Lecture 9 - Allocation to Reproduction: When & How Much
The story of clutch size and tradeoffs between size and number worked their way around the basic question of life history. That question is usually phrased in some way to ask how to schedule allocation to reproduction through the lifespan of the organism. How much should be allocated at each age? We've already seen one general model of the question in the form of graphs for iteroparous and semelparous species, in which current reproduction and residual reproductive value were plotted against age for semelparous and iteroparous species. But why should a species evolve to be iteroparous versus semelparous? If being iteroparous is advantageous, how is lifetime reproductive effort scheduled? This, then, brings us neatly to consider reproductive effort in relation to reproductive strategies. My take on the subject differs a bit from text treatments. To consider reproductive effort, I begin by comparing semelparity, with a maximum reproductive effort expended at an optimized age and/or parental size, with iteroparity, with time and age dependent optima in the expenditure of energy on reproduction `designed' to maximize lifetime fitness. Semelparity versus Iteroparity The first part of the question of when to reproduce, having looked at effects of a and clutch size, is whether to reproduce only once, i.e. semelparity or big-bang reproduction, or whether to reproduce more moderately but repeatedly, i.e. iteroparity. From different points of view it might seem apparent that advantage accrues to either one strategy or the other. Reproducing early, and according to the big- bang approach (so that the organism needn't worry about possible effects on adult survivorship) caution can be 'thrown to the winds', and G considerably shortened. This should clearly increase 'r'. However, consider the opposite approach. Even if every litter were somewhat smaller, the iteroparous species can have many such litters, and a much larger number of offspring (R0) over a life cycle. It seems as if, over that lifespan, over the long run, numbers should pile up. How are we to quantitatively assess the relative merits of these two alternatives? The comparison is part of Cole's (1954) classic paper, and comes to what, at the outset, seems to be a shocking conclusion. Cole assumed that the semelparous species has perfect survivorship to age 1 year, then reproduces, producing a litter of size b. The iteroparous species has perfect survivorship, not only until it begins reproducing at age 1, but also thereafter; it produces a litter of size b annually. The population growth can then be compared. The advantage of the iteroparous species, with an indefinite lx of 1 is surprisingly small. Looking first at the semelparous species, and beginning with exponential growth as a model: Nt = N0 ert if t = 1 year, and each female has a litter of size b, then the growth equation can be re-written: Nt/N0 = er = b or rs = ln (b) The calculations for the iteroparous species involve another infinite sum, with the approximate result that: ri = ln (b+1) Cole's way of stating this comparative result is clear and concise: 'for an annual species, the absolute gain in intrinsic population growth which could be achieved by changing to the perennial reproductive habit would be exactly equivalent to adding one individual to the average litter size.' Not only that, but the gain, logically, is a function of litter size and the age of first reproduction, which aren't considered in this basic comparison. The gain from changing to iteroparity (when the litter size of the semelparous species is equal) increases both with delay in first reproduction (i.e. increasing a) and with decreasing litter size. These effects should follow logically. Consider litter size first. If it takes one extra in the litter for a semelparous species to keep up, that represents a bigger proportional increase in reproductive effort when litter size is small than when it's large (e.g. a 50% increase if b = 2, but only a 1% increase if litter size is 100). It's a little harder to think in terms of alpha, but recognize that the semelparous species has bouts of reproduction only every alpha years, while, once started, the iteroparous species reproduces every year. If alpha increased from 1 to 5 for both the iteroparous and semelparous species being compared, then by the time grandchildren are born in the semelparous species, the iteroparous parent will have produced offspring at ages 6,7,8 and 9, each time with a litter of size b. That's clearly a bigger advantage than accrued when alpha was 1. Cole produced a graph showing the combined effects of alpha and b on the percent gain from becoming iteroparous, and it shows clearly that iteroparous life histories are most advantageous for species limited to small litter sizes and delayed reproduction. This general pattern fits with observations. Most semelparous species tend to have short pre-reproductive periods. That minimizes the advantage that might be gained by becoming iteroparous. A few examples make the basic point. Annual plants (many weeds) and almost all insects complete their life cycles in a single year, and most which do not complete life cycles in 2 years instead (e.g. most salmonids, biennial plants such as weedy thistles, teasel, onions, garlic). There are extreme exceptions, such as the 'century' agave and some bamboos, but they will be the subject later. Semelparous species also typically have very large litter sizes. Many produce 106 eggs or more, e.g. Musca domestica, the common housefly, oysters, or the salmon. These observations, and many others which could be presented, suggest that in most cases semelparous species fit the life history patterns which would minimize the gain from becoming iteroparous. The problem can also be approached from the opposite point of view. It is clearly advantageous, from an evolutionary view, to increase the intrinsic rate of increase 'r', 'all else being equal'. A change in 'r' could result from becoming iteroparous while maintaining litter size, or from an increase in the semelparous litter size. Since either change could be equally effective, we can look at the change in semelparous litter size required to achieve the same 'r' as would be reached by switching to iteroparity while just maintaining litter size. Once more, Cole produced the figure which demonstrates the requirements for equivalence. The change in litter size required can be dramatic. Take the lowly tapeworm as an example: The approximate daily litter size of the mature tapeworm is 100,000 eggs. Including larval development time, the maturation time, or alpha, is approximately 100 days. If this species were to become indefinitely iteroparous, we find from Cole's graph that the equivalent semelparous litter size to achieve the same growth rate would be about 800,000. The species is not, of course, indefinitely iteroparous, and the required semelparous litter size is not quite so large. This comparison, and particularly this figure, make it clear that the apparent 'advantage' of semelparity, i.e. the ability to catch up by adding only 1 to the litter size, strongly depends on the length of pre-reproductive life and on litter sizes involved. Thus, although this began by making it seem that there was little advantage in bet-hedging to permit repeated reproduction, there are real situations which suggest a considerable advantage (in an evolutionary sense) to iteroparity. At ths point Cole introduced a figure you've already seen, the one which demonstrates the proportional gain in 'r' from increasing the number of reproductive cycles. The only thing to add to what's already been said is to recognize that the advantage gained by additional reproduction declines for all cases, but particularly for those with low alpha. In an evolutionary sense, that means that the selective pressure to increase the period alpha to omega decreases, and beyond the first few reproductions, the slight advantage that might accrue from further reproduction may easily be balanced by other pressures. Cole's results have, since their publication, been a thorn in the side of life history theory. Nobody claims Cole was wrong, Cole was correct, rather a large number of theoreticians have tried to show that the unreality in Cole's assumed life history is responsible for the smallness of the difference between iteroparity and semelparity. The key assumption in Cole's treatment was the assumption that all lx in both strategies were = 1. Adding mortality schedules have clarified some of the results. The outcome of making survivorship more realistic was initially possibly even more controversial. Bryant (1971) showed that under assumptions of 1) constant litter size and 2) a monotonically decreasing lx = e-mx, or, for that matter, any monotonically decreasing lx, the value of 'r' for an iteroparous species is not even increased as much as by adding 1 to the semelparous litter size. That's logical, if you stop and think about it. If Cole showed equality by adding one to the litter size when the iteroparous species was immortal, less is contributed by a mortal species, since the contribution to the sum lxmx is decreased by declining survivorship. For the case of a perfect type II curve, as evaluated by Bryant, equality occurs with a growth (or litter size for the semelparous species): r = ln (b+1) - m where, remember, m is the constant describing the death rate. If the same mortality occurs also in the first year of life, then the growth rate of the iteroparous species is: r = ln (b) - m The valuable indication from Bryant's attempt to move closer to reality is probably not the exact mathematical formulae, but the recognition that for type II species, semelparity becomes more likely as the mortality rate m increases. This, too, fits with natural history observations. At this point you might wonder why there is such a thing as a long-lived iteroparous species. A more recent attempt to add reality to Cole's model will show us when and why. Charnov and Schaffer (1973) used a more general approach to correct for Cole's generous assumption about survivorship. Their model includes, but separates, pre- and post alpha mortality. As a result, you will see that they can suggest where iteroparity should evolve. The comparison begins again between an annual and a perennial species. Assume that the litter sizes for the two types of species are Ba for the annual species and Bp for the perennial species. The survivorship pattern in the first year is l1 = C for both types. Following reproduction in the first year, the semelparous species dies, and the perennial species continues with an annual proportional survivorship px = P. The comparison is easiest if we compare finite rates of increase, l = er, and t = 1 time unit, usually a year, so that: N(t+1) = l N(t) For an annual species the number alive to breed is C x N(t), and each of these has a litter of size Ba, or: N(t+1) = C x N(t) x Ba and l a = Ba x C For the perennial species there is adult survivorship and repeated reproduction as well. Counting noses just before reproduction, so that surviving adults haven't yet added the additional litters, we get: N(t+1) = Bp x C x N(t) + P x N(t) and l p = Bp x C + P For an annual species to make up the advantage of iteroparity, the growth rates must be equal, therefore: Ba x C = Bp x C + P Ba = Bp + P/C Now, let's go back and consider previous cases. Cole suggested that we disregard survivorship to develop an initial model. With immortality both P and C are taken as 1, their ratio is 1, and the result here is identical to that Cole obtained. Bryant suggested that if we impose type II survivorship after alpha, then an advantage less than 1 in litter size accrues. His survivorship pattern is equivalent to saying P is fixed, and less than C; the advantage here is again less than 1. Then, when is iteroparity favored? To determine that we need to look at the relationship between P and C, i.e. between proportional survivorship through the reproductive period and pre-reproductive survivorship. Consider the Deevey survivorship curves. For type III its obvious that P is far larger than C, the early part of the curve is very steep, and the curve is relatively flat through reproduction. For type II (and remember, for comparisons of real numbers we need to convert back from the usual log scale to a linear one) P and C are more similar, but the curvature makes it 'flatter' during than before reproduction. For the mammalian type I curve, you might think that P and C are equal, but remember Caughley's basic pattern; it showed an initially moderately high qx, or equivalently an initial decline in lx, before an extended, flat, low set of values through reproduction, i.e. C is less than P. Using a simple graphical treatment, early survivorship is compared to the reproductive period in slopes of the curves. If early survivorship is steeper than the later period, then the perennial habit is favored to that degree. We can extend this analysis by using somewhat more realistic models for semelparity and iteroparity, one in which reproduction does not necessaarily occur in the first year, but rather at age K (and in each subsequent year if the species is iteroparous). The comparison now uses Euler's equation. In this system of equations, for purposes of simplicity and clarity, l stands for lambda, the finite rate of increase. For the iteroparous species: 1 = Bi x C [1/lK + P/lK+1 + P2/lK+2 + ...] and 1 = Bi x C/lK [ 1/(1 - P/l)] for the semelparous species: 1 = Bs x C/lK or lK = Bs x C setting the growth rates to equivalence, by substitution we obtain: Bi/Bs = 1 - P/l That is, life history equilibrium leans in favor of iteroparity when the iteroparous litter can be much smaller than the semelparous litter which produces the same population growth rate. That occurs when either: a) the adult survivorship px or P, is very high, or alternatively b) the finite rate of increase (or annual population growth) is very low. That, of course, is exactly what intuition suggests. The higher the adult proportional survivorship the more the advantage to be gained from iteroparity, since that means many more litters will be produced over the lifespan. An Energetics View of Iteroparity vs. Semelparity The various approaches used by Cole and his followers to test the advantage of iteroparity are all based on comparison of population growth rates; they do not consider the position of the individual committed to a strategy. A final view of the contrast between iteroparity and semelparity, and when each should be expected, considers instead the energetics of the reproducing animal. It is, therefore, a little less abstract in approach. An animal reproducing iteroparously must save energy for future reproduction; that energy is required for maintenance and possibly growth. An animal reproducing semelparously, to maximize success, should energetically commit all available (divertable) energy to reproduction at the expense of all other structures in the body, since it will not survive to reproduce again. This suggests the possibility of using cost/benefit comparisons related to economics to decide what conditions should lead to different strategies. That approach, in the form of a set of graphs, was used by Gadgil and Bossert (1970) to suggest patterns which lead to iteroparity. At any age the amount of reproductive effort which should be expended is determined by balancing the profit to be gained by reproduction (measured by the reproductive value at that age, i.e. offspring plus future expectations) against the costs inevitably incurred. To compare all possibilities, Gadgil and Bossert defined 3 shapes of profit and cost functions to be plotted against reproductive effort. Reproductive effort is defined, for the purposes of these graphs, as the proportion of total energy devoted to reproduction. The graphs are in arbitrary units, i.e. we won't assign real numbers, but indicate the shapes of patterns. The 3 kinds of curves are concave, linear and convex. So that the patterns have an underpinning of reality let's consider a few examples: Consider the cost and profit functions for migrating salmonid (e.g. Atlantic and Pacific salmon) reproduction. The initial effort required to spawn even one egg is the enormous cost of migration from deep ocean to upstream fresh water. Thus the curve rises very sharply at low reproductive effort. However, the additional cost to spawn more eggs is basically the metabolic cost of egg tissue production, which is much more modest and basically flat (i.e. each egg costs about the same amount, independent of how many have been already formed). That combination produces a cost curve which is 'extremely' convex. For simplicity, the curve can be drawn with a less extreme rise, and a not quite flat top (things aren't usually that dramatic) to reflect the more general pattern. Meanwhile, the profit from increases in reproductive effort, i.e. the number of offspring, increases at least in direct proportion to the number of eggs. If there are advantages to schooling of fish fry, then the profit curve might not be linear, but a bit concave, reflecting the improved survivorship (lx, i.e. not just numbers but the expectation of survivorship for each individual) when offspring numbers increase and schools are formed. The combination of a convex cost curve and a linear or concave profit curve predicts maximum gain at maximum reproductive effort - be semelparous (see below for the complete consideration of curve combinations. Which curves might fit the mammalian situation? Avoid thinking of man. With that caveat, I suggest that the cost function could range from linear (if we consider the direct costs, including parental care, there is no obvious reason to suggest either declining or increasing costs per offspring as litter size changes) to concave (if we also consider indirect costs, e.g. homeothermic stress, increasing risk of predator tracking with increased litter size). It probably isn't strongly concave, but at least slightly non-linear in that direction. The profit function is probably convex, in parallel with what we've seen for the provisioning of birds, from the decreasing individual size of individual offspring with increasing brood size. Again, the curvature is probably not dramatic, since homeothermy leads to some sharing of warmth among members of a brood, which helps, but also sharing of teats, which limits food intake no matter how hard the mother works. Where is the benefit/cost ratio maximized for mammals. For the salmon costs to reproduce at all are high, but once reproduction begins benefits rise much faster than costs as effort increases. The maximum ratio occurs at maximum reproductive effort, suggesting the animal spend everything it can on reproduction, i.e. be semelparous. For the mammal costs rise slightly faster than linear as litter size increases, but profits rise at a rate at least slightly below linear. The maximum ratio occurs at some intermediate level, the exact effort determined by the curvatures of benefit and cost curves, i.e. save a considerable fraction of total energy, and reproduce iteroparously. There are, based on 3 curve shapes for each of benefit and cost, 9 combinations. Most make a clear prediction of semelparity or iteroparity, a few depend for their predictions on recognition of survivorship and cost per unit. In those cases the ratio remains constant, but long-term total profit changes. To see how each graph is taken to indicate semelparity or iteroparity, scale the x axis (reproductive effort) from 0 to 1. A big-bang reproducer should achieve the best benefit-cost ratio at an effort of 1, an iteroparous species at some intermediate level, retaining energy for maintenance and growth. When is it advantageous to withhold energy from reproduction? a) If the profit function is convex. In this case, above some intermediate reproductive effort the profits cannot keep pace with the proportional increase we might expect for metabolic costs per offspring. With costs increasing faster than profits, energy should not be spent inefficiently, but retained for use in the next bout of reproduction, when they can be spent with greater efficiency, at moderate reproductive effort, where gains increase most rapidly with effort. This is just the 'law of diminishing returns' applied to reproductive ecology. The efficiency argument even applies when the ratio remains constant. For that, the middle case, the total number of offspring produced from a given amount of energy can be maximized by reducing reproductive effort, even if benefit-cost ratio has no maximization. b) If the cost function is concave. In this case the cost per unit gain in fitness becomes too high at high reproductive effort. Retaining a portion of the energy available, the animal can produce offspring (or increments in fitness) at a lower cost per unit in later bouts of reproduction. c) In all other circumstances animals should wait until the maximum benefit-cost ratio has been reached, then put all available energy into reproduction. Under these circumstances the semelparous reproductive habit is optimum. That incudes the case where profit and cost are both linear. There is no change in cost per unit with effort, and we now know the advantage of early reproduction. There is no advantage to restraint, especially given survivorship factors, so semelparity should result. d) If more complex functions for benefit and/or cost are considered, e.g. sigmoid shapes, there will almost always be some intermediate level of effort at which the curve goes through an inflection point, i.e. a change from concave to convex. In most cases that inflection will be the critical point at which benefit-cost ratio will be maximized, and an iteroparous strategy will result. Almost all views of the balance between iteroparity and semelparity have now been considered. Their assembly leads to one last evaluation, how long should the period alpha to omega be? This clearly also relates to the intensity of reproductive effort in iteroparous species. Obviously, that depends on the security of survivorship (px), and on the variability in reproductive success (one possible indicator being initial survivorship l1). If survival is relatively assured, then no single bout of reproduction is under severe pressure to produce success. On the other hand, if survivorship is low or variable, then the pressure for success from any single bout (or a few) is much higher, and more effort (and a shorter alpha-omega is likely. This is a hypothesis developed by Murphy (1968). His data comes from marine fisheries, and show a tight relationship between the reproductive period and variability in success (measured as a ratio of highest/lowest success). Unpredictability in annual success rate is exactly what we might expect of species in mature communities. A good example might be a climax forest. The only places young are successful is where openings develop due to death or chance destruction of mature individuals. Such clearings are rare, chance events. So each year a tree puts out a crop of seeds, but it may be many years of suppressed growth before even one is successful in such a chance clearing. The profit function is therefore convex, i.e. the chance of a clearing happening cannot be missed, so its necessary to put out a seed crop each year, but there's no use overdoing it, there's little advantage in putting out a huge crop. Energy is retained to improve survivorship, so that the individual is likely to survive to a time when an opening develops, and be capable of producing offspring to colonize that opening. Whether we call evaluation of this strategy as resulting from unpredictability in reproductive success, a convex benefit function, or a relationship in which C << P, the result is the same. If some reasonable level of success is relatively assured, i.e. variance in success is low, then the reproductive span is shortened, ultimately to semelparity. Again any of the models can be invoked. Rather than pursue that, let's look at a summary view produced by Murphy (1968), but clearly fitting, with appropriate changes in terminology, any of the models. Its a 2 x 2 table in which lifespans (really reproductive spans for Murphy) and variability in reproductive success (or P/C comparisons, or benefit functions) are combined: long-lived short-lived reproductive success see below (?) semelparous steady (assured) strategies reproductive success iteroparous not possible variable Two of these boxes have already been discussed as (or more) thoroughly as necessary. The upper right hand box, semelparous strategies, is a necessary association of lx and mx. If a species is short-lived, quantifiable as a small e0, then the only pattern to reproduction which will permit persistance is steady, assured success. Else, as the next paragraph describes, extinction will follow. The lower, right hand box is also simply explained. This is what happens to a short-lived species does not have assured success. Extinction is the inevitable result when a species attempts reproduction only once (or possibly a few times) while the variability in reproductive success is high. That variability ensures that at some time a few bad years will follow in succession, and prevent an entire mature population from producing any surviving offspring, i.e. local extinction. These are species that have adopted a short-lived,i.e. a low P, but also a low C strategy. In its simplest form this just won't work. The closest real species come to this is to have facultative (that is have the potential for) dormancy in offspring. In this way the low survivorship of parents and low annual success in offspring can be mitigated through appearance of offspring (release from dormancy) when chances of offspring success are high. Looked at in terms of the end success of offspring, rather than annual success rates, this strategy becomes a special case of the upper right hand box, short adult life but predictable offspring success. This strategy is fairly common in weeds, whose seeds may remain dormant for more than 100 years, and in some desert plants. The desert plants produce seeds that, at the time of dispersal, contain inhibitors which must be washed out before germination will occur. The limiting factor on the desert is sufficient water. Heavy desert rains will wash out those inhibitors, and also guarantee a sufficient supply of water to complete a growth cycle. This is a biochemical form of buffering against environmental variability. The box in the upper left has a ?. There are a number of approaches to indicate why that box should not be occupied by observed reproductive strategies. The most intuitive of them considers the effect of such a strategy on species interactions. This is a species which is long-lived and has predictable reproductive success. That should make this population very successful. If the species in question is a prey item, its predator will evolve to more extensively utilize a species which is predictable, either through numerical or functional responses. An optimally evolved predator should probably adopt a type 3 strategy, i.e. specialize on this prey through formation of a search image if the predator is capable of that kind of behavioural response. The result of increased predation on this prey, whose life history we are following, will be either a reduced lifespan or greater variability in reproductive success (or adaptations to make their accessibility to predators less predictable). That moves the strategy for the species out of the ? box and into either of the more usual strategies. In fish species the tendency is toward shortened life and steady reproductive success. In a number of plant species (particularly long-lived trees) the opposite adaptation has appeared. These trees (apple trees are an example of one kind of response) have variable reproductive success; some years a heavy seed crop is produced (so-called mast years) and other years the crop is much smaller. In nature this can be considered an adaptation to restrict insect (or other) herbivores by starvation, though it can also be a necessary reponse to energetic demands of reproduction. In this latter sense, it is a cost of reproduction. Having reproduced heavily in one year, the 'cost' is a very restricted reproduction in the following year. The pattern stands, whether the mechanism is energetics or predator avoidance. If these strategies are well established, do all species fit one of the possible strategies? Exceptions - There Are Always Exceptions! There are always exceptions. If it seems like the possibilities have been neatly pidgeon-holed, but it's time to see what can be learned from the oddballs. The most common form of exception to the strategy table developed by Murphy is the presence of a variety of long-lived semelparous species. 13 and 17 year cicadas are obvious examples, but in terms of lifespans, they're small change compared to the plant examples. We'll look at 2 different rationales which produce long-lived semelparity in plants, using semelparous bamboos and the agave ('century plant') as examples. The Bamboos Not all bamboos are exceptions to the established life history patterns. Many species are iteroparous perennials; these grasses have more or less extended pre-reproductive periods, then flower and set seed annually until senescence. There are, however, a number of perennial, monocarpic bamboos, and included among them seem to be all of the economically important bambo species. An aside: this fact is a problem, as well as an incitement to scientific interest. Populations of these bamboos are, therefore, managed, and natural cohorts are inevitably mixed with agriculturally selected strains. Long-term genetic implications of the apparent strategy may not, as a result, be testable. The studies of bamboos are largely the result of the work of Janzen, summarized in a review paper (1976), and, for a different group of bamboos with a differing explanation, by Gadgil and his collaborators (1984). What evidence is there that something unique is going on in semelparous bamboo life histories? Janzen uses history to pique our curiosity. Historical records indicate that a major Chinese bamboo species, Phyllostachys bambusoides, flowered en masse (that is simultaneously over hundreds of square miles) in 919 and again in 1114, but not at any point in between. Cuttings of the rhizomes of this species were brought to Japan and established there. Those cuttings flowered during the period between 1716 and 1735, then again in 1844-1847, but not during any intervening year (if there are records of flowering between 1114 and 1716, Janzen did not find them). Transplants from Japan, as well as the parental stock, flowered next in the 1950's. Those transplants were scattered in England, Russia, and Alabama among other places. All flowered within 3-4 years of each other. It was this widespread mass flowering that aroused Janzen's curiosity. The flowering appears to be somehow genetically programmed and fixed. That program is essentially unaffected in its Swiss clock-like precision by the enormous variation in environmental conditions represented at its flowering sites (Japan, England, European Russia, Alabama, etc.). Many other bamboo species also flower in relative synchrony, and with quite long intermast intervals. Among bamboos this life history contrasts with another pattern which is also common; many species produce seed crops annually after a maturation period of varying length. A partial list of the species which reproduce synchronously and have long intermast intervals is shown in the table below. The flowering in species like P. bambusoides is 'unique' in 2 ways. One is its freedom from environmental perturbation. Unlike most other mast reproducing species like oaks, beeches, and many fruit tree species (all of which have far shorter inter-mast periods) there is no apparent environmental cue to initiate mast year reproduction; unlike the others few (almost certainly none) of the potential seed predators are likely to survive the inter-mast period. Yet seed predation is hypothesized by Janzen to be the selective force behind this, as well as other masting phenomena. How can seed predation be so important? To understand that we need to recognize 1) how large the seed crop can be and 2) how large the response and variety of seed predators can be. It seems almost everybody (including man) likes to eat bamboo seed. It is (surprisingly, to me at least) slightly more nutritious than either rice (brown, of course) or wheat among commonly consumed grains in the human diet. Among the 'natural' consumers are small rodents, wild pigs, and the jungle fowl (the progenitor of the domestic chicken). Janzen claims, possibly controversially, that domestication of the chicken and pig may have been possible because of their dependence on bamboo seed crops, and the ability of man to substitute managed annual seed crops for natural and mast seed crops. The response of natural seed predators to this mast crop is dramatic. The functional response includes an increase of 50-100% in the number of eggs/clutch in the jungle fowl (remember that this species is an indeterminate egg layer, but has a fixed brood size, normally 2). Numerical responses through migrations of enormous proportion are anecdotally reported in that historical literature. Rat 'plagues' follow mast years as a result of migration plus reproduction; in Africa movements of flocks of weaver finches numbering in the millions follow geographic 'migration' of the mast crops. Table 1 The range of intermast intervals in bamboos which flower synchronously over large areas. Genera Locations Intermast Interval Arundinaria spp. Kenya, Himalayas 11 - >50 Bambusa spp. India, Burma,Brazil 31 - 150+ Chusquea spp. Jamaica, Chile,Brazil 15 - 34 Dendrocalamus spp. India, Burma 15 - 117 Phyllostachys spp. China, Japan 13 - 120 The responses observed in P. bambusoides follow logically when you know the size of the crop. Though the reports may be extreme (remember, Janzen's trying to make a case) seed crops 5-6 inches deep (a solid layer of seeds) below parental stalks are observed. Larger seeded species prevented accurate surveys by endangering the workers; seeds fell in such profusion that equipment was damaged and workers injured. This level of mast crop production is a partial explanation for the observed life history. A crop of this proportion can satiate seed predators, and therefore permit some of the seeds to escape predation to establish the next generation. But why is the masting cycle 1)so long and 2) so tight in timing? The explanation for length and tight timing, both under genetic control, comes, in part, from the effect of the seed predators. There will be relative synchrony in flowering in bamboos because they are wind-pollinated and apparently obligate outcrossers. That alone would impose local synchrony; it would cause high levels of local pollen flow, but severly limit genetic exchange between demes. Seed predators sharpen that synchrony, and impose it over larger geographical areas. Janzen argues that plants which anticipate the mast year (say by one year) are unlikely to produce sufficient seed to satiate seed predators. However, predator populations are likely to be of moderate size, since there has been no recent mast crop, and it's possible that a few seeds might escape. those that delay until after the mast year will face insurmountable problems. They face predation from a fully expanded predator population (from both functional and numerical responses), and are very unlikely to escape seed predation. Seed crops of these plants will be wiped out. Only man, by lazily harvesting only when its easy, i.e. during the mast year, may select against synchrony. The loss of genotypes which flower slightly out of synchrony explains why the masting cycle is so tight. (Note again the potential effect of artificial selection, working against this pattern). It should be mentioned that mast year crops don't, in nature, wait around for slow- witted predators. They germinate quite rapidly, and seedlings are not heavily predated. The question of long inter-mast periods remains. How does an interval of approximately 120 years evolve? Janzen hypothesizes a scenario that begins with an annually iteroparous bamboo, representing the most common life history among bamboo species. Since seed predators are common, and escape of seed rare (unpredictable reproductive success), an individual that switched to semelparity (a chance mutation within the population) and was able to produce a much larger seed crop might satiate the local, numerically adapted population of seed predators and increase the number of seeds escaping predation. Its larger seed crop means that among escapees, offspring of the semelparous mutant will slowly increase their proportion in the population. This, of course, occurring at the expense of parental death. Janzen believed this switch would likely have been successful only in the tropics. Predictable rainy seasons would bring escape through germination, and the commonness of territoriality among seed predator species would limit local numerical responses. Once semelparous, mutations which produce delay will be selected for against the 'wild-type'(iteroparous) parental stock. The longer these new mutants wait, the larger their energy reserves, seed output, and success compared to whatever increases in predation they draw to the seed crop of the parental+mutant population. When the iteroparous parental stock has been completely replaced, slight further shifts in alpha are strongly selected against. This follows from the explanation for why timing is so tight. Tails of the distribution of seed production are more completely devoured than the peak, since seed predator adaptations are designed for mast reproduction. We now have a semelparous population with a moderate (??) inter-mast period. How are extremely long inter-mast intervals achieved? By doubling the previous period. Such a mutation permits the bearer to produce larger numbers of seeds than those who lack it, yet achieves the buffering (protection) of producing seed simultaneous with the parental populations. The same kind of advantage that led to the switch to semelparity now leads to replacement by a doubled-population. Toward the end of the replacement process, selection against the parental stock may be quite strong. Although details may differ, predator satiation is also argued to be the mechanism by which periodical cicadas evolved (Lloyd and Dybas 1966). Thus the basic ideas of evolution of long-lived perennial semelparity are not unique to bamboos, after all. To fully consider the possible reasons for delayed reproduction in bamboos, it's important to recognize there may be reasons other than seed predator satiation. Most 'tree-like' plants increase in biomass logistically. The relative growth rate (the realized 'r' or growth rate per head) declines with size and age, since height growth and structural tissue is supported by a 'crown' of photosynthetic leaves which reach a 'relatively' constant biomass. That's not true of bamboos. They are grasses, reproducing vegetatively to produce large clumps (genets) in which each culm (ramet) grows to full adult height, producing a full adult compliment of leaves and maintaining a green stem. Thus photosynthetic and support tissues increase in parallel, and genet growth remains exponential over an extended period. That means that the biomass potentially available for allocation to reproduction also continues to increase rapidly (exponentially) until mast seeding. How much reproduction are we talking about? You already have an image of the total seed crop beneath synchronized, mast flowering bamboos. To indicate how common such species are Gadgil and Prasad (1984) found that 70 of 72 Indian bamboo species were perennial monocarps, but that only 8 were synchronized over wide geographic areas. The basic life history is, therefore, common, but Janzen's arguments of the importance of mobile seed predators in producing and synchronizing it possibly less common. Can the idea of exponential growth increasing seed production without reference to predators also explain a massive mast reproduction. Let's consider it on the basis of flowering per adult stem. Flowers on grasses are organized on spikes, with a spike of flowers at each node (the slightly thicker rings on a piece of dried bamboo). Gadgil found in one of the synchronized, mast flowering species, Bambusa arundinacea the following flowering rates: 65 flower bearing nodes/ramet x 133 spikes per node x 156 flowers per spike = 1.3 x 106 flowers/culm at mast flowering x 50-200 culms/genet Even with the limitations of wind pollination, 24% of seeds had developed endosperm, resulting in 150-800 Kg of seeds/genet, and an allocation of biomass to reproduction of between 20-30%. Not only is the total impressive, but the allocation to reproduction in bamboos is far higher than in trees (usually at most a few percent). This is without reference to predators. Both 'stories', taken together make the advantage of delayed, mast flowering clear. Cactus flower re-visited - but not the movie Optimization of fitness as maximization of the sum of current reproduction and residual reproductive value. Curves predicting semelparity are concave; those predicting iteroparity are convex. Are predator satiation and/or clonal growth the only mechanisms which can produce perennial monocarpy? Not if interpretations of life history forces in Agaves are correct. Schaffer, in a series of papers with many coauthors, came to the conclusion that, in theory, any species should maximize the sum of current fecundity (or mx) and expected future reproductive value (which can be determined from proprtional survivorship and reproductive value of the next age class, i.e. px and Vi+1). Graphing these two components on separate axes, a maximum is achieved by greatest distance from the origin. Maximization of the sum is, of course, the way to maximize fitness. If the curve is concave, maximum distance from the origin is at one of the end points, i.e. either retain all energy for future reproduction, or use all available energy. Concave curves produce semelparity, with delay if, early on, expectation of future reproduction exceed possible present offspring production. Convex curves produce iteroparity, with partial allocation to present reproduction. How can this fit with Janzen's (or Gadgil's) explanation for bamboos. An intermediate reproductive effort (and iteroparity) might be swallowed up, literally and figuratively, by seed predators, but the percentage seed set increases with bi through satiation in Janzen's view. Gadgil notes that until genet 'senescence', at least in growth rate, the expectation of future reproduction with clonal growth markedly exceeds present reproductive output potential. Neither of these is what the Schaffer's see in Agaves. Instead, they argue that optimal foraging by pollinators will maximize the seed set of individuals making the largest reproductive effort. This, too, selects for semelparity in isolated, individual Agave plants. If it costs a pollinator considerable energetic output to get from isolated plant to isolated plant, he should logically choose those which offer the most food for the least flight cost, i.e. those with more flowers (or greater reproductive effort from the plant's point of view). That's just optimal foraging in a very simple form. Now, what evidence is there that Agaves are pollinated by foragers functioning optimally, and that optimal foraging leads to delayed semelparity? a) At least for the group of semelparous Agaves, but not for congeneric iteroparous species, there is a significant positive correlation between the percent of flowers which successfully produce fruit and the size of the inflorescence. Note that this is not a correlation with total flower number. The number of fruits would logically increase with number. This is a tougher challenge. The positive correlation is with percentage of flowers developing fruit. This corresponds to the curvilinear profit function associated with semelparity. b) The same conclusion can be reached from the opposite point of view, i.e. from the point of view of pollinator behaviour. The number of pollinators observed on a plant per centimeter of inflorescence was positively correlated with inflorescence length (which is proportional to the number of flowers). More pollinators were attracted to each flower in larger floral displays. This correlation was larger in semelparous species of agave than in iteroparous ones, even though the same pollinator, Bombus sonoris, works both semelparous and iterparous agave species. An interesting, but unanswered question, is why pollinator selectivity should be different in agaves with differing life histories when the flowers look virtually identical. Are There Semelparous Mammals? Thus far two long-lived semelparous plants have been the examples of life histories representing exceptions to the patterns expected a priori. We expect semelparous species to be short-lived. At the same time, we expect mammals, relative to other land animals usually considered K-types, to be long-lived and iteroparous, with typically Deevey type I survivorship curves. Thus equally exotic is the idea of a short-lived, semelparous mammal. There is at least one exception of this type, a marsupial mouse genus, Antechinus, from Australia. Species within the genus vary in life history. Females of all species are iteroparous; at least moderate numbers survive to reproduce in a second year. Males differ among species. Some are similarly iteroparous. Those species live in the tropical rain forests of New Guinea, where resources are predictably available, or in arid central Australia, where resource availability is highly unpredictable. In the former conditions, much like the situation in mature forests, adult survivorship is relatively predictable as well. However, with populations consistently near carrying capacity, juvenile success is not well assured. Whether you want to consider Murphy's model of the predictability of success or compare the P and C for these populations, the predicted and observed strategy is iteroparity. With extremely unpredictable resources, as in central Australia, the argument can be made that adults are 'more experienced' and 'better buffered' from stored energy against unpredictability. Lump this together as a hypothesis of tolerance. Once more, therefore, P is much larger than C and iteroparity appears to be the predicted strategy. More evidence about the survivorship patterns in these populations would help to overcome hand-waving, but it hasn't, to my knowledge, been collected. Other species, however, have semelparous males. They occur in highly predictable, but highly seasonal environments; forests, woodlands and heaths of coastal forest regions along much of eastern and southern Australia support these species. Their reproductive cycles are strongly adapted to the seasonal pattern. The period from gestation through lactation takes about 4 months, and weaning occurs between November and February, i.e. during the southern hemisphere summer. If an additional cycle of reproduction were to occur during a single year, as it does in other, ecologically similar, placental (eutherian) mammals in similar temperate environments, the longer cycle in the marsupial would place maximum resource demands at an inappropriate time (winter) with respect to resource abundance. At the time of lactation and weaning for the second brood there would be little insect (the key food) abundance to support it. Given limited survivorship of males to reproduce in a second year in a seasonal environment, it's possible that selection could (and/or should) maximize reproductive effort in the first year for these marsupials. If there is to be but one chance to reproduce, the behavioural responses of Antechinus males, and the consequences of the behaviour pattern, become logical. At the time of breeding, males become highly aggressive and disperse widely. Dominant males sire a great preponderance of the offspring, and others are driven off. The effort required to achieve dominance is very high. The relationship between effort and reproductive success is, therefore, very shallow (approximately 0 success at low to medium effort) then rises very steeply at the right hand (high effort) side of a graph. This cost curve is one which predicts semelparity. Associated with the increased aggressiveness is increqased adrenocortical activity. By the end of the mating season males suffer from a form of the Selye stress syndrome. As was hypothesized to explain microtine cycling, the stress syndrome means that there is a lack of appropriate response to normal levels of stress - the protective kind of response - as well as immune suppressive responses associated with adrenal hormone titre changes, and complete regression of the testes. While, in theory, males could survive to a second year, in practice no males survive the post-reproductive period. There is also an interesting corollary to this in the energetics and resource availability which result from male semelparity. Females raise their litters in the absence of an adult male population, and thus in the absence of food requirements to support those males. Litter sizes can therefore be larger, as well as the size of the littermates, in species with semelparous males. Does the shift in size fit with the basic hypotheses formulated by Cole in constructing the paradox, or with the modifications made to improve reality? Is there a sufficient increase in litter size for these 'semelparous' males to match the population growth of an iterparous Antechinus? Larger litter sizes are consistently observed in the male-semelparous Antechinus species, with average litter size in the range of 10-12 young, than in iteroparous congeners, with litter sizes from <8-10. Now compare with the paradox. for Antechinus is 1 year. Pre-reproductive survivorship is considerably less than 1, but in a highly seasonal environment the adult survivorship is also much less than 1 if the species were iteroparous. Thus, there is a rough simiilarity to the scheme Cole used to construct the paradox, and an appropriately larger litter size, i.e. 1 or 2 larger, in the semelparous species to achieve approximately equal population growth. So we finish this section hjaving found that Cole's paradox is not only correct in theory, but may have a parallel 'proof' in the real world. References Bell, G. 1984. Measuring the cost of reproduction. I. The correlation structure of the life table of a plankton rotifer. Evolution 38:300-313. Braithwaite, R.W. and A.K. Lee. 1977. A mammalian example of semelparity. Amer. Natur. 111:151-154. Bryant, E.H. 1971. Cole's result revisited. Amer. Natur. 105:75-77. Cole, L. 1954. The population consequences of life history phenomena. Quart. Rev. Biol. 29:103-137. Gadgil, M. and P. Prasad. 1984. Ecological determinants of life history evolution of two Indian bamboo species. Biotropica 16:161-172 Janzen, D.H. 1976. Why bamboos wait so long to flower. Ann.Rev.Ecol.Syst. 7:347-391. Linden. M. 1988. Reproductive tradeoff between first and second clutches in the great tit Parus major: an experimental study. Oikos 51:285-290. Mertz, D.B. 1975. Senescent decline in flour beetle strains selected for early adult fitness. Physiol. Zool. 48:1-23. Murphy, G.I. 1968. Patterns in life history and environment. Amer. Natur. 102:390-404. Nur. N. 1988. The consequences of brood size for breeding blue tits. III. Measuring the cost of reproduction: survival, future fecundity, and differential dispersal. Evolution 42:351-362. Schaffer, W.M. and M.V. Schaffer. 1977. The adaptive significance of variations in reproductive habit in the Agavaceae. pp.261-276. in Evolutionary Ecology. B. Stonehouse and C. Perrins, eds. MacMillan, N.Y. Smith, J. 1981. Does high fecundity reduce survival in song sparrows. Evolution 35:1142. Vermet, P. and J.L. Harper. 1980. The costs of sex in seaweeds. Biol. J. Linnean Soc. 13:129-138. Willson, M. 1983. Plant Reproductive Ecology. Wiley, New York.