variables the relationships between them may be informative. Often model parameters represent environmental conditions that can also be viewed as state variables. Experimental manipulation of the environment has several advantages as a test, but a problem is uncertainty over how much the organism's policy will adjust. As an example we allow birds to use different assumptions about how well past weather predicts future weather. We advocate mirroring planned empirical investigations on the computer to investigate which manipulations and predictions will best test a model. Copyright 2000 The Association for the Study of Animal Behaviour.     

A Nonparametric Estimator of Heterogeneity Variance with Applications to SMR‐ and Proportion‐Data

In this paper the situation of extra population heterogeneity is discussed from a analysis of variance point of view. We first provide a non‐iterative way of estimating the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself for Poisson and binomial counts. The consequences of the presence of heterogeneity in the estimation of the mean are discussed. We show that if the homogeneity assumption holds, the pooled mean is optimal while in the presence of strong heterogeneity, the simple (arithmetic) mean is an optimal estimator of the mean SMR or mean proportion. These results lead to the problem of finding an optimal estimator for situations not represented by these two extreme cases. We propose an iterative solution to this problem. Illustrations for the application of these findings are provided with examples from various areas.     

Plant defence and stochastic risk of herbivory

Summary The influence of risk of herbivory and its variation in time on the optimal defence strategy in plants is analysed by a simple optimization model. We contrast two possible defence strategies; a constitutive defence with an invariant defence level in time and an idealized induced defence, that is, a strategy that adjusts the defence level to the prevailing risk of herbivory. We also take into account effects of the efficiency of the defence. If there is no variation in risk of herbivory over years, constitutive and induced defence should have the same expected optimal defence level and both strategies are equally fit. The optimal defence level increases as the maximum fecundity and the adult to juvenile survival ratio of the plants both increase. If the risk of herbivory varies stochastically, the expected optimal level of the constitutive defence is either increased or unaffected by the variation, whereas the induced defence strategy may result in both higher or lower expected optimal defence levels as variance increases. This outcome is dependent on the mean risk of herbivory. It also depends on the defence efficiency, i.e. the shape (convex, concave or linear) of the defence function that relates the probability of survival if encountered by a herbivore to defence level. Thus, the defence level of plants interacting with variable herbivore populations cannot be unambiguously predicted unless the defence strategy (constitutive or induced), mean risk of herbivory, the form of the defence function and plant life history are known.     

Individual adaptations in stochastic environments

Summary Many natural populations undergo radical and unpredictable fluctuations, associated with stochastic environmental conditions. Under such circumstances, fitness of a genotype (or strategy) is defined as the geometric mean of the intergenerational genotypic population growth ratel(t). Unfortunately, this population-level criterion has proved difficult to apply at the level of individual organisms.After developing a formula for the variance ofl as the sum of developmental and environmental variance, we discuss several models of individual adaptations, involving clutch size, progeny size and number, and foraging behaviour under risk of predation, based on the geometric-mean fitness concept. We then show how the method of dynamic programming can be extended to deal with facultative behaviour in stochastic environments. Finally we discuss the concept of an evolutionarily stable strategy in a stochastic environment.Our analysis suggests several novel interpretations of field and laboratory observations. Under the geometric mean criterion behaviour may be determined primarily by the worst likely environment; behaviour may appear suboptimal if observed only under normal or average conditions. For example,except under extreme environmental conditions, avian clutches larger than those that are observed might result in increased fecundity, with little if any cost of reproduction in terms of parental survival; however, in unusually bad years such large clutches might be disastrous, in terms of parental survival. This consideration may help explain some recently reported experimental clutch-size manipulation results. Similarly, our analysis indicates that the known phenomenon of seasonal reduction in seed size may constitute a double bet-hedging strategy, determined by parental mortality risk and future seed survival probability. We also discuss circumstances in which phenotypic polymorphism is an adaptation to environmental uncertainty. Thus almost any individual life history or behavioural adaptation may be affected by environmental stochasticity.     

Oxygen balance for small organisms: an analytical model

An analytical model is developed that describes oxygen transport and oxygen consumption for small biological structures without a circulatory system. Oxygen inside the organism is transported by diffusion alone. Oxygen transfer towards the organism is retarded by a thin static fluid film at the surface of the organism. The thickness of this film models the outward water conditions, which may range from completely stagnant water conditions to so-called well-stirred water conditions. Oxygen consumption is concentration-independent above a specified threshold concentration (regulator behaviour) and is proportional to the oxygen concentration below this threshold (conformer behaviour). The model takes into account shape and size of the organism and predicts the transition from (pure) regulator behaviour to (pure) conformer behaviour, as well as the mean oxygen consumption rate. Thereby the model facilitates a proper analysis of the physical constraints set on shape and size of organisms without an active internal oxygen transport mechanism. This analysis is carried out in some detail for six characteristic shapes (infinite sheet, cylinder and beam; finite cylinder, sphere and block). In a well-stirred external medium, a flattened shape appears to be the most favourable for oxygen supply, while a compact shape (cube) is more favourable if the external medium is nearly stagnant. The theoretical framework is applied to oxygen consumption data of eight teleost embryos. This reveals relative insensitivity to external flow conditions in some species (e.g., winter flounder, herring), while others appear to rely on external stirring for a proper oxygen supply (e.g., largemouth bass). Interestingly, largemouth bass is the only species in our analysis that exhibits ‘fin-fanning’.     

Towards a unified framework for connectivity that disentangles movement and mortality in space and time

Predicting connectivity, or how landscapes alter movement, is essential for understanding the scope for species persistence with environmental change. Although it is well known that movement is risky, connectivity modelling often conflates behavioural responses to the matrix through which animals disperse with mortality risk. We derive new connectivity models using random walk theory, based on the concept of spatial absorbing Markov chains. These models decompose the role of matrix on movement behaviour and mortality risk, can incorporate species distribution to predict the amount of flow, and provide both short‐ and long‐term analytical solutions for multiple connectivity metrics. We validate the framework using data on movement of an insect herbivore in 15 experimental landscapes. Our results demonstrate that disentangling the roles of movement behaviour and mortality risk is fundamental to accurately interpreting landscape connectivity, and that spatial absorbing Markov chains provide a generalisable and powerful framework with which to do so.     

Interaction Mortality: Senescence May Have Evolved because It Increases Lifespan

Given an extrinsic challenge, an organism may die or not depending on how the threat interacts with the organism''s physiological state. To date, such interaction mortality has been only a minor factor in theoretical modeling of senescence. We describe a model of interaction mortality that does not involve specific functions, making only modest assumptions. Our model distinguishes explicitly between the physiological state of an organism and potential extrinsic, age-independent threats. The resulting mortality may change with age, depending on whether the organism''s state changes with age. We find that depending on the physiological constraints, any outcome, be it ‘no senescence’ or ‘high rate of senescence’, can be found in any environment; that the highest optimal rate of senescence emerges for an intermediate physiological constraint, i.e. intermediate strength of trade-off; and that the optimal rate of senescence as a function of the environment is driven by the way the environment changes the effect of the organism''s state on mortality. We conclude that knowledge about the environment, physiology and their interaction is necessary before reasonable predictions about the evolution of senescence can be made.     

Optimal birthweights in Peruvian populations at high and low altitudes

This study tests the hypothesis that optimum birthweight for survival is lower among hospital-born infants in Puno, Peru (altitude 3860 m) than that among their counterparts at low altitude in Tacna, Peru (altitude 600 m). The data are derived from hospital birth records for 1971 and 1972 and municipal death records for 1971 through 1973. Linking these records permits analysis of the patterns of mortality in relation to birthweight. Stabilizing selection upon birthweight is operating in both populations. The high altitude population has a lower mean birthweight and a lower optimal birthweight. The Puno population is closer to its optimal birthweight distribution and, as a result of mortality during infancy, is approaching its optimum birthweight distribution for survival more rapidly than the Tacna population. It appears that the high altitude Puno population may well be adapted to its environment in the sense that there is less selective mortality on birthweight phenotypes.     

The effects of spatial food distribution and group size on foraging behaviour in a benthic fish

Animals foraging in heterogeneous environments benefit from information on local resource density because it allows allocation of foraging effort to rich patches. In foraging groups, this information may be obtained by individuals through sampling or by observing the foraging behaviour of group members. We studied the foraging behaviour of goldfish (Carassius auratus) groups feeding in pools on resources distributed in patches. First, we determined if goldfish use sampling information to distinguish between patches of different qualities, and if this allowed goldfish to benefit from a heterogeneous resource distribution. Then, we tested if group size affected the time dedicated to food searching and ultimately foraging success. The decision of goldfish to leave a patch was affected by whether or not they found food, indicating that goldfish use an assessment rule. Giving-up density was higher when resources were highly heterogeneous, but overall gain was not affected by resource distribution. We did not observe any foraging benefits of larger groups, which indicate that grouping behaviour was driven by risk dilution. In larger groups the proportion searching for food was lower, which suggests interactions among group members. We conclude that competition between group members affects individual investments in food searching by introducing the possibility for alternative strategies, such as scrounging or resource monopolisation.     

Landscapes of Coexistence for terrestrial carnivores: the ecological consequences of being downgraded from ultimate to penultimate predator by humans

Fear of predation can have major impacts on the behaviour of prey species. Recently the concept of the ecology of fear has been defined and formalised; yet there has been relatively little focus on how these ideas apply to large carnivore species which, although not prey sensu stricto, also experience fear as a result of threats from humans. Large carnivores are likely also subject to a Landscape of Fear similar to that described for prey species. We argue that although fear is generic, ‘human‐caused mortality’ represents a distinct and very important cause of fear for large carnivores, particularly terrestrial large carnivores as their activities overlap with those of humans to a greater degree. We introduce the idea of a ‘Landscape of Coexistence’ for large carnivores to denote a subset of the Landscape of Fear where sufficient areas of low human‐caused mortality risk are present in the landscape for long term coexistence of large carnivores and humans. We then explore aspects of terrestrial large carnivore behavioural ecology that may be best explained by risk of human‐caused mortality, and how the nature of a Landscape of Coexistence for these large carnivores is likely to be shaped by specific factors such as habitat structure, wild and domestic prey base, and human distribution and behaviour. The human characteristics of this Landscape of Coexistence may be as important in determining large carnivore distribution and behavioural ecology as the distribution of resources. Understanding the Landscape of Coexistence for terrestrial large carnivores is therefore important for their biology and conservation throughout large parts of their remaining ranges. Synthesis The Landscape of Fear concept describing the relationship between predator and prey also applies to the relationship between humans and top carnivores. We synthesise current research to introduce the Landscape of Coexistence concept, arguing that top predators respond to the risks of human‐caused mortality through spatiotemporal partitioning of activities to reduce contact with people. The character of the Landscape of Coexistence may be more important than the distribution of resources in determining large carnivore distribution and behavioural ecology in human dominated landscapes. Understanding their behavioural responses to human threats is crucial to successful conservation of large carnivores.     

Heuristic optimization of the general life history problem: A novel approach

Summary The general life history problem concerns the optimal allocation of resources to growth, survival and reproduction. We analysed this problem for a perennial model organism that decides once each year to switch from growth to reproduction. As a fitness measure we used the Malthusian parameterr, which we calculated from the Euler-Lotka equation. Trade-offs were incorporated by assuming that fecundity is size dependent, so that increased fecundity could only be gained by devoting more time to growth and less time to reproduction. To calculate numerically the optimalr for different growth dynamics and mortality regimes, we used a simplified version of the simulated annealing method. The major differences among optimal life histories resulted from different accumulation patterns of intrinsic mortalities resulting from reproductive costs. If these mortalities were accumulated throughout life, i.e. if they were senescent, a bangbang strategy was optimal, in which there was a single switch from growth to reproduction: after the age at maturity all resources were allocated to reproduction. If reproductive costs did not carry over from year to year, i.e. if they were not senescent, the optimal resource allocation resulted in a graded switch strategy and growth became indeterminate. Our numerical approach brings two major advantages for solving optimization problems in life history theory. First, its implementation is very simple, even for complex models that are analytically intractable. Such intractability emerged in our model when we introduced reproductive costs representing an intrinsic mortality. Second, it is not a backward algorithm. This means that lifespan does not have to be fixed at the begining of the computation. Instead, lifespan itself is a trait that can evolve. We suggest that heuristic algorithms are good tools for solving complex optimality problems in life history theory, in particular questions concerning the evolution of lifespan and senescence.     

Stress, resource allocation, and mortality

We model the optimal allocation of limited resources of an animalduring a transient stressful event such as a cold spell or thepresence of a predator. The animal allocates resources betweenthe competing demands of combating the stressor and bodily maintenance.Increased allocation to combating the stressor decreases themortality rate from the stressor, but if too few resources areallocated to maintenance, damage builds up. A second sourceof mortality is associated with high levels of damage. Thus,the animal faces a trade-off between the immediate risk of mortalityfrom the stressor and the risk of delayed mortality due to thebuild up of damage. We analyze how the optimal allocation ofthe animal depends on the mean and predictability of the lengthof the stressful period, the level of danger of the stressorfor a given level of allocation, and the mortality consequencesof damage. We also analyze the resultant levels of mortalityfrom the stressor, from damage during the stressful event, andfrom damage during recovery after the stressful event ceases.Our results highlight circumstances in which most mortalityoccurs after the removal of the stressor. The results also highlightthe importance of the predictability of the duration of thestressor and the potential importance of small detrimental dropsin condition. Surprisingly, making the consequences of damageaccumulation less dangerous can lead to a reallocation thatallows damage to build up by so much that the level of mortalitycaused by damage build up is increased. Similarly, because ofthe dependence of allocation on the dangerousness of the stressor,making the stressor more dangerous for a given level of allocationcan decrease the proportion of mortality that it causes, whilethe proportion of mortality caused by damage to condition increases.These results are discussed in relation to biological phenomena.