How Many Babies Does a Sloth Have in a Litter

Am Nat. Author manuscript; available in PMC 2010 Jun 28.

Published in final edited form as:

PMCID: PMC2892970

NIHMSID: NIHMS205563

Mammal Reproductive Strategies Driven by Offspring Mortality-Size Relationships

Richard M. Sibly

¹ School of Biological Sciences, University of Reading, Reading RG6 6AS, United kingdom of great britain and northern ireland; and Centre for Integrated Population Ecology, Section of Environmental, Social and Spatial Change, Roskilde Academy, DK-4000 Roskilde, Denmark

James H. Brown

² Department of Biology, University of New Mexico, Albuquerque, New Mexico 87131; and Santa Fe Institute, Santa Fe, New Mexico 87501

Abstract

Merchandise-offs accept long been a major theme in life-history theory, simply they accept been hard to certificate. We introduce a new method that reveals patterns of divergent merchandise-offs subsequently adjusting for the pervasive variation in charge per unit of resource allocation to offspring as a office of body size and lifestyle. Results suggest that preweaning vulnerability to predation has been the major factor determining how female placental mammals allocate product between a few big and many pocket-sized offspring inside a litter and between a few large litters and many modest ones within a reproductive flavour. Artiodactyls, perissodactyls, cetaceans, and pinnipeds, which give nascence in the open on land or in the sea, produce a few large offspring, at infrequent intervals, considering this increases their chances of escaping predation. Insectivores, fissiped carnivores, lagomorphs, and rodents, whose offspring are protected in burrows or nests, produce large litters of pocket-size newborns. Primates, bats, sloths, and anteaters, which bear their young from birth until weaning, produce litters of one or a few offspring considering of the demand to ship and care for them.

Keywords: life-history theory, trade-off, litter size, offspring size, litter frequency, litter mass

Introduction

A constructed conceptual framework that tin account for the broad variation in mammal life histories has remained elusive, despite decades of vigorous theoretical investigation (due east.grand., Charnov 1991, 2001; Kozlowski and Weiner 1997; Oli 2004; Dobson 2007), meticulous collection and assay of information (due east.g., Gaillard et al. 1989; Promislow and Harvey 1990; Purvis and Harvey 1995; Jones and MacLarnon 2001; Charnov and Ernest 2006; Bielby et al. 2007), and a rich literature documenting how females classify resources to reproduction (Charnov et al. 2007). It has long been recognized that the mass-specific rate of biomass production scales allometrically with developed female body mass, Grand, as approximately M ^−1/4 to Thousand ^−1/3. This is similar to the scaling of mass-specific metabolic charge per unit, which fuels the growth and development of offspring through gestation and lactation (Brown et al. 2004). Recently, we have shown that productivity differs between taxonomic and lifestyle groups of mammals in anticipated means (Sibly and Brown 2007). A lifestyle is a way of making a living that is made possible by a unique combination of anatomical, physiological, and behavioral traits. Productivity increases when adaptations exploit abundant, reliable food supplies, and it decreases when adaptations reduce predation. The evolution of these combinations appears to be relatively conservative, and so lifestyles are typically deeply rooted in clades and widely shared inside taxonomic groups. Evidence of their adaptive significance comes from their independent and convergent evolution in distantly related lineages. These lifestyle adaptations stand for a second major centrality of life-history variation, orthogonal to the pervasive effect of torso mass (Dark-brown and Sibly 2006; Dobson 2007; Sibly and Dark-brown 2007). Here we consider how much, how oft, and why production is allocated to individual offspring and evidenced in the cardinal life-history trade-offs.

Traditionally, both theoretical and empirical analyses of life histories accept focused on hypothesized trade-offs: for example, between survival and reproduction, between "fast" and "slow" life histories, between juvenile and adult survival, and between the numbers and sizes of offspring. Many attempts to analyze these trade-offs have non explicitly considered the primal allometries of production and survival. For example, there is necessarily a negative correlation betwixt product and survival: smaller animals with higher birth rates must accept correspondingly higher death rates. Similarly, for animals of the same size, adaptations that increase production necessarily result in increased death rates (reduced survival) as a effect of "ecological compensation" (Sibly and Calow 1986, 1987; Sutherland et al. 1986).

Several recent analyses of life histories have explicitly considered allometric correlates of body size (eastward.g., Gaillard et al. 1989; Charnov 1993; Bielby et al. 2007; Dobson 2007; Sibly and Brown 2007). These have chosen attending to other hypothesized trade-offs such as that betwixt number and size of offspring or betwixt juvenile and adult survival, which are not directly consequences of the allometry of production but instead depend on how production is allocated amid dissimilar components of the life history. Such trade-offs should be evidenced every bit negative relationships in the residual variation that remains afterward accounting for the allometry of production inside and between taxonomic and lifestyle groups. They can be empirically evaluated almost powerfully and realistically by manipulating the relevant variables, such as in field experiments that dispense clutch size and nest predation in birds (east.g., Fontaine and Martin 2006) or allocation to egg yolk in reptiles (e.g., Sinervo and Huey 1990). Like experiments with eutherian mammals are more difficult considering females retain developing embryos within the body during gestation and nourish them during lactation. Withal, these unique features of mammalian life history offer opportunities to develop and exam a more general and comprehensive theoretical framework.

Hither nosotros consider ii potential merchandise-offs in how production is allocated to reproduction: (1) between the number of offspring in a litter and the size of the offspring and (2) between the number of litters and the biomass of each litter produced over a reproductive flavor. Our approach differs from that of most recent analyses in that it is explicitly mechanistic. We focus on variation among species, taxa, and lifestyle groups in the rate of mass-specific production and how this energy is allocated within and amid litters.

Theoretical Framework and Predictions

Conservation of mass and energy constrains how resources are divided amid multiple functions, and so allocating more to ane part ways that less is available for allocation elsewhere. This "principle of allocation" has long been a fundamental supposition of life-history theory (Cody 1966). We use the principle twice hither. First, productivity, measured as reproductive biomass produced per year, is assumed to be the product of litter mass and litter frequency, as in equation (3a). 2d, litter mass is the product of offspring size and number, as in equation (3b).

Resource are assumed to exist allocated and so as to maximize the Darwinian fettle of the life history, which we define every bit the per-copy rate of increase of a cistron for a specified set of life-history traits (Charlesworth 1980; Sibly and Curnow 1993). Darwinian fitness is given past an analog of the Euler-Lotka equation. The simplest life history that embraces the complexity nosotros demand has two stages—juvenile and adult—and for each we require measures of survivorship and duration. We distinguish the stages past subscripts (j for juvenile and a for adult) and permit South and t denote survivorship and durations, respectively. Thus Southward _j; and S _a correspond juvenile and adult survivorship, t _j is the historic period at first breeding, and t _a is the interval between breeding attempts, each of which results in due north offspring. And then the Euler-Lotka equation defining fitness, F, is

1 = ½n S _j e ^{−F t _j} +S _a e ^{−F t _a}

(1)

(Sibly and Calow 1986). The primal aim of life-history theory is to detect the life-history parameters northward, t _j, t _a, S _j, and Southward _a that maximize F subject to constraints imposed past the principle of allocation, that is, equations (3a) and (3b). Our immediate objective here is to notice optimal offspring mass, merely this depends on its furnishings on life-history variables. The simplest possibility is that offspring size affects only n, beingness inversely proportional as a result of the principle of allocation. Alternatively, it may also bear upon juvenile survivorship and/or age at first reproduction, the first being more important here; this is illustrated in figure 1B. In figure 1A and 1C, offspring size has no effect on juvenile survivorship, and the optimal strategy is to produce offspring as many and as small-scale equally possible. In effigy 1B and 1D, offspring size has a marked positive upshot on juvenile survivorship, but there are diminishing returns, so the optimal strategy is to produce offspring of intermediate size. Thus, everything else being equal, natural selection favors college birth rates and hence many small offspring (fig. 1A, 1C). Everything else is not ever equal, nevertheless, and larger offspring can be adaptive if juvenile survivorship increases with offspring size (fig. 1B, 1D). Additionally, everything else being equal, natural selection favors producing many modest litters rather than a few large ones and then as to avoid the chance that the female parent dies or the litter is discovered past a predator before it can be weaned. Again, still, circumstances of lifestyle and ecology, such as restrictive seasonal convenance opportunities, can override this tendency.

How neonate size may affect juvenile survivorship (A, B) and Darwinian fitness (C, D). Graphs plotted using equation (1) with parameter values north × neonate size = ten, t _j, = t _a = ane, S _a = 0.9.

In testing predictions we "corrected for" the variation in production with body mass and across dissimilar taxonomic and lifestyle groups past plumbing fixtures parallel-line models, as in figure 2. Each line (color coded in fig. ii) corresponds to a different functional or taxonomic group. This process is justified theoretically and empirically for the data of figure 2A in Sibly and Brownish (2007), which shows how variation in product rate orthogonal to the torso size centrality is due to lifestyle. Because both torso size and lifestyle affect product, both may affect its components, so these also were analyzed using parallel-line models equally detailed below. Parallel-line models are appropriate because our chief involvement is in comparing the heights of the lines (as quantified by the intercepts, i.e., normalization constants of the allometric equations). Post-obit Sibly and Brownish (2007) for a life-history trait w, nosotros regressed log w on log K to obtain a regression equation of grade

Variation in productivity (A) and the components of reproduction (B–E) as a role of body size. Productivity is measured as specific production rate, y ⁻ⁱ defined every bit the product of (litter mass)/(adult mass) and litter frequency (litters per year). (Litter mass)/(adult mass) is the product of offspring per litter and (newborn mass)/(adult mass). All scales are logarithmic to base 10. Symbols as in A throughout. The lines in each panel have the same slopes and are colour coded according to taxon. The regression coefficients (slopes) are shown at the top right of each panel. The four outlying information points for fissipeds to the right of A, C, and E are bears of the family Ursidae. For clarity, only taxonomic/lifestyle groups with ≥10 species are shown.

where west_i is a normalization constant (equivalent to a y-intercept) specific to the ith taxonomic or lifestyle group, b_westward is the regression coefficient of trait west and is assumed to remain constant across all groups, and One thousand is adult female trunk mass. Permit 10 denote (neonate mass)/(developed body mass), n be offspring per litter, z exist (litter mass)/(developed torso mass), y be the number of litters produced each year, and q be mass-specific production. Because (litter mass)/(developed body mass), z, is defined as the product 10 × northward, and considering mass-specific production, q, is defined as the product z × y, we have

and combining these equations with equations of the course of equation (2), we accept, using obvious note,

q _i  −b _q logM =z _i  −b _z logM +y _i  −b _y logM,

(4a)

z _i  −b _z logM =10 _i  −b _x logM +n _i  −b _{due north} logM.

(4b)

Equating coefficients, we have

and

Thus, our modeling arroyo is predicated on the supposition that each of the life-history traits should calibration allometrically with body mass, as in equation (2). Our method of obtaining the normalization constants of specified taxonomic or lifestyle groups is shown in effigy 3A. To analyze for merchandise-offs between pairs of traits that are due to the principle of resource allotment, the normalization constants for the two traits are plotted against each other, equally shown in figure 3B. In the simple instance illustrated in figure 3B, there is no variation between the three lifestyle groups in the quantity of resources, z, being allocated. In more than complicated cases, it is necessary to allow for variation between lifestyle groups in their z normalization constants, and for this reason strategies with the same values of z are indicated past dashed brown lines in figures iv and ​ 5. Where desired, allowance for variation in z values tin be achieved by moving points perpendicular to the z contours and assembling them on a common reference profile, as shown in figure 3C. The relative positions of the standardized points are the same irrespective of which z profile is chosen for standardization. This procedure allows assay of trade-offs after standardization for the quantity of resource bachelor for resource allotment.

Schematic illustration of our belittling methods. A, Get-go, the allometry of each trait is analyzed in a log-log plot (as in fig. 2). Here nosotros prove three hypothetical traits, x, north, and z, in relation to body mass, indicated past dashed, solid, and dotted lines, respectively, for each of three unlike lifestyle groups, a, b, and c, colored red, green, and bluish. The variable z represents (litter mass)/(adult mass), n represents offspring per litter, and 10 represents (offspring mass)/(developed mass), so for each lifestyle and for each adult mass, z = n × x and log z = log n + log x (see "Methods"). At any torso mass, a, b, and c all accept the aforementioned value of trait z, but a has a higher value than b or c for trait n and a lower value for trait x. The key feature of each lifestyle group is the relative pinnacle of its trait lines, which are indexed by their y-intercepts, here called normalization constants. B, To analyze for trade-offs between traits, the normalization constants are plotted against each other, and a trade-off betwixt traits ten and northward is revealed past the negative gradient. In this instance, all three lifestyle groups accept the same normalization constants for trait z, so their normalization constants for traits north and 10 lie on a direct line, shown in brown, and the labeled points satisfy the equation log z = log northward + log 10. In this example, the amount of resource being allocated, z, does not differ between the lifestyle groups when allometry of torso mass is accounted for. C, Generally the quantity of resource being allocated differs between lifestyle groups, so the points prevarication on different lines. We correct for this variation by projecting trait values onto a standard reference line, as shown here.

Scatterplots analyzing the two trade-offs between number of litters per year and litter mass (A) and between number of offspring per litter and offspring size (B) past plotting the normalization constants of the main mammal taxonomic/lifestyle groups. Numerical values of normalization constants are given, together with their standard errors (which are mostly <0.05) in tabular array A1. Ellipses enclose the classes of mammalian life histories referred to in the text. A, Litters per twelvemonth as a function of (litter mass)/(adult mass). Dashed brown lines connect strategies having the same values of specific product rate (q) and satisfy equation (6a). B, Offspring per litter as a function of (newborn mass)/(adult mass). Dashed brown lines bespeak strategies with the aforementioned values of (litter mass)/(developed mass) (z) and satisfy equation (6b) (meet fig. 3 for a rationale). Logarithms are to base 10.

Scatter diagrams analyzing the ii major trade-offs by plotting residuals within Artiodactyla (A, B), Lagomorpha (C, D), and Pinnipedia (E, F). A, C, East, Litters per year as a office of (litter mass)/(adult mass). B, D, F, Offspring per litter as a function of (newborn mass)/(developed mass). Residuals are calculated for each species from figure two as the vertical distance of the species from the lines of the same color in figure ii. Thus, residuals represent the divergence between log₁₀ life-history traits and the values expected from the species' trunk mass for members of the species' taxonomic/lifestyle grouping. Solid black lines are fitted regressions and are shown where correlations are significant (P < .05; table 1). Dashed brown lines connect strategies with the same resource allocation every bit in figure 4.

This conceptual framework allows us to predict theoretically and evaluate empirically how natural selection, responding primarily to the sensitivity of juvenile survivorship to neonate size, as in figure ane, has shaped the life histories of eutherian mammals. Nosotros now use this framework to brand bold statements almost the resource allotment strategies of different taxonomic and lifestyle groups and well-nigh the environmental conditions that have shaped the trade-offs. These statements represent plausible testable hypotheses that are consistent with current information on mammal life histories. Our hypotheses/predictions are:

1. A trade-off between number and size of offspring in a litter will be evidenced as a negative correlation among the normalization constants of the lifestyle groups. Groups that produce larger offspring should take smaller litters.

2. Artiodactyls, perissodactyls, cetaceans, and pinnipeds should requite birth to a relatively small number of large, precocial offspring. Their offspring are born unprotected on the basis or in the body of water. Offspring survival depends critically on offspring size, every bit in figure 1B, because large, well-developed offspring are better able to escape predators and require less fourth dimension to mature. Additionally, thermoregulation is enhanced by the larger size and better insulation of the precocial condition.

3. Primates, bats, sloths, and anteaters should also accept a few large offspring. These mammals mostly carry their young, which reduces risk of predation but limits the number considering newborn offspring must be sufficiently developed to agree on and to thermoregulate exterior the protective microclimate of a nest or burrow. Additionally, just a pocket-size number of offspring can be closely attended while the mother forages, interacts with conspecifics, and escapes from predators.

4. Insectivores, fissiped carnivores, lagomorphs, and rodents should produce big litters of relatively small altricial neonates. This should be true in particular for representatives of these groups that rear their dependent immature in burrows or nests, so that survival from nascence to weaning is not greatly affected past offspring size (meet fig. 1A).

5. Putting together predictions 2–4, most mammals should separate into two classes: those producing either a few big, precocial offspring (artiodactyls, perissodactyls, cetaceans, pinnipeds, primates, bats, and xenarthrans) or many modest, altricial offspring (insectivores, fissipeds, lagomorphs, and rodents).

6. The negative correlations predicted in hypothesis i should likewise be observed in the residuals for species within lifestyle groups later on accounting for the furnishings of torso size. So, for example, caviomorphs (guinea pigs and relatives) within the rodents, and hares inside the lagomorphs, which give birth to precocial neonates, should produce litters of fewer, larger offspring. The ocean otter, which differs from other fissiped carnivores in that information technology gives nascence at sea, where risk of predation and costs of thermoregulation are loftier, should also produce litters of a few big, precocial neonates.

7. A trade-off between allotment per litter and number of litters per reproductive season should be evidenced as a negative correlation among the normalization constants of the various taxonomic/lifestyle groups. Groups that produce more than litters per year should classify less production to each litter.

Methods

We used recent compilations of mammalian life-history data for placental, nonvolant mammals (Ernest 2003) and for Chiroptera (K. E. Jones, unpublished information). These data sets record offspring per litter, litters per yr, neonate and weaning masses, and adult body mass. Analyses were conducted for 628 species, representing 366 genera, 88 families, and 11 orders, for which data on offspring per litter, litters per year, neonate mass, and adult torso size were available for at least five species per order. We did not consider monotremes or marsupials, which are long-divergent lineages with dramatically different reproductive biologies: egg laying and pouch rearing, respectively. The availability of data dictates that we use the mass of offspring at birth to appraise the predicted trade-off betwixt the size and number of offspring in a litter. We are aware that female mammals typically allocate much more production to lactation than to gestation, only neonate mass is a constant ratio of weanling mass inside lifestyle groups and this ratio varies only from 0.ten to 0.thirty among lifestyle groups (Sibly and Brown 2007). Data manipulation and statistical analyses were performed using Minitab 15.1, and parallel lines of the form of equation (2) were fitted to the data of figure 2 using general linear modeling.

Results

Mass-specific product rate and the other life-history variables for 628 species of eutherian mammals are plotted as a function of adult body mass on logarithmic axes in figure 2. Figure 2A shows specific production rate, our best estimate of annual resources investment in reproduction. Figure 2B and 2C shows how this is allocated among the litters that are produced each year to make up one's mind litter frequency (fig. 2B) and mass (fig. 2C). Figure 2d and 2E shows how litter mass is divided among offspring according to their number. Notice that the parallel-lines model generally fits the data well (fitting nonparallel-lines models increases the adapted R ² value by only 2%, 3%, 1%, 0%, and 0% for fig. 2A–2E, respectively; tables A1, ​ A3).

Values of the normalization constants and results of ANOVAs are given for the parallel-lines model in table A1, showing that the normalization constants differ markedly among the taxonomic/lifestyle groups for each trait (P ≪ .001). Normalization constants for the different groups based on taxonomy and lifestyle are plotted in figure 4, and residuals for species within these groups are plotted in figures v and ​ A1.

These analyses can at present be used to evaluate the predictions to a higher place.

• 1. A trade-off between the number and size of offspring in a litter should be evidenced as a negative correlation amid the normalization constants for the taxonomic/lifestyle groups. Figure 4B shows that these traits are indeed negatively correlated (r _ix = −0.73, P = .01). To command for lack of independence betwixt closely related species, we repeated these analyses using genus and family means and plant similar relationships (r ₉ = −0.72 and −0.79 for genus and family, respectively; P = .01; fig. A2).

• 2, iii. Two groups should have a relatively small number of large precocial offspring: (i) artiodactyls, perissodactyls, cetaceans, and pinnipeds, whose young are born unprotected in the open, and (two) primates, bats, sloths, and anteaters, which comport their young from nascence until weaning. These predictions are supported. After standardization for the rate of production using the method in figure three, in that location were differences between the precocial, the carried, and the altricial groups (one-way ANOVA: F _two,viii = 71.4, P < .001). The precocial and the carried groups of effigy 4B are farther to the right along a common z profile than the altricial group (Dunnett's multiple comparison tests: P < .001). Using genus and family means gave similar results (P < .001; information in fig. A2), and the results are robust to errors in the allometric regression coefficients (data in fig. A3).

• iv. Insectivores, fissiped carnivores, lagomorphs, and rodents, whose offspring are protected in burrows or nests, should take many pocket-sized, altricial offspring. These groups exercise indeed produce large litters of small offspring, as shown in figure 4B (statistics every bit in evaluation of predictions [2] and [3]). Outliers tend to be species such every bit caviomorph rodents and hares, which give birth to well-adult immature in exposed environments (run across [6], beneath).

• 5. Putting together predictions (2)–(four), most mammals should separate into 2 classes, with litters containing either a few large, precocial offspring (artiodactyls, perissodactyls, cetaceans, pinnipeds, primates, bats, and xenarthra) or many small, altricial offspring (fissipeds, insectivores, lagomorphs, and rodents). This is indeed the observed pattern, as shown in figure 4B.

• six. The negative correlations predicted in (i) should likewise be observed among species residuals inside lifestyle groups subsequently the effects of body size have been deemed for. Scatterplots of residuals are shown in figures 5, ​ A1, and correlation coefficients are given in tabular array ane. If the predictions were perfectly supported, then the data would lie along the dashed brown lines in figures 5, ​ A1. Prediction (1) suggests that, subsequently accounting for variation due to trunk size, species in the same taxonomic/lifestyle group that produce more offspring per litter might be expected to produce offspring of smaller torso size. This prediction is supported in most groups (plots in right-manus columns of figs. 5, ​ A1; table 1) and is observed almost conspicuously in the lagomorphs (fig. 5D). Note that, in groups in which there is ordinarily but i offspring per litter, only express variation is possible. This accounts for the unusual distributions observed in the plots for cetaceans, pinnipeds, and, to a lesser extent, artiodactyls, bats, and primates (figs. 5, ​ A1). Caviomorph rodents and sea otters (Enhydra lutris) produce litters of relatively few, large, precocial neonates, as predicted (fig. A1), only there is only limited support from hares (genus Lepus; fig. 5D).

  Table i

  Correlation coefficients r and associated P values for the correlations between the residuals of allotment per litter (z) and number of litters per reproductive flavor (y) and of size of offspring (x) and their number (n)

  Social club	No. species	rzy	P	rxn	P
  Artiodactyla	75	−.253	.029	−.572	.000
  Cetacea	18	.070	.783	−.553	.017
  Chiroptera	105	.172	.079	−.299	.002
  Fissipeds	71	.383	.001	−.302	.011
  Insectivora	28	−.089	.654	−.238	.223
  Lagomorpha	19	−.411	.080	−.682	.001
  Pinnipeds	25	−.221	.288	.195	.349
  Primates	81	−.191	.088	−.289	.009
  Rodentia	190	.238	.001	−.656	.000

• seven. A merchandise-off between allocation per litter and number of litters per reproductive season will be evidenced as a negative correlation amidst the normalization constants of the various taxonomic/lifestyle groups. This prediction is non supported overall (r _nine = −0.05, non pregnant; fig. 4A). Any evidence for the merchandise-off is obscured by the variation in productivity, p, among the lifestyle groups, which results in variation perpendicular to the q contours.

However, when variation in productivity is corrected for using the standardization procedure of figure 3, there were differences betwixt the precocial, the carried, and the altricial groups (one-way ANOVA: F _2,viii = 7.1, P = .02). The precocial mammals are farther to the right along a common q contour than the altricial group (Tuke's multiple comparison exam: P < .05). Using genus and family means gave similar results (P < .05 for genus, P < .07 for family; data in fig. A2), and the results are robust to errors in the allometric regression coefficients (data in fig. A3). Mammals that carry their offspring are intermediate between the precocial and the altricial mammals only are non significantly different from either. If this same trade-off holds within lifestyle groups, species that produce more litters per year should classify less biomass to a litter. There is little back up for this prediction in most groups (plots in left-paw columns of figs. 5, ​ A1; table 1), with any trade-off being obscured by wide variations in productivity among species.

Discussion

Nosotros begin by emphasizing that we regard our predictions as plausible testable hypotheses and that the above data and analyses are only preliminary support for the predictions. We take that additional analyses using improved techniques and more and better data would be desirable. For instance, for businesslike reasons, we adopted parallel-lines models to identify differences betwixt lifestyle groups in figure 2, fifty-fifty though in some cases nonparallel-lines models increment the proportion of variance explained. Our method allows unambiguous quantitative comparisons of trait values among groups across the unabridged range of torso sizes. Alternative methods that let slopes to vary requite differences in trait value among groups that vary with body size. Additional theoretical and empirical work is required to assess the extent to which the framework that we have presented provides boosted insights into the observed variation in mammalian life histories.

There is a long, rich literature on life-history theory (e.k., MacArthur 1962; Charlesworth 1980; Charnov 1982). There is likewise a rich literature of accumulating data on components of the life histories of diverse organisms, including mammals (e.g., Gaillard et al. 1989; Promislow and Harvey 1990; Purvis and Harvey 1995; Jones and MacLarnon 2001; Charnov and Ernest 2006; Bielby et al. 2007). Much of this literature is phenomenological. It provides adaptive interpretations of patterns of variation in terms of trade-offs, but it does not provide a conceptual framework based on specified evolutionary mechanisms and constraints. By contrast, our theory provides an explicitly mechanistic account of the evolution of mammal life histories. These life histories are powerfully constrained past the ability of females to larn resources and convert them into reproductive biomass. The rate of production depends first on body size and second on lifestyle, as shown in effigy 2A in Sibly and Brown (2007; see also Brown and Sibly 2006). Mass-specific productivity decreases every bit body size increases considering of unavoidable increases in the costs of transporting resources around larger bodies. Productivity likewise depends on lifestyle, all the same, and this has two important components: diet and bloodshed. When body size is allowed for, mammals with more than reliable and abundant foods have higher rates of production, whereas mammals with reduced mortality rates have lower productivity (Brown and Sibly 2006; Sibly and Brown 2007).

Our analyses focus on the resource allotment of productivity to offspring between and within litters. The gene of primary importance is how preweaning mortality varies with offspring size (fig. ane). Adaptive responses to mortality-size relationships have resulted in the frequently observed precocial and altricial strategies, which segregate at opposite ends of the merchandise-off between number and size of young in a litter (fig. 4B). At one extreme, survival of offspring built-in unprotected by a nest or couch depends critically on their abilities to escape predation and to thermoregulate, which in turn depend on size and developmental state at birth, equally in figure 1B. In these mammals, offspring number is traded for size, so that females produce a few big, precocial offspring, and offspring size is further increased by reducing litter frequency to increase litter mass. Thus, selection increases offspring size in both trade-offs so that some species produce only a unmarried big offspring, once per year. At the other extreme, juvenile survival is relatively secure because offspring are protected in burrows or nests, and then the strategy is to produce many small, altricial offspring. This is adaptive because, other things being equal, more is better (i.due east., results in higher fitness; fig. 1C), and other things are more or less equal because survival earlier weaning is not greatly affected by offspring size. Litters are frequent, and, concomitantly, litter mass is small, thereby minimizing the number of offspring that die if the mother abandons them or dies before weaning. A third distinct strategy is exhibited by mammals that carry their young from birth until weaning. Their offspring are non particularly large or precocial, only they practise accept adaptations to cling to the mother every bit she engages in all activities. At that place are few offspring per litter primarily because of the difficulty of transporting and caring for more dependent offspring.

Mammals offer special challenges in developing and testing life-history theory. For one thing, maternal investment in gestation and lactation makes it much more difficult to perform the direct experimental manipulations of number and size of offspring that are possible in other groups such as birds and reptiles (e.g., Sinervo and Huey 1990; Fontaine and Martin 2006). Additionally, our results suggest that, to business relationship for the observed trade-offs in resource allotment of production, the single most important factor is predation on juveniles and the style this varies with neonate size. Unfortunately, few reliable data on the mortality-size relationship are available, due to the inherent difficulties in measuring pre- and postweaning mortality of free-living wild mammals (eastward.g., see Sibly et al. 1997). Here we nowadays a theoretical framework that overcomes some of these limitations by using a new method to analyze resources-allotment trade-offs. Our framework corrects for variation in both body mass and rate of production (fig. three) to reveal patterns of divergence along trade-off axes. The usefulness of the method is particularly clear in effigy 4A, where the deviation between altricial and precocial mammals is non credible until variation in productivity is accounted for. This framework allows usa to become beyond earlier treatments in identifying the particular merchandise-offs and lifestyles associated with the altricial, the precocial, and the offspring-carrying strategies. The trade-off between offpring size and offspring number in figure 4B has been shown previously (Read and Harvey 1989; Charnov and Ernest 2006), every bit has the finding that precocial neonates are heavier than altricial neonates (Martin 1984). When a lifestyle group is constrained to produce altricial or precocial neonates, there are additional consequences and opportunities for pick and adaptation (Martin 1984; Martin and McLarnon 1985; Harvey and Read 1988; Derrickson 1992).

Our assay shows how ecological relationships have led to the evolution of life-history trade-offs. When the pervasive constraint of the allometry of product and the effects of lifestyle have been accounted for, how preweaning bloodshed depends on offspring size is the master factor determining the merchandise-offs in allocation of resources to reproduction. Farther work is needed to assess similarities and differences amid species within and among taxonomic and lifestyle groups (due east.one thousand., fig. five) due to the interplay between phylogenetic evolutionary relationships and environmental conditions.

Acknowledgments

We thank One thousand. E. Jones for supplying the bat information, E. Fifty. Charnov and members of the University of New Mexico/Santa Fe Establish Scaling Group and the Integrating Macroecological Pattern and Processes across Scales (IMPPS)/National Science Foundation (NSF)–funded Research Coordination Network (RCN; DEB-0541625) for helpful discussions, and S. Beissinger and two reviewers for comments. This is IMPPS RCN publication two and was supported by a Royal Social club Travel Grant to R.M.S. and an NSF grant (DEB-0083422) and a Packard Interdisciplinary Science Grant to J.H.B.

Appendix: Normalization Constants and Allometric Regression Coefficients of Production Ratesti and Life-History Characters

Tabular array A1

Normalization constants of production rates and life-history characters (±SEs)

Society	No. species	Product rate per adult mass, qi	Litters per yr, yi	Litter mass per adult mass, z i	Offspring per litter, ni	Newborn mass per adult mass, teni
Artiodactyla	75	.614 ± .040	.526 ± .026	.088 ± .028	.400 ± .021	−.312 ± .031
Cetacea	18	.701 ± .076	.234 ± .049	.467 ± .053	.425 ± .040	.042 ± .058
Chiroptera	105	−.067 ± .052	.235 ± .033	−.303 ± .036	.142 ± .028	−.445 ± .040
Fissipeds	71	.106 ± .035	.421 ± .023	−.315 ± .025	.734 ± .019	−i.048 ± .027
Insectivora	28	.172 ± .061	.375 ± .039	−.203 ± .043	.756 ± .033	−.959 ± .047
Lagomorpha	19	.716 ± .063	.794 ± .040	−.078 ± .044	.763 ± .033	−.842 ± .048
Perissodactyla	9	.422 ± .094	.288 ± .061	.134 ± .066	.389 ± .050	−.255 ± .072
Pinnipeds	25	.755 ± .059	.496 ± .038	.259 ± .041	.346 ± .032	−.087 ± .045
Primates	81	.008 ± .034	.264 ± .022	−.256 ± .024	.289 ± .018	−.545 ± .026
Rodentia	190	.339 ± .038	.543 ± .025	−.205 ± .027	.721 ± .020	−.925 ± .029
Xenarthra	seven	.197 ± .099	.382 ± .063	−.185 ± .069	.389 ± .053	−.573 ± .075
F x, 616		36.half-dozen	38.4	29.i	152.eight	104.nine
Adjusted Rtwo		73%	56%	69%	75%	68%

Table A2

Fitted regression coefficients with their SEs

Parameter	Regression coefficient	SE
bq	−.3664	.017
by	−.1076	.011
bz	−.2587	.012
bn	−.0673	.009
bx	−.1914	.013

Table A3

Statistics for a comparison of parallel-lines and nonparallel-lines models

Parameter	F 10, 606	P (parallel-lines model)	Adapted R 2 (%)
Production rate per developed mass, qi	5.3	.000	75
Litters per year, yi	6.half-dozen	.000	59
Litter mass per adult mass, zi	2.eight	.002	lxx
Offspring per litter, ni	1.ii	NS	75
Newborn mass per adult mass, x i	ane.eight	NS	69

Figure A1

Scatter diagrams like those in figure 5 for the taxonomic/lifestyle groups not shown in that figure. 1 point did not fit in the left-hand column, a conduct (Fissipeds, Ursidae) with coordinates (−1.twenty, −0.03). Dashed brown lines connect strategies with the same value of the resources existence allocated. Thus, the equation of the line in the left-hand panels is (z – $\bar{z}$ ) + (y – ȳ) = 0; here (z – $\bar{z}$ ) represents the balance of z and (y – ȳ) the balance of y. The line goes through the point (0, 0) because the hateful of the residuals of each trait is 0. Similarly, the line in the right-hand panels has the equation (ten – $\bar{x}$ ) + (n – $\bar{n}$ ) = 0. The caviomorphs are arrowed within the rodents and the sea otter inside the fissipeds (run across main text).

Figure A2

Scatterplots as in effigy 4 (peak) together with repeats of the analyses using genus ways (center) and family means (bottom).

Figure A3

Scatterplots as in figure four, with allometric regression coefficients varied past ± 2 SE.

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Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2892970/

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