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45.3A: Life History Patterns and Energy Budgets - Biology

45.3A: Life History Patterns and Energy Budgets - Biology


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Energy budgets and life history strategies determine the type of reproductive capacity displayed by a population.

Learning Objectives

  • Describe the energy budgets of, and the life history strategies used in, reproduction

Key Points

  • The amount of parental care given to an individual offspring is inversely related to the reproductive capacity of an animal species.
  • Animal species that produce many small, vulnerable offspring tend to provide little or no care for them due to their energy budget constraints; just enough offspring survive to maintain the species.
  • Animal species that have few offspring expend large amounts of their energy budgets on caring for helpless offspring that need to develop before being on their own.
  • Plants with low fecundity produce few energy-rich seeds with high germination rates, while plants with high fecundity usually have many small, energy-poor seeds with poor survival rates.
  • Species that reproduce early ensure a greater chance of having surviving offspring than do those that must survive to a later reproductive age.
  • Semelparous species use all of their reproductive budgets on one single reproductive event, while iteroparous species spend it on multiple mating seasons.

Key Terms

  • iteroparous: reproducing more than once in a lifetime
  • semelparous: reproducing only once in a lifetime
  • fecundity: number, rate, or capacity of offspring production

Life history patterns and energy budgets

Energy is required by all living organisms for their growth, maintenance, and reproduction. At the same time, energy is often a major limiting factor in determining an organism’s survival. Plants, for example, acquire energy from the sun via photosynthesis, but must expend this energy to grow, maintain health, and produce energy-rich seeds to produce the next generation. Animals also have the additional burden of using some of their energy reserves to acquire food. In addition, some animals must expend energy caring for their offspring. Thus, all species have an energy budget in which they must balance energy intake with their use of energy for metabolism, reproduction, parental care, and energy storage, as when bears build up body fat for winter hibernation.

Parental care and fecundity

Fecundity is the potential reproductive capacity of an individual within a population. In other words, it describes how many offspring could ideally be produced if an individual has as many offspring as possible, repeating the reproductive cycle as soon as possible after the birth of the offspring. In animals, fecundity is inversely related to the amount of parental care given to an individual offspring. Species that produce a large number of offspring, such as many marine invertebrates, usually provide little if any care for those offspring, as they would not have the energy or the ability to do so. Most of their energy budget is used to produce many tiny offspring. Animals with this strategy are often self-sufficient at a very early age. This is because of the energy trade-off these organisms have made to maximize their evolutionary fitness. Since their energy is used for producing offspring instead of parental care, it makes sense that these offspring have some ability to be able to move within their environment to find food and perhaps shelter. Even with these abilities, their small size makes them extremely vulnerable to predation, so the production of many offspring allows enough of them to survive to maintain the species.

Animal species that have few offspring during a reproductive event usually give extensive parental care, devoting much of their energy budget to these activities, sometimes at the expense of their own health. This is the case with many mammals, such as humans, kangaroos, and pandas. The offspring of these species are relatively helpless at birth, needing to develop before they achieve self-sufficiency.

Plants with low fecundity produce few energy-rich seeds (such as coconuts and chestnuts) that have a good chance to germinate into a new organism. Plants with high fecundity usually have many small, energy-poor seeds (as do orchids) that have a relatively-poor chance of surviving. Although it may seem that coconuts and chestnuts have a better chance of surviving, the energy trade-off of the orchid is also very effective. It is a matter of where the energy is used: for large numbers of seeds or for fewer seeds with more energy.

Early versus late reproduction

The timing of reproduction in a life history also affects species survival. Organisms that reproduce at an early age have a greater chance of producing offspring, but this is usually at the expense of their growth and the maintenance of their health. Conversely, organisms that start reproducing later in life often have greater fecundity or are better able to provide parental care, but they risk not surviving to reproductive age. Examples of this can be seen in fish. Small fish, such as guppies, use their energy to reproduce rapidly, but never attain the size that would give them defense against some predators. Larger fish, such as bluefin tuna and mako sharks, use their energy to attain a large size, but do so with the risk that they will die before they can reproduce or reproduce to their maximum. These different energy strategies and trade-offs are key to understanding the evolution of each species as it maximizes its fitness and fills its niche.

Single versus multiple reproductive events

Some life history traits, such as fecundity, timing of reproduction, and parental care, can be grouped together into general strategies that are used by multiple species. Semelparous species are those that only reproduce once during their lifetime and then die. Such species use most of their resource budget during a single reproductive event, sacrificing their health to the point that they do not survive. Examples of semelparity are bamboo, which flowers once and then dies, and the Chinook salmon, which uses most of its energy reserves to migrate from the ocean to its freshwater nesting area, where it reproduces and then dies. In contrast, iteroparous species reproduce repeatedly during their lives. Some animals are able to mate only once per year, but survive multiple mating seasons. Primates, including humans and chimpanzees, are examples of animals that display iteroparity.


45.4 Population Dynamics and Regulation

By the end of this section, you will be able to do the following:

  • Give examples of how the carrying capacity of a habitat may change
  • Compare and contrast density-dependent growth regulation and density-independent growth regulation, giving examples
  • Give examples of exponential and logistic growth in wild animal populations
  • Describe how natural selection and environmental adaptation leads to the evolution of particular life-history patterns

The logistic model of population growth, while valid in many natural populations and a useful model, is a simplification of real-world population dynamics. Implicit in the model is that the carrying capacity of the environment does not change, which is not the case. The carrying capacity varies annually: for example, some summers are hot and dry whereas others are cold and wet. In many areas, the carrying capacity during the winter is much lower than it is during the summer. Also, natural events such as earthquakes, volcanoes, and fires can alter an environment and hence its carrying capacity. Additionally, populations do not usually exist in isolation. They engage in interspecific competition : that is, they share the environment with other species competing for the same resources. These factors are also important to understanding how a specific population will grow.

Nature regulates population growth in a variety of ways. These are grouped into density-dependent factors, in which the density of the population at a given time affects growth rate and mortality, and density-independent factors, which influence mortality in a population regardless of population density. Note that in the former, the effect of the factor on the population depends on the density of the population at onset. Conservation biologists want to understand both types because this helps them manage populations and prevent extinction or overpopulation.

Density-Dependent Regulation

Most density-dependent factors are biological in nature (biotic), and include predation, inter- and intraspecific competition, accumulation of waste, and diseases such as those caused by parasites. Usually, the denser a population is, the greater its mortality rate. For example, during intra- and interspecific competition, the reproductive rates of the individuals will usually be lower, reducing their population’s rate of growth. In addition, low prey density increases the mortality of its predator because it has more difficulty locating its food source.

An example of density-dependent regulation is shown in Figure 45.11 with results from a study focusing on the giant intestinal roundworm (Ascaris lumbricoides), a parasite of humans and other mammals. 3 Denser populations of the parasite exhibited lower fecundity: they contained fewer eggs. One possible explanation for this is that females would be smaller in more dense populations (due to limited resources) and that smaller females would have fewer eggs. This hypothesis was tested and disproved in a 2009 study which showed that female weight had no influence. 4 The actual cause of the density-dependence of fecundity in this organism is still unclear and awaiting further investigation.

Density-Independent Regulation and Interaction with Density-Dependent Factors

Many factors, typically physical or chemical in nature (abiotic), influence the mortality of a population regardless of its density, including weather, natural disasters, and pollution. An individual deer may be killed in a forest fire regardless of how many deer happen to be in that area. Its chances of survival are the same whether the population density is high or low. The same holds true for cold winter weather.

In real-life situations, population regulation is very complicated and density-dependent and independent factors can interact. A dense population that is reduced in a density-independent manner by some environmental factor(s) will be able to recover differently than a sparse population. For example, a population of deer affected by a harsh winter will recover faster if there are more deer remaining to reproduce.

Evolution Connection

Why Did the Woolly Mammoth Go Extinct?

It's easy to get lost in the discussion about why dinosaurs went extinct 65 million years ago. Was it due to a meteor slamming into Earth near the coast of modern-day Mexico, or was it from some long-term weather cycle that is not yet understood? Scientists are continually exploring these and other theories.

Woolly mammoths began to go extinct much more recently, when they shared the Earth with humans who were no different anatomically than humans today (Figure 45.12). Mammoths survived in isolated island populations as recently as 1700 BC. We know a lot about these animals from carcasses found frozen in the ice of Siberia and other regions of the north. Scientists have sequenced at least 50 percent of its genome and believe mammoths are between 98 and 99 percent identical to modern elephants.

It is commonly thought that climate change and human hunting led to their extinction. A 2008 study estimated that climate change reduced the mammoth’s range from 3,000,000 square miles 42,000 years ago to 310,000 square miles 6,000 years ago. 6 It is also well documented that humans hunted these animals. A 2012 study showed that no single factor was exclusively responsible for the extinction of these magnificent creatures. 7 In addition to human hunting, climate change, and reduction of habitat, these scientists demonstrated another important factor in the mammoth’s extinction was the migration of humans across the Bering Strait to North America during the last ice age 20,000 years ago.

The maintenance of stable populations was and is very complex, with many interacting factors determining the outcome. It is important to remember that humans are also part of nature. We once contributed to a species’ decline using only primitive hunting technology.

Life Histories of K-selected and r-selected Species

While reproductive strategies play a key role in life histories, they do not account for important factors like limited resources and competition. The regulation of population growth by these factors can be used to introduce a classical concept in population biology, that of K-selected versus r-selected species.

The concept relates to a species’ reproductive strategies, habitat, and behavior, especially in the way that they obtain resources and care for their young. It includes length of life and survivorship factors as well. Population biologists have grouped species into the two large categories—K-selected and r-selected—although the categories are really two ends of a continuum.

K-selected species are species selected by stable, predictable environments. Populations of K-selected species tend to exist close to their carrying capacity (hence the term K-selected) where intraspecific competition is high. These species have few, large offspring, a long gestation period, and often give long-term care to their offspring (Table 45.2). While larger in size when born, the offspring are relatively helpless and immature at birth. By the time they reach adulthood, they must develop skills to compete for natural resources. In plants, scientists think of parental care more broadly: how long fruit takes to develop or how long it remains on the plant are determining factors in the time to the next reproductive event. Examples of K-selected species are primates (including humans), elephants, and plants such as oak trees (Figure 45.13a).

Oak trees grow very slowly and take, on average, 20 years to produce their first seeds, known as acorns. As many as 50,000 acorns can be produced by an individual tree, but the germination rate is low as many of these rot or are eaten by animals such as squirrels. In some years, oaks may produce an exceptionally large number of acorns, and these years may be on a two- or three-year cycle depending on the species of oak (r-selection).

As oak trees grow to a large size and for many years before they begin to produce acorns, they devote a large percentage of their energy budget to growth and maintenance. The tree’s height and size allow it to dominate other plants in the competition for sunlight, the oak’s primary energy resource. Furthermore, when it does reproduce, the oak produces large, energy-rich seeds that use their energy reserve to become quickly established (K-selection).

In contrast, r-selected species have a large number of small offspring (hence their r designation (Table 45.2)). This strategy is often employed in unpredictable or changing environments. Animals that are r-selected do not give long-term parental care and the offspring are relatively mature and self-sufficient at birth. Examples of r-selected species are marine invertebrates, such as jellyfish, and plants, such as the dandelion (Figure 45.13b). Dandelions have small seeds that are wind dispersed long distances. Many seeds are produced simultaneously to ensure that at least some of them reach a hospitable environment. Seeds that land in inhospitable environments have little chance for survival since their seeds are low in energy content. Note that survival is not necessarily a function of energy stored in the seed itself.

Characteristics of K-selected species Characteristics of r-selected species
Mature late Mature early
Greater longevity Lower longevity
Increased parental care Decreased parental care
Increased competition Decreased competition
Fewer offspring More offspring
Larger offspring Smaller offspring

Modern Theories of Life History

By the second half of the twentieth century, the concept of K- and r-selected species was used extensively and successfully to study populations. The r- and K-selection theory, although accepted for decades and used for much groundbreaking research, has now been reconsidered, and many population biologists have abandoned or modified it. Over the years, several studies attempted to confirm the theory, but these attempts have largely failed. Many species were identified that did not follow the theory’s predictions. Furthermore, the theory ignored the age-specific mortality of the populations which scientists now know is very important. New demographic-based models of life history evolution have been developed which incorporate many ecological concepts included in r- and K-selection theory as well as population age structure and mortality factors.

Footnotes

    N.A. Croll et al., “The Population Biology and Control of Ascaris lumbricoides in a Rural Community in Iran.” Transactions of the Royal Society of Tropical Medicine and Hygiene 76, no. 2 (1982): 187-197, doi:10.1016/0035-9203(82)90272-3. Martin Walker et al., “Density-Dependent Effects on the Weight of Female Ascaris lumbricoides Infections of Humans and its Impact on Patterns of Egg Production.” Parasites & Vectors 2, no. 11 (February 2009), doi:10.1186/1756-3305-2-11. N.A. Croll et al., “The Population Biology and Control of Ascaris lumbricoides in a Rural Community in Iran.” Transactions of the Royal Society of Tropical Medicine and Hygiene 76, no. 2 (1982): 187-197, doi:10.1016/0035-9203(82)90272-3. David Nogués-Bravo et al., “Climate Change, Humans, and the Extinction of the Woolly Mammoth.” PLoS Biol 6 (April 2008): e79, doi:10.1371/journal.pbio.0060079. G.M. MacDonald et al., “Pattern of Extinction of the Woolly Mammoth in Beringia.” Nature Communications 3, no. 893 (June 2012), doi:10.1038/ncomms1881.

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    Early reproductive maturity among Pumé foragers: Implications of a pooled energy model to fast life histories

    Life history theory places central importance on relationships between ontogeny, reproduction, and mortality. Fast human life histories have been theoretically and empirically associated with high mortality regimes. This relationship, however, poses an unanswered question about energy allocation. In epidemiologically stressful environments, a greater proportion of energy is allocated to immune function. If growth and maintenance are competing energetic expenditures, less energy should be available for growth, and the mechanism to sustain rapid maturation remains unclear. The human pattern of extended juvenile provisioning and resource sharing may provide an important source of variation in energy availability not predicted by tradeoff models that assume independence at weaning. We consider a group of South American foragers to evaluate the effects that pooled energy budgets may have on early reproduction. Despite growing up in an environment with distinct seasonal under-nutrition, harsh epidemiological conditions, and no health care, Pumé girls mature quickly and initiate childbearing in their midteens. Pooled energy budgets compensate for the low productivity of girls not only through direct food transfers but importantly by reducing energy they would otherwise expend in foraging activities to meet metabolic requirements. We suggest that pooled energy budgets affect energy availability at both extrinsic and intrinsic levels. Because energy budgets are pooled, Pumé girls and young women are buffered from environmental downturns and can maximize energy allocated to growth completion and initiate reproduction earlier than a traditional bound-energy model would predict. Am. J. Hum. Biol., 2009. © 2009 Wiley-Liss, Inc.


    Pooled energy budget and human life history

    Human life history contains a series of paradoxes not easily explained by classical life history theory. Although overall reproductive output is higher than in related primates, juvenile growth is slower and age-specific reproductive rates decline faster with age. A simple energetic model would predict that growth and reproductive rates should be positively correlated and that reproductive effort should not decelerate with age. The pattern of negative correlations in humans suggest the presence of trade-offs among peak reproductive rate, childhood growth, and reproductive rate at older ages. To address this puzzle, we propose a synthesis of reproductive ecology and behavioral ecology focused on intra- and inter-somatic energy transfers. This integration includes three concepts: the mother as final common pathway through which energy must pass to result in offspring a distinction between direct and indirect reproductive effort, proposing the latter as a novel net energy allocation category relative to growth and direct reproductive effort and a pooled energy budget representing the energetic contributions and withdrawals of all members of a breeding community. Individuals at all reproductive life stages are considered in light of their contributions to the pooled energy budget. Am. J. Hum. Biol., 2009. © 2009 Wiley-Liss, Inc.


    Discussion

    This study provides perhaps the first direct empirical evidence that varying levels of extrinsic mortality across species drive adaptive interspecific differences in allocation to growth and reproduction. To my knowledge, all previous, substantial examinations of cross-species relationships between mortality and growth and reproduction [e.g., [38-41]] were unable to discern whether mortality was extrinsic or intrinsic. Therefore, it is impossible to determine directionality in previous studies. Mortality may have influenced optimal allocation, or it could have been the outcome of optimal allocation (for instance, if increased reproductive effort lowered survivorship). The current study examined allocation for several species, with estimates of a clear, extrinsic source of mortality. The trematode parasitic castrator species (operating stolen host bodies) whose individuals were more likely to die from dominant species allocated less to growth and more to reproduction than did species with greater life expectancies. Interestingly, both genders of uninfected snails fit into the patterns observed among the parasitic castrator species, allocating as much to growth and to reproduction as expected given their probability of reproductive death (castration by trematode parasites). Because the data further indicate that the species did not plastically respond to local levels of risk, the consistent species differences in allocation patterns appear to result from adaptation to different selective regimes—specifically, different overall levels of extrinsic mortality.

    The findings also buttress the perspective outlined in the introduction regarding how to consider adaptation of parasitically castrated and uninfected hosts. Except for seemingly rare systems where parasitic castrator infections die with appreciable frequency and the host recuperates [e.g., [42,43]], a castrated host's reproductive value is zero. Therefore, with respect to fitness of castrated host bodies, selection will not act on host populations, but on the parasitic castrator populations (barring limited circumstances when kin selection might operate). Hence, parasitic castrators are truly 'body snatchers'. To understand uninfected host resource allocation, we apply basic life history principles to uninfected hosts. To understand resource allocation of parasitically castrated hosts, we apply the same principles to the castrators, not to their reproductively dead hosts. Supporting this point of view, in this study, castrated hosts allocated resources in the direction predicted by applying theory to the parasitic castrators, not the hosts. This perspective may help clarify future empirical and theoretical work addressing parasitic castration.

    A general methodological implication of this study comes from the surprising finding that the species' gonadosomatic indices did not correlate with their relative reproductive allocation indices. The relative reproductive allocation index directly factored in variation in allocation to growth. It should therefore more accurately indicate reproductive effort than should the completely static gonadosomatic index. Indeed, the relationship between extrinsic mortality and reproductive effort was only apparent when using the relative reproductive allocation index. The apparent inadequacy of the gonadosomatic index to compare reproductive efforts of these species may partly explain the inconsistent relationship between that index and dominance rank documented in Hechinger et al. [10]. More broadly, the incongruence between the two indices suggests researchers must take extra caution when using the gonadosomatic index in comparative estimates of reproductive effort for organisms with indeterminate growth, or any species where allocation to somatic tissues may strongly vary.

    An interesting issue arises regarding possible differences in overall productivity between uninfected and infected snails. Despite having a high relative reproductive allocation (driven by low growth rates), it is striking that uninfected snails had among the lowest gonadosomatic indices and the lowest growth rates. Thus, compared to the average trematode species operating stolen host bodies, uninfected snails may allocate absolutely less to both direct reproductive output and to growth. If so, this may reflect advantages of trematode clonal reproduction compared to the sexual dioecy of uninfected snails. Future work should detail the entire energy budgets (including behavioral expenditures) for parasitic castrator species and their uninfected hosts to more fully understand absolute and relative species differences in resource allocation. Such work should also factor in offspring survivorship, for which there is coarse evidence that it influences optimal allocation schemes of trematode parasitic castrators [10,44].

    The growth findings here also directly bear on an issue that has long interested students of parasitic castrator systems. For decades, researchers have noted that parasitic castrators—particularly trematodes in snails�n cause gigantism, increasing growth of infected hosts relative to uninfected hosts [reviewed in [16-18,37]]. However, gigantism was not detected in the first three studies that directly quantified growth for long-lived marine snails infected and uninfected by trematode parasitic castrators [26,37,45]. This lack of detecting gigantism led to the development of conceptual theory explaining why gigantism should not occur in long-lived host species (those living > 1.5 years [37] or 4 years [46]). This theory relied on postulated differences in the allocation schemes of host species with different longevities and on parasitic castrator constraints on energy use. However, the results presented here, along with those of Miura et al. [47] on a single trematode species, clearly indicate that trematode parasitic castrators can cause gigantism in long-lived marine snails. Some workers have postulated that gigantism might be adaptive for the parasitic castrators, by increasing fecundity or survivorship [e.g., [15,16,18,23,47,48]]. However, it appears there has never been an explanation for why uninfected hosts would not also benefit from growing larger. The perspective and findings of this paper provide a simple potential answer: uninfected hosts would not benefit from growing larger because they will not live as long. Higher extrinsic mortality for uninfected hosts compared to parasitic castrators can select for a lower allocation to growth for uninfected hosts compared to the amount allocated by parasitic castrators. Minchella [49] did predict that gigantism would tend to occur for longer-lived host species, but for a different reason. He hypothesized gigantism was adaptive for the host, by increasing the probability of outliving the castrator infection. This seems unlikely to provide a general explanation, given that long-lived hosts do not generally outlive infection [16,29,30,50,51]. If gigantism is comparatively frequent in longer-lived host species, it may be because the longevity of such hosts makes more possible the differential life expectancies necessary to select for detectably different allocation schemes between parasitic castrators and uninfected hosts.

    The finding that trematodes generally increased growth appears to contradict previous work on the same system. Sousa [37] reported that some trematode species (including several studied here) did not affect growth, and that some slightly stunted growth. It is possible that growth was different 25 years ago in the northern part of the California horn snail's range, where and when Sousa's work was carried out. However, it is also possible that trematodes did increase growth in Sousa's study, but that this went undetected due to methodological artifacts arising from the overdispersed growth characterizing these species. First, for overdispersed data, lower sample sizes underestimate the mean [52,53]. Therefore, in Sousa [37], the relatively low sample sizes for individual trematode species compared to uninfected snails may have yielded underestimates of growth for trematode species. Additionally, the application of standard ANCOVA to overdispersed data could have also contributed to misleading conclusions. Ongoing studies of California horn snail growth in northern populations will help to clarify these conflicting results. In another study, Lafferty [26] quantified growth for snails infected by a single trematode species (euha) and for uninfected snails. He reported that 'euha' grew slower than uninfected snails. In the current study, 'euha' grew more slowly than did uninfected females, but at a rate similar to uninfected males. Because Lafferty pooled males and females in his uninfected class, uninfected snails would have grown faster on average than did 'euha'-infected snails. Therefore, Lafferty's findings are not contradictory but are expected given the data presented here.

    Instead of using dominance rank as a proxy, this study directly estimated field rates of differential extrinsic mortality based on the probability of being killed by dominant species. This turned out to be important because there was a lack of complete correspondence between dominance rank and extrinsic mortality. Two subordinate trematode species experienced the lowest levels of extrinsic mortality. One of these species (renc) suffered relatively low differential mortality because it appears to tolerate co-infection with some low- and mid-ranking species, consequently occurring relatively frequently in mixed-species infections. Species such as 'renc' appear to gain at least a partial refuge from co-infecting trematodes by using a different tissue site within the infected hosts than that used by most of the trematode species (using the mantle, versus the visceral mass) [30,54,55]. The low differential mortality for the other subordinate species (smcy) occurred because the bulk of its population recruited to areas in the estuaries where dominants did not occur, driving the lack of being killed by dominants. This is interesting, because the typical situation for guilds of trematode parasitic castrators is for spatial and temporal covariance in species' distributions to increase overall levels of competitive loss [56]. Future ecological study will examine whether certain species typically gain spatial refugia, despite this not being the overriding case in these guilds. It may also be important to conduct the research over broader spatial scales to increase the likelihood of detecting such refugia.

    Multiple infections by the same trematode species can occur naturally in other larval trematode-snail systems [e.g., [57-60]]. Such multi-clone infections may have occurred undetected in this study. Theory predicts that increased frequency of multi-clone infections, and the resulting increase in intraspecific competition, can select for greater parasite reproductive effort [e.g., [61-63]]. For the species in this study, there is no data on the extent of intraspecific competition. However, one would predict that the relative importance of intraspecific competition would be greater for those species with a lower risk of mortality from dominant species. If increased intraspecific competition selects for increased reproduction at the expense of growth, it would diminish the effects observed in the current study. However, the relationships of growth and reproduction with mortality caused by interspecific antagonism were all strong (all |r|s between 0.81 and 0.88). Nevertheless, there was some unexplained variation, part of which might be explained by differences in the nature of the intraspecific interactions characterizing these parasitic castrators.


    DISCUSSION

    This study showed that striped hamsters lactating at 5°C had a significantly higher food intake but a lower change in body mass than hamsters lactating at 23 and 30°C. During late lactation, litters raised by females at 5°C had significantly lower mass compared with the other two groups. RMR was significantly higher in females exposed to 5°C than females exposed to 23 and 30°C. Neither cold nor hot exposure imposed a significant effect on serum PRL levels. Differences in any variables mentioned above were not significant between females lactating at 23 and 30°C.


    4 WHAT AGEING MECHANISMS CAN TELL US ABOUT THE ROLE OF TRADE-OFFS

    Most discussion of the role of trade-offs is divorced from what is known about the mechanisms of ageing. To some extent, this gap is bridged in the literature searching for specific genes and genetic patterns that might underlie antagonistic pleiotropy or mutation accumulation (Austad & Hoffman, 2018 Hughes et al., 2002 ) nonetheless, the individual genes are not the mechanisms, and there are insights to be gained from asking how known mechanisms could be modulated by trade-offs. A thorough review of ageing mechanisms is beyond the scope of this article accordingly, we choose several illustrative examples from the well-known framework of the Hallmarks of Aging (Lopez-Otin, Blasco, Partridge, Serrano, & Kroemer, 2013 ), as well as a few other mechanisms which were not included in that framework but which are broadly accepted (dysregulation after psychological stress McEwen, 1998 , structural damage Rueppell, 2009 and age-related clonal hematopoiesis Shlush, 2018 ).

    At a relatively macro level, the role of insulin-like growth factor (IGF)-1 and related pathways supports the role of trade-offs in determining ageing rate. Within vertebrates, increased IGF-1 levels are broadly associated with increases in both somatic growth and reproduction, but also with decreases in life span and accelerated ageing (Dantzer & Swanson, 2012 ). Crucially, IGF-1 may explain life-history variation at both the intra-individual and interspecific levels: it responds to environmental changes to mediate intra-individual trade-offs, but also appears to explain lineage-specific differences in growth and ageing, such as in dog breeds (Greer, Hughes, & Masternak, 2011 ). Furthermore, the IGF-1 receptor gene is a canonical example of a conserved genetic mechanism by which life span can be extended in organisms ranging from yeast to mammals (Tatar, Bartke, & Antebi, 2003 ). IGF-1 would thus appear to be the ideal mechanistic candidate to explain life-history trade-offs in vertebrates, although more work needs to be done to fully confirm this (Swanson & Dantzer, 2014 ). One attractive hypothesis is that IGF-1 and related pathways are a ‘public' mechanism by which multiple other ‘private', or species-specific, mechanisms are regulated (Partridge & Gems, 2002 ).

    Many of the downstream processes likely controlled by IGF-1 and related pathways also lend themselves relatively easily to a trade-off-based understanding of ageing. For example, DNA damage accumulation can likely be modulated, at least to some extent, by investing in mechanisms such as antioxidant protection and repair, which may be resource intensive. Loss of proteostasis as well would seem to be modulable by allocation of resources to clearance of proteins, an ATP-dependent process (Kaushik & Cuervo, 2015 ). On the other hand, other ageing mechanisms appear to be more strongly associated with various biological and physiological constraints that would not be subject to modulation via greater allocation of resources. In particular, many known ageing mechanisms are essentially cancer protection mechanisms, notably telomere attrition, cellular senescence and the inflammatory cascades that can result (Schosserer, Grillari, & Breitenbach, 2017 Shay & Wright, 2011 ). This is a canonical example of the above-mentioned mortality source trade-offs, where a trade-off between ageing and cancer creates a higher-order constraint. Direct allocation of resources (energetic or otherwise) would be unlikely to reduce cellular senescence, since a decrease in cellular senescence would imply an increase in cancer risk, and presumably selection has optimized the balance between the two.

    A second example of a constraint-based mechanism is the dysregulatory effects of chronic psychological stress in vertebrates. Organisms appear unable to fully return to a baseline physiological state after prolonged stress (McEwen, 1998 ), creating a long-term dysregulation which can accelerate other ageing mechanisms through positive feedback loops (Tomiyama et al., 2012 ). This mechanism is, as far as we know, completely independent of resource allocation strategies or other trade-offs, and reflects an inherent weakness in the structure of the underlying regulatory networks, a constraint.

    The distinction between trade-off-based and constraint-based mechanisms is not always clear. For example, while the level of DNA damage might be adjustable via resource allocation, some minimal level is probably unavoidable and might be considered a constraint. Likewise, rates of DNA damage might have impacts on the rates of cellular senescence (d'Adda di Fagagna, 2008 ), such that even if the mechanism itself represents a constraint, upstream changes in resource allocation could modulate rates of accumulation of senescent cells. Despite these nuances, however, it is clear that many ageing mechanisms are not subject to much modulation by resource allocation or trade-offs. Perhaps the clearest examples are the impacts of chronic stress and structural damage such as wing wear in insects. Another example is age-related clonal hematopoiesis, a process by which natural selection among different clonal stem cell lineages can produce decreases in diversity, with impacts on ageing (Shlush, 2018 ). This loss of diversity does not appear to be in any way resource related, as far as we know.

    Broadly, then, it is useful to consider to what extent ageing mechanisms can be modulated via trade-offs, versus to what extent they are inherent in the physiological nature of the species in question (constraints). The mortality source trade-offs noted above are an interesting case: they are trade-offs at a lower level of organization that produce constraints at a higher level.


    Discussion

    Kooijman’s DEB theory is emerging as a powerful tool for relating metabolic organization within organisms to those aspects of physiological performance that impact higher levels of biological organization, especially population dynamics and ecosystem processes. But the theory is highly abstract with neither the state variables nor the internal energy or material fluxes being directly measurable. The high level of abstraction acts as a deterrent to its wider use, but is the key to its generality. In this review we have provided formulae for common bioenergetic measurements in terms of the state variables and fluxes in a ‘standard’ DEB model. Although our examples involve fish, the equations presented here (Relating Kooijman’s DEB theory to other bioenergetic approaches) are general and can be used to interconnect bioenergetic measurements with DEB variables and fluxes for any animal.

    Nisbet et al. (Nisbet et al., 2010) recently reviewed the extent to which the individual–population connection could be achieved with simpler, empirically based models where the state of an animal was characterized by one variable (size). They concluded that remarkably simple mass-balance models, well supported by empirical data and resembling those described here as traditional bioenergetic models, are often adequate for connecting the performance of a well-studied organism to the history of its environment. But they also highlighted the serious downsides of such pragmatism: (1) the loss of connection to theory describing interspecific variation in physiological rates, and (2) the parameter richness of empirically based models for a complete life cycle.

    The motivation for the two applications in this paper of Kooijman’s more abstract approach to DEB theory came from recognition of these limitations. Each fish model was a variant of Kooijman’s ‘standard’ DEB model (Sousa et al., 2010), and relied for parameter estimation on the capacity of DEB theory to offer a unified description of the full life cycle. The salmon study also exploits the body-size scaling relationships. The decision to use the full DEB model in each application was therefore justified, even on pragmatic grounds. Yet there is a large body of empirical literature on the bioenergetics and biomechanics of both species that is constructed around the simpler paradigm. We faced (and still face) challenges figuring out how to relate these data to the DEB models, thereby giving added precision to the models in applications. In this paper, we made connections that relied on the formulae presented, and identified further issues that must be part of future research.

    A more ambitious ecological motivation for better understanding the interconnections between the different modeling approaches is that there are some systems where the simplifying assumptions of ‘standard’ DEB theory may be invalid. We have already noted the potential importance of changes in the theory that are required to cover anaerobic processes (Childress and Somero, 1990), and we have discussed situations where mechanical work represents a significant contribution to the energy budget. Both situations require extensions of the thermodynamic underpinnings of DEB theory (Sousa et al., 2006).

    Notwithstanding the remaining challenges, our take-home message for ecologists is that the rigorous conceptual framework offered by Kooijman’s theory has the potential to allow better experimental design, open the door for creative utilization of hard-earned data, and help predict individual growth and reproduction in hitherto unobserved environments. We have tried to demystify the theory by clarifying the connections to measurements commonly obtained in physiological ecology. Further case studies are needed to further sharpen our understanding of the connections over time, these should in turn lead to improved theory.


    Contents

    The theory presents simple mechanistic rules that describe the uptake and allocation of energy (and nutrients) and the consequences for physiological organization throughout an organism's life cycle, including the relationships of energetics with aging and effects of toxicants. [1] [2] [4] [6] [8] Assumptions of the DEB theory are delineated in an explicit way, the approach clearly distinguishes mechanisms associated with intra‐ and interspecific variation in metabolic rates, and equations for energy flows are mathematically derived following the principles of physics and simplicity. [1] [2] [18] [19]

    Cornerstones of the theory are:

    • conservation of mass, energy and time,
    • relationships between surface area and volume constraints on production
    • organizational uncoupling of metabolic modules (assimilation, dissipation, growth)
    • strong and weak homeostasis (composition of compartments is constant composition of the organism is constant when the food is constant)
    • substrate(s) from the environment is/are first converted to reserve(s) before being used for further metabolism

    The theory specifies that an organism is made up two main compartments: (energy) reserve and structure. Assimilation of energy is proportional to surface area of the structure, and maintenance is proportional to its volume. Reserve does not require maintenance. Energy mobilization will depend on the relative amount of the energy reserve, and on the interface between reserve and structure. Once mobilized, the energy is split into two branches:

    • a fixed proportion (termed kappa, κ) is allocated to growth (increase of structural mass) and maintenance of structure, while
    • the remaining proportion (1- κ) is allocated to processes of maturation (increase in complexity, installation of regulation systems, preparation for reproduction) and maintaining the level of attained maturity (including, e.g., maintenance of defense systems).

    The κ-rule therefore states that the processes of growth and maturation do not directly compete. Maintenance needs to be paid before allocating energy to other processes. [4] [8]

    In the context of energy acquisition and allocation, the theory recognizes three main developmental stages: embryo, which does not feed or reproduce, juvenile, which feeds but does not reproduce, and adult, which both feeds and is allocating energy to reproduction. Transitions between these life stages occur at events specified as birth and puberty, which are reached when energy invested into maturation (tracked as 'level of maturity') reaches a certain threshold. Maturity does not increase in the adult stage, and maturity maintenance is proportional to maturity. [1] [2] [4] [8]

    Biochemical composition of reserve and structure is considered to be that of generalised compounds, and is constant (the assumption of strong homeostasis) but not necessarily identical. Biochemical transformation from food to reserve (assimilation), and from reserve to structure (growth) include overhead costs. These overheads, together with processes of somatic and maturity maintenance and reproduction overheads (inefficiencies in transformation from reserve to reproductive material), all contribute to the consumption of oxygen and production of carbon dioxide, i.e. metabolism. [1] [4] [6] [8]

    All dynamic energy budget models follow the energy budget of an individual organism throughout its life cycle by contrast,"static" energy budget models describe a specific life stage or size of an organism. [14] [20] The main advantage of the DEB-theory based model over most other models is its description of energy assimilation and utilization (reserve dynamics) simultaneously with decoupled processes of growth, development/ maturation, and maintenance. [11] [21] [22] DEB theory specifies reserves as separate from structure: these are the two state variables that contribute to physical volume, and (in combination with reproduction buffer of adults) fully define the size of an individual. Maturity (also a state variable of the model) tracks how much energy has been invested into maturation, and therefore determines the life stage of the organism relative to maturity levels at which life stage transitions (birth and puberty) occur. Dynamics of the state variables are given by ordinary differential equations which include the major processes of energy uptake and use: assimilation, mobilization, maintenance, growth, maturation, and reproduction. [1] [2] [4] [5] [7] [8]

    • Food is transformed into reserve, which fuels all other metabolic processes. The feeding rate is proportional to the surface area food handling time and the transformation efficiency from food to reserve are independent of food density.
    • A fixed fraction (kappa) of mobilized reserve is allocated to somatic maintenance plus growth (soma), the rest on maturity maintenance plus maturation or reproduction. Maintenance has priority over other processes. Somatic maintenance is proportional to structural body volume, and maturity maintenance to maturity. Heating costs for endotherms and osmotic work (for fresh water organisms) are somatic maintenance costs that are proportional to surface area.
    • Stage transitions occur if the cumulated investment into maturation exceeds threshold values. Life stages typically are: embryo, juvenile, and adult. Reserve that is allocated to reproduction is first accumulated in a buffer. The rules for converting the buffer to gametes are species-specific (e.g. spawning can be once per season).

    Parameters of the model are individual specific, but similarities between individuals of the same species yield species-specific parameter estimations. [8] [14] [23] DEB parameters are estimated from several types of data simultaneously. [14] [23] [24] [25] Routines for data entry and parameter estimation are available as free software package DEBtool implemented in the MATLAB environment, with the process of model construction explained in a Wiki-style manual. Estimated parameters are collected in the online library called the Add-my-pet project.

    The standard DEB model Edit

    The standard model quantifies the metabolism of an isomorph (organism that does not change in shape during ontogeny) that feeds on one type of food with a constant composition (therefore the weak homeostasis applies, i.e. the chemical composition of the body is constant). The state variables of the individual are 1 reserve, 1 structure, maturity, and (in the adult stage) the reproduction buffer. Parameter values are constant throughout life. The reserve density at birth equals that of the mother at egg formation. Foetuses develop similarly, but receive unrestricted amount of reserve from the mother during development.

    Extensions of the standard model Edit

    DEB theory has been extended into many directions, such as

    • effects of changes in shape during growth (e.g. V1-morphs and V0-morphs)
    • non-standard embryo->juvenile->adult transitions, for example in holometabolic insects [26]
    • inclusion of more types of food (substrate), which requires synthesizing units to model
    • inclusion of more reserves (which is necessary for organisms that do not feed on other organisms) and more structures (which is necessary to deal with plants), or a simplified version of the model (DEBkiss) applicable in ecotoxicology [27][28]
    • the formation and excretion of metabolic products (which is a basis for syntrophic relationships, and useful in biotechnology)
    • the production of free radicals (linked to size and nutritional status) and their effect on survival (aging)
    • the growth of body parts (including tumours)
    • effects of chemical compounds (toxicants) on parameter values and the hazard rate (which is useful to establish no effect concentrations for environmental risk assessment): the DEBtox method
    • processes of adaptation (gene expression) to the availability of substrates (important in biodegradation)

    A list and description of most common typified models can be found here.

    The main criticism is directed to the formal presentation of the theory (heavy mathematical jargon), number of listed parameters, the symbol heavy notation, and the fact that modeled (state) variables and parameters are abstract quantities which cannot be directly measured, all making it less likely to reach its intended audience (ecologists) and be an "efficient" theory. [2] [18] [19] [29]

    However, more recent publications aim to present the DEB theory in an "easier to digest" content to "bridge the ecology-mathematics gap". [2] [18] [19] The general methodology of estimation of DEB parameters from data is described in van der Meer 2006 Kooijman et al 2008 shows which particular compound parameters can be estimated from a few simple observations at a single food density and how an increasing number of parameters can be estimated if more quantities are observed at several food densities. A natural sequence exists in which parameters can be known in principle. In addition, routines for data entry and scripts for parameter estimation are available as a free and documented software package DEBtool, aiming to provide a ready-to-use tool for users with less mathematical and programing background. Number of parameters, also pointed as relatively sparse for a bioenergetic model, [10] [20] vary depending on the main application and, because the whole life cycle of an organism is defined, the overall number of parameters per data-set ratio is relatively low. [14] [15] [30] Linking the DEB (abstract) and measured properties is done by simple mathematical operations which include auxiliary parameters (also defined by the DEB theory and included in the DEBtool routines), and include also switching between energy-time and mass-time contexts. [2] [1] [31] [9] Add my pet (AmP) project explores parameter pattern values across taxa. The DEB notation is a result of combining the symbols from the main fields of science (biology, chemistry, physics, mathematics) used in the theory, while trying to keep the symbols consistent. [8] As the symbols themselves contain a fair bit of information [1] [2] [8] (see DEB notation document), they are kept in most of the DEB literature.

    Dynamic energy budget theory presents a quantitative framework of metabolic organization common to all life forms, which could help to understand evolution of metabolic organization since the origin of life. [5] [8] [10] As such, it has a common aim with the other widely used metabolic theory: the West-Brown-Enquist (WBE) metabolic theory of ecology, which prompted side-by-side analysis of the two approaches. [3] [14] [15] [32] Though the two theories can be regarded as complementary to an extent, [11] [33] they were built on different assumptions and have different scope of applicability. [3] [11] [14] [15] In addition to a more general applicability, the DEB theory does not suffer from consistency issues pointed out for the WBE theory. [3] [11] [15]

    Applications Edit

      project is a collection of DEB models for over 1000 species, and explores patterns in parameter values across taxa. Routines for parameter exploration are available in AmPtool.
  • Models based on DEB theory can be linked to more traditional bioenergetic models without deviating from the underlying assumptions. [11][31] This allows comparison and testing of model performance .
  • A DEB-module (physiological model based on DEB theory) was successfully applied to reconstruct and predict physiological responses of individuals under environmental constraints [34][35][36]
  • A DEB-module is also featured in the eco-toxicological mechanistic models (DEBtox implementation) for modeling the sublethal effects of toxicants (e.g., change in reproduction or growth rate) [27][28][37][38][39]
  • Generality of the approach and applicability of the same mathematical framework to organisms of different species and life stages enables inter- and intra-species comparisons on the basis of parameter values, [3][21] and theoretical/empirical exploration of patterns in parameter values in the evolutionary context, [40] focusing for example on development, [41][42][22][43] energy utilization in a specific environment, [44][45][46] reproduction, [47] comparative energetics, [48][49] and toxicological sensitivity linked to metabolic rates. [50]
  • Studying patterns in body size scaling relationships: The assumptions of the model quantify all energy and mass fluxes in an organism (including heat, dioxygen, carbon dioxide, ammonia) while avoiding using the allometric relationships. [8][21][40] In addition, same parameters describe same processes across species: for example, heating costs of endotherms (proportional to surface area) are regarded separate to volume-linked metabolic costs of both ectotherms and endotherms, and cost of growth, even though they all contribute to metabolism of the organism. [8] Rules for the co-variation of parameter values across species are implied by model assumptions, and the parameter values can be directly compared without dimensional inconsistencies which might be linked to allometric parameters. [14][21] Any eco-physiological quantity that can be written as function of DEB parameters which co-vary with size can, for this reason, also be written as function of the maximum body size. [8]
  • DEB theory provides constraints on the metabolic organisation of sub-cellular processes. [4][10] Together with rules for interaction between individuals (competition, syntrophy, prey-predator relationships), it also provides a basis to understand population and ecosystem dynamics. [10][51]
  • Many more examples of applications have been published in scientific literature. [12]


    Bulmer, M. (1994). Theoretical Evolutionary Ecology, Sinauer.

    Calow, P. (1981). Resource utilization and reproduction, in Physiological Ecology An Evolutionary Approach to Resource Use, C. E. Townsend and P. Calow (Eds), Blackwell, pp. 245–270.

    Charnov, E. L. (1993). Life History Invariants Some Explorations of Symmetry in Evolutionary Ecology, Oxford University Press.

    Engen, S. and B. E. Sæther (1994). Optimal allocation of resources to growth and reproduction. Theor. Popul. Biol. 46, 232–248.

    Finch, C. (1990). Longevity, Senescence, and the Genome, University of Chicago Press.

    Fisken, Ø. (1997). Allocation patterns and diel vertical migration: modeling the optimal daphnia. Ecology 78, 1446–1456.

    Gabriel, W. (1982). Modelling reproductive strategies of daphnia. Arch. Hydrobiol. 95, 69–80.

    Gurney, W. C. and D. A. J. Middleton (1996). Optimal resource allocation in a randomly varying environment. Funct. Ecol. 10, 602–612.

    Heino, M. and V. Kaitala (1996). Optimal resource allocation between growth and reproduction in clams: why does indeterminate growth exists? Funct. Ecol. 10, 245–251.

    Heino, M. and V. Kaitala (1999). Evolution of resource allocation between growth and reproduction in animals with indeterminate growth. J. Evol. Biol. 12, 423–429.

    Iwasa, Y. and D. Cohen (1989). Optimal growth schedule of perennial plant. Am. Natural. 133, 480–505.

    Kleiber, M. (1932). Body size and metabolism. Hilgardia 6, 315–353.

    Kooijman, S. A. L. M. (2000). Dynamic Energy and Mass Budgets in Biological Systems, Cambridge University Press.

    Kooijman, S. A. L. M. (2001). Quantitative aspects of metabolic organization a discussion of concepts. Phil. Trans. R. Soc. B 356, 331–349.

    Kozłowski, J. (1992). Optimal allocation of resources to growth and reproduction: implications for age and size at maturity. Trends Ecol. Evol. 7, 15–19.

    Kozłowski, J. (1993). Measuring fitness in life-history studies. Trends Ecol. Evol. 8, 84–85.

    Kozłowski, J. (1996). Optimal initial size and adult size of animals: consequences for macroevolution and community structure. Am. Natural. 147, 101–114.

    Leeuwen, I. M. M. v., F. D. L. Kelpin and S. A. L. M. Kooijman (2002). A mathematical model that accounts for the effects of caloric restriction on body weight and longevity. Biogerontology (to appear).

    Lika, K. and R. M. Nisbet (2000). A dynamic energy budget model based on partitioning of net production. J. Math. Biol. 41, 361–386.

    Masoro, E. J. and S. N. Austad (1996). The evolution of the antiaging action of dietary restriction: a hypothesis. J. Gerontol. Biol. Sci. A 51, B387–B391.

    Maynard Smith, J. (1982). Evolution and the Theory of Games, Cambridge University Press.

    Meszéna, G. and E. Pásztor (1990). Population regulation and optimal life-history strategies, in Organizational Constraints on the Dynamics of Evolution, J. Maynard Smith and G. Vida (Eds), Manchester University Press, pp. 321–331.

    Metz, J. A. J., R. M. Nisbet and S. A. H. Geritz (1992). How should we define ‘fitness’ for general ecological scenarios? Trends Ecol. Evol. 7, 198–202.

    Mylius, S. D. and O. Diekmann (1995). On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos 74, 218–224.

    Nisbet, R. M., E. B. Muller, K. Lika and S. A. L. M. Kooijman (2000). From molecules to ecosystems through dynamic energy budget models. J. Anim. Ecol. 69, 913–926.

    Perrin, N. (1992). Optimal resource allocation and the marginal value of organs. Am. Natural. 139, 1344–1369.

    Perrin, N. and R. M. Silby (1993). Dynamic models of energy allocation and investment. Ann. Rev. Ecol. Systemat. 24, 379–410.

    Perrin, N., R. M. Silby and N. K. Nichols (1993). Optimal growth strategies when mortality and production rates are size-dependent. Evolutionary Ecol. 7, 576–592.

    Roff, D. A. (1992). The Evolution of Life Histories Theory and Analysis, Chapman and Hall.

    Ross, A. H. and R. M. Nisbet (1990). Dynamic models of growth and reproduction of the mussel Mytilus edulis L. Funct. Ecol. 4, 777–787.

    Sibly, R. M., P. Calow and N. Nichols (1985). Are patterns adaptive? J. Theor. Biol. 112, 553–574.

    Stearns, S. C. (1992). The Evolution of Life Histories, Oxford University Press.

    Taylor, B. and W. Gabriel (1992). To grow or not to grow: optimal resource allocation for Daphnia. Am. Natural. 139, 248–266.

    Taylor, B. and W. Gabriel (1993). Optimal growth of Daphnia in seasonal environment. Funct. Ecol. 7, 513–521.

    Taylor, H. M., R. S. Gourley, C. E. Lawrence and R. S. Kaplan (1974). Natural selection of life history attributes: an analytical approach. Theor. Popul. Biol. 5, 104–122.

    Whithers, P. C. (1992). Comparative Animal Physiology, Fort Worth: Saunders College Publishing.


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