Biphasic growth in fish II: empirical assessment

In [Quince, et al., 2008. Biphasic growth in fish I: Theoretical foundations. J. Theor. Biol., doi:10.1016/j.jtbi.2008.05.029], we developed a set of biphasic somatic growth models, where maturation is accompanied by a deceleration of growth due to allocation of energy to reproduction. Here, we use growth data from both hatchery-raised and wild populations of a large freshwater fish (lake trout, Salvelinus namaycush) to test these models. We show that a generic biphasic model provides a better fit to these data than the von Bertalanffy model. We show that the observed deceleration of somatic growth in females varies directly with gonad weight at spawning, with observed egg volumes roughly 50% of the egg volumes predicted under the unrealistic assumption of perfectly efficient energy transfer from somatic lipids to egg lipids. We develop a Bayesian procedure to jointly fit a biphasic model to observed growth and maturity data. We show that two variants of the generic biphasic model, both of which assume that annual allocation to reproduction is adjusted to maximise lifetime reproductive output, provide complementary fits to wild population data: maturation time and early adult growth are best described by a model with no constraints on annual reproductive investment, while the growth of older fish is best described by a model that is constrained so that the ratio of gonad size to somatic weight (g) is fixed. This behaviour is consistent with the additional observation that g increases with size and age among younger, smaller breeding females but reaches a plateau among older, larger females. We then fit both of these optimal models to growth and maturation data from nineteen wild populations to generate population-specific estimates of ‘adapted mortality’ rate: the adult mortality consistent with observed growth and maturation schedules, given that both schedules are adapted to maximise lifetime reproductive output. We show that these estimates are strongly correlated with independent estimates of the adult mortality experienced by these populations.     

Polyfluorochrome marking slows growth only during the marking month in the green sea urchin Strongylocentrotus droebachiensis

Abstract. Used singly, the fluorochrome tags tetracycline and calcein have yielded important insights into sea urchin biology, especially regarding growth. We present a new method of tagging using sequential fluorochrome markers, as well as a more precise method of quantifying growth. Such polyfluorochromes enable repeated markings that allow measurement of multiple growth points and unique identification of individuals or groups. We marked sea urchins, Strongylocentrotus droebachiensis , with four fluorochromes: alizarin complexone, calcein, calcein blue, and tetracycline. All fluorochromes marked both by injection and immersion. We examined the clarity of the mark produced with low, metabolically scaled doses, and higher doses similar to those that have been previously used. We tested the effect of fluorochromes on survival, growth, jaw size, and gonad size by marking a size range (3.9–44.3 mm in diameter) of urchins with either one or all four fluorochromes. We quantified growth using a nominal diameter, that is a fitted constant, times the cube root of weight, which increased the precision of measurements by a factor of six relative to measured diameter. Growth rate was a decreasing function of diameter except for a growth lag in the smallest urchins. Growth rate data for all sizes were fitted using: gamma distributions; Tanaka functions; and, for larger sizes, straight lines (von Bertalanffy model). All treatments produced clear marks, with higher doses producing more reliably clear marks. Tetracycline marking did not affect growth; other treatments produced only transient slowing of growth in the marking month. Growth rate, survival, gonad production, and jaw weight did not differ between control and treatments during the following 6 months. Thus, polyfluorochromes produce reliable marks that do not significantly affect growth or gonad production.     

Experimental testing of dynamic energy budget models

1. Dynamic energy budget (DEB) models describing the allocation of assimilate to the competing processes of growth, reproduction and maintenance in individual organisms have been applied to a variety of species with some success. There are two contrasting model formulations based on dynamic allocation rules that have been widely used (net production and net assimilation formulations). However, the predictions of these two classes of DEB models are not easily distinguished on the basis of simple growth and fecundity data.
2. It is shown that different assumptions incorporated in the rules determining allocation to growth and reproduction in two classes of commonly applied DEB models predict qualitatively distinct patterns for an easily measured variable, cumulative reproduction by the time an individual reaches an arbitrary size.
3. A comparison with experimental data from Daphnia pulex reveals that, in their simplest form, neither model predicts the observed qualitative pattern of reproduction, despite the fact that both formulations capture basic growth features.
4. An examination of more elaborate versions of the two models, in which the allocation rules are modified to account for brief periods of starvation experienced in the laboratory cultures, reveals that a version of the net production model can predict the qualitative pattern seen for cumulative eggs as a function of mass in D. pulex . The analysis leads to new predictions which can be easily tested with further laboratory experiments.     

The importance of growth and mortality costs in the evolution of the optimal life history

A central assumption of life history theory is that the evolution of the component traits is determined in part by trade-offs between these traits. Whereas the existence of such trade-offs has been well demonstrated, the relative importance of these remains unclear. In this paper we use optimality theory to test the hypothesis that the trade-off between present and future fecundity induced by the costs of continued growth is a sufficient explanation for the optimal age at first reproduction, alpha, and the optimal allocation to reproduction, G, in 38 populations of perch and Arctic char. This hypothesis is rejected for both traits and we conclude that this trade-off, by itself, is an insufficient explanation for the observed values of alpha and G. Similarly, a fitness function that assumes a mortality cost to reproduction but no growth cost cannot account for the observed values of alpha. In contrast, under the assumption that fitness is maximized, the observed life histories can be accounted for by the joint action of trade-offs between growth and reproductive allocation and between mortality and reproductive allocation (Individual Juvenile Mortality model). Although the ability of the growth/mortality model to fit the data does not prove that this is the mechanism driving the evolution of the optimal age at first reproduction and allocation to reproduction, the fit does demonstrate that the hypothesis is consistent with the data and hence cannot at this time be rejected. We also examine two simpler versions of this model, one in which adult mortality is a constant proportion of juvenile mortality [Proportional Juvenile Mortality (PJM) model] and one in which the proportionality is constant within but not necessarily between species [Specific Juvenile Mortality (SSJM) model]. We find that the PJM model is unacceptable but that the SSJM model produces fits suggesting that, within the two species studied, juvenile mortality is proportional to adult mortality but the value differs between the two species.     

The commercial potential of the common sea urchin Echinus esculentus from the west coast of Scotland

Sea urchin roe is a valuable food product. The commercial potential of Echinus esculentusL. (Echinodermata: Echinoidea) was assessed both by surveying field populations and gonad growth in response to artificial feeds. Urchins were collected from four locations on the Scottish west coast between June and August of 1998. The roe content was found to be of variable quality. A relatively low percentage of urchins (34.9%) had roe which was considered marketable both in terms of yield and colour. Urchins with a marketable yield of roe were found where algal growth or encrusting organisms were most prolific. Good roe colours and high roe yields were not necessarily coincident. The data suggest an urchin fishery is likely to be impractical economically. In tank-based trials large E. esculentus were fed either commercially available salmon feed, a pelletised urchin diet or the macroalgae Laminaria saccharina. Urchins fed the artificial diets increased in test diameter during the 24-week experiment. At the end of the trial urchins fed salmon feed had a significantly higher gonad and alimentary index than those in the other treatments. E. esculentusis able to successfully exploit a diet rich in animal-origin oils. The diets also influenced gonad colour. The proportion of urchins with marketable gonad colours was highest (85%) in the treatment receiving salmon feed. As this species appears robust in culture and as artificial diets promote somatic and gonadal growth, an investigation into the practicalities of a fully farmed approach to gonad production may be worthwhile.     

Optimal resource allocation of the marine bivalve Yoldia notabilis: The effects of size-limited reproductive capacity and size-dependent mortality

The effects of the morphological constraint of maximum reproductive output (reproductive capacity) and the size at which individuals can avoid heavy mortality (refuge size) on the resource allocation pattern between growth and reproduction are investigated using a dynamic modelling approach for a population of Yoldia notabilis (Mollusca: Bivalvia) in Otsuchi Bay, northeastern Japan. A state variable model is developed using field data on shell length, somatic weight, production, survivorship and reproductive capacity of the bivalve. The optimal allocation pattern is characterized by sudden switching from growth to reproduction without the assumption of reproductive capacity, while simultaneous investment in growth and reproduction becomes optimal when maximum reproductive output is limited by reproductive capacity. Size-specific reproductive effort, size at maturity and the growth curve predicted by the latter model fit more closely to the field data, suggesting that size-limited reproductive capacity can play an important role in the evolution of the observed resource allocation pattern. The mortality pattern affects optimal size at maturity, but not size-specific reproductive effort after maturity. When refuge size is fixed, optimal size at maturity increases with survivorship above refuge size. Optimal size at maturity changes in a more complex way with changes in refuge size. Size at maturity remains constant when refuge size is small, increases when it is intermediate, and decreases when it is large. The results suggest that refuge size is an important factor in the evolution of size at maturity, although its contribution varies depending on the values of other factors, such as size-dependent production and survivorship above refuge size. This revised version was published online in July 2006 with corrections to the Cover Date.     

Seasonal patterns of carbon assimilation and allocation of a summer-green forest herb, <Emphasis Type="Italic">Parasenecio</Emphasis> <Emphasis Type="Italic">auriculata</Emphasis> (Senecioneae; Asteraceae)

Summer-green herbs inhabiting deciduous forests often put out aerial shoots under bright conditions before tree-canopy closure and grow until late summer under the closed canopy. Some of them produce leaves continuously even after the initiation of canopy closure, indicating an exploitation of the low light period. The manner of carbon assimilation during bright and shade periods within a growth season should reflect the seasonal patterns of vegetative growth and reproductive allocation of individual species. We examined the seasonal patterns of assimilation, partitioning of photosynthate between reproduction and storage, and the budget of reproduction of a perennial understory herb, Parasenecio auriculata. Although photosynthetic rates per unit leaf area decreased with the seasonal reduction in light level, net assimilation at the whole-plant level was maintained at a high level even after canopy closure owing to the increase in the total leaf area. Stored resource in tubers contributed to the rapid development of aerial shoots in the early season, and annual tuber growth was completed before flowering. Instant photosynthetic products considerably contributed to the maintenance of flowers but not to fruit development because of low assimilation rate during fruiting. These findings indicated that carbon assimilation during flowering contributes to sexual reproduction without influencing the development of storage organs. Stable carbon assimilation over summer by shade-acclimatized leaves enabled the maintenance of high productivity associated with high sexual reproduction.     

Conserved ontogeny and allometric scaling of resource acquisition and allocation in the Daphniidae

Life histories vary widely among taxa, but within phylogenetic groups there may be a fundamental framework around which trait variation is organized, perhaps as a consequence of lineage-specific developmental constraints. In organisms with indeterminate growth, there is an ongoing problem of optimally allocating resources between growth and reproduction, and that allocation decision may manifest itself through allometric scaling. Previous work on freshwater zooplankton has shown that the ontogenetic pattern of resource allocation can be described by simple mathematical functions. An important component of understanding how such functions can explain life-history variation is to discover which parameters in these functions are robust, with respect to both resource availability and evolutionary diversification, and which parameters exhibit interspecific allometry. To shed light on these issues, detailed life table experiments were conducted on eight species in the family Daphniidae (Crustacea) at high and low levels of resources. Using data on growth, reproduction, and instar duration, the ontogeny of resource allocation to growth and reproduction could be described as functions that plateau at or shortly after the onset of maturity. To be sure that the results were not an artifact of phylogenetic structure, the parameters were tested in a phylogenetically controlled fashion. The results suggest a simple set of resource allocation rules for daphniids, whereby all species exhibit a similar form of ontogenetic change in allocation, and reach a plateau where approximately 94% of available resources are allocated to reproduction. The asymptotically maximal rate of net resources incorporated in growth and reproduction was positively related to size at maturity, whereas the rates of approach to plateaus (for both net resource assimilation and proportional allocation to reproduction) were negatively related to body size. Per-offspring investment was positively related to the square root of size at maturity. Using this approach, a wide range of interspecific variation in life-history features can be related to a single underlying trait, the size at first reproductive investment.     

苹果果实生长的数学模型及各生长指标间的相关性分析

以富士苹果(Malus domestica‘Fuji’)为试材,测定其果实生长发育期间各生长指标的动态变化,选择5种理论生长方程对纵径、横径、单果重、体积、干重进行拟合,并根据拟合结果确定合适的生长方程建立各生长指标的数学模型,采用多项式拟合建立果形指数变化的数学模型,同时对果实各生长指标之间进行相关性分析。结果表明,果实纵径、横径生长适合选择Logistic方程,单果重、体积、干重适合选择Gompertz方程,果形指数的变化适合采用多项式拟合;果实纵径、横径、单果重、体积、干重两两之间均呈显著正相关,果形指数、果实干物质相对含量均与纵径、横径、单果重、体积、干重之间呈显著负相关,果实密度与纵径、横径、单果重、体积、干重之间呈显著负相关,而与果形指数、果实干物质相对含量之间呈显著正相关。     

The effect of feeding or starvation on resource allocation to body components during the reproductive cycle of the sea urchin Sphaerechinus granularis (Lamarck)

To determine the effects of feeding or starvation on resource allocation to body components during the reproductive cycle of Sphaerechinus granularis, sea urchins were placed in laboratory tanks and either fed ad libitum or starved during two different periods of their biological cycle, i.e. the mature stage and the recovery stage. The urchin growth was monitored over the whole experimental period, the gonad, gut, lantern indices and organic matter levels of different organs were determined at the end of the experiment. During the mature stage sea urchins in good nutritional conditions did not increase in size, but allotted energy to gonad production and stored reserves in body wall. Limiting food stopped the gonadal growth without complete regression. During the recovery period food allowed somatic growth, i.e. test growth and the storage of reserves in gonad somatic cells. This somatic production did not occur under food-limited conditions and the resources allotted for survival and maintenance were taken from different body components.     

Twelve fundamental life histories evolving through allocation‐dependent fecundity and survival

An organism's life history is closely interlinked with its allocation of energy between growth and reproduction at different life stages. Theoretical models have established that diminishing returns from reproductive investment promote strategies with simultaneous investment into growth and reproduction (indeterminate growth) over strategies with distinct phases of growth and reproduction (determinate growth). We extend this traditional, binary classification by showing that allocation‐dependent fecundity and mortality rates allow for a large diversity of optimal allocation schedules. By analyzing a model of organisms that allocate energy between growth and reproduction, we find twelve types of optimal allocation schedules, differing qualitatively in how reproductive allocation increases with body mass. These twelve optimal allocation schedules include types with different combinations of continuous and discontinuous increase in reproduction allocation, in which phases of continuous increase can be decelerating or accelerating. We furthermore investigate how this variation influences growth curves and the expected maximum life span and body size. Our study thus reveals new links between eco‐physiological constraints and life‐history evolution and underscores how allocation‐dependent fitness components may underlie biological diversity.     

Some effects of light on the energetics of Daphnia pulex and implications for the significance of vertical migration

Energy budgets were computed from data obtained for Daphnia pulex cultured under nine light intensities, polarized light and four wavelength ranges. The percent assimilation of preadult animals is highest at intensities above 7 ft-c. Net efficiency of growth was highest (> 50%) and the net efficiency of respiration was lowest ( < 49%) at intensities less than 28 ft-c. The percent assimilation of adult animals was highest ( > 10%) at 110, 55 and 14 ft-c. Under the nine intensities the gross efficiencies of growth were less than 1 % and net efficiencies of growth varied from 3.9 to 7.3%. Gross efficiencies of respiration were highest above 7 ft-c. The net efficiency of respiration usually varied between 20 and 30% and the lowest was 9.8% at 1.7 ft-c. and the highest was 50.1% at 110 ft-c. Gross efficiency of reproduction varied from 2.6% at 3.5 ft-c to 12.6% at 14 ft-c and generally varied between 4 and 7.5%. Net efficiency of reproduction varied from 45.9% at 110 ft-c to 84.3% at 1.7 ft-c and usually varied from 62 to 75% at other light intensities. The ratio of energy of respiration to energy of growth and reproduction ranged from 12% to 1.7 ft-c to 105.3% at 110 ft-c. This ratio usually varied from 25 to 34% at 14 ft-c or less and exceeded 37% at intensities above 14 ft-c. The percent assimilation (3.5%), gross (2.0%), and net (56.3%) efficiencies of respiration of preadult animals raised under polarized light were higher than for those at a similar, nonpolarized, intensity. The net efficiency of growth (43.7%) was lower under polarized light. The percent assimilation, gross efficiencies of growth, reproduction and respiration, net efficiencies of growth and reproduction of adult animals under polarized light (6.6 ft-c) were lower than for those under 7 ft-c. For preadult animals assimilation efficiencies were lower in wavelength treatments than in white light or darkness. The gross efficiencies of growth and respiration were lowest under red wavelengths and the net efficiencies of growth were lowest and respiration highest under green wavelengths. For adult animals, the assimilation efficiencies were lower in the wavelength treatments than those obtained in other light treatments. While the gross efficiencies of growth, reproduction and respiration were generally lower, the net efficiencies of growth and reproduction were generally within the range of values for other light conditions. The net efficiencies of respiration, except for red wavelengths, were lower than those for other light conditions except at 1.7 ft-c. The ratio of energy of respiration to energy of growth and reproduction showed similar trends. The effects of wavelength are generally separable from the effects of light intensity.     

Growth and reproduction of the bay scallop, Argopecten irradians (Lamarck) at its southern distributional limit

Growth and reproduction in a Florida population of bay scallop, Argopecten irradians (Lamarck), existing at the southern limit of its distribution, was monitored over a 3-yr period. Somatic growth accompanied increasing water temperature between May and August, when maximum mantle, digestive gland, and adductor muscle weights and indexes were observed. From July through September, reproductive development was correlated with a decline in adductor muscle weight and index. Maximum gonad weight, gonad index, and oocyte diameter were found in late September and early October. Spawning commenced at this time in conjunction with decreasing water temperature.In comparison to more northern populations, the reproductive cycle of the Florida bay scallop occurs later in the year and is characterized by a higher gametogenic initiation temperature, a decreased maximum gonad index and decreased oocyte diameter, and a shift in reproductive energy resources from digestive gland (available food) to adductor muscle (pre-stored reserves). Increased metabolic rate associated with higher temperature and coupled with decreased food supply results in the Florida bay scallop having less energy available for reproduction, ultimately limiting its southern distribution.     

Allocation of pyloric caecum reserves in FED and starved sea stars, Pisaster giganteus (Stimpson): somatic maintenance comes before reproduction

Pyloric caeca were removed through the raytips of sea stars, Pisaster giganteus (Stimpson), beginning their seasonal period of gonad growth. Four months later their feeding rate, gonad growth, and gametogenic activity were lower than those of intact animals, while body growth rate remained the same. Removal of only the raytips also depressed feeding rate and gonad growth. When sea stars were starved, gonad growth and gametogenic activity were lower in animals without pyloric caeca, but body weight loss was the same as in intact animals. We conclude that when food is abundant, materials are utilized to enhance somatic and gonad growth. With decreasing reserves, due either to reduced food intake and/or pyloric caecum removal, somatic maintenance and growth have priority over gonad growth in material and energy allocation. Such a pattern of resource allocation is appropriate for long-lived iteroparous animals, such as these sea stars.     

Plant reproductive allocation predicts herbivore dynamics across spatial and temporal scales

Life-history theory suggests that iteroparous plants should be flexible in their allocation of resources toward growth and reproduction. Such plasticity could have consequences for herbivores that prefer or specialize on vegetative versus reproductive structures. To test this prediction, we studied the response of the cactus bug (Narnia pallidicornis) to meristem allocation by tree cholla cactus (Opuntia imbricata). We evaluated the explanatory power of demographic models that incorporated variation in cactus relative reproductive effort (RRE; the proportion of meristems allocated toward reproduction). Field data provided strong support for a single model that defined herbivore fecundity as a time-varying, increasing function of host RRE. High-RRE plants were predicted to support larger insect populations, and this effect was strongest late in the season. Independent field data provided strong support for these qualitative predictions and suggested that plant allocation effects extend across temporal and spatial scales. Specifically, late-season insect abundance was positively associated with interannual changes in cactus RRE over 3 years. Spatial variation in insect abundance was correlated with variation in RRE among five cactus populations across New Mexico. We conclude that plant allocation can be a critical component of resource quality for insect herbivores and, thus, an important mechanism underlying variation in herbivore abundance across time and space.     

Resource-dependent sex-allocation in a simultaneous hermaphrodite

Most sex allocation theory is based on the relationship between the resource investment into male and female reproduction and the consequent fitness returns (often called fitness-gain curves). Here we investigate the effects of resource availability on the sex allocation of a simultaneously hermaphroditic animal, the free-living flatworm Macrostomum lignano. We kept the worms under different resource levels and determined the size of their testes and ovaries over a period of time. At higher resource levels, worms allocated relatively more into the female function, suggesting a saturating male fitness-gain curve for this species. A large part of the observed effect was due to a correlated increase in body size, showing size-dependent sex allocation in M. lignano. However, a significant part of the overall effect was independent of body size, and therefore likely due to the differences in resource availability. Moreover, in accordance with a saturating male fitness-gain curve, the worms developed the male gonads first. As the group size was kept constant, our results contrast with expectations from sex allocation models that deal with local mate competition alone, and with previous experiments that test these models.     

Testing for the Effects of Seasonal and Lunar Periodicity on the Reproduction of the Edible Sea Urchin <Emphasis Type="Italic">Tripneustes gratilla</Emphasis> (L) in Kenyan Coral Reef Lagoons

The annual and lunar reproductive cycle of the widely distributed edible sea urchin Tripneustes gratilla (L) was examined through measurements of gonad index, histological examination of gametogenesis, and induction of spawning with KCl injections. The population density and morphological characteristics of urchins at Diani, Kanamai, and Vipingo reef lagoons were also studied as well as the effects of seawater temperature and light on reproduction. Gonad growth started early during the northeast monsoon and reached a peak in June at the beginning of the southeast monsoon followed by a sharp decrease in gonad size of 50% in July and August towards the end of the southeast monsoons. Histological examination of gonads, revealed many different stages of gametogenesis with gametes present throughout the year, indicating continuous reproduction. There was a significant relationship between gonad index and lunar day with spawning occurring between lunar day 7 and 21, but spawning was not in perfect synchrony in the population. The population density of urchins at each reef is variable from year to year and was highest on average at Vipingo. Urchins at Kanamai had the lowest gonad indices, the largest jaws and smallest individuals an indication of food limitation. The gonads (roe) of T. gratilla at all three sites, were perpetually ‘runny’ an attribute that is not suitable for urchin fisheries. Studies to develop techniques to improve roe quality are recommended.     

Growth allocation between height and stem diameter in nonsuppressed reproducing Abies mariesii trees

To understand the growth patterns with respect to competition and leaf‐mass increase in reproducing trees, growth allocation between height and stem diameter was examined for nonsuppressed reproducing Abies mariesii trees in a subalpine forest in northern Honshu, Japan. The growth allocation was analyzed by dividing the relative growth rate of the stem volume into the relative contributions of height and stem‐diameter growth. During a 9‐yr period, height growth and seed‐cone production showed obvious annual variation, while stem‐diameter growth recorded moderate variation. For two of three years of seed‐cone production during the 9‐yr period, trees with larger seed‐cone production were associated with less height growth in the following year of seed‐cone production; however, there was no trend of height growth in the year of seed‐cone production. In the following year of mast seeding, trees with larger stem‐volume growth were associated with less height growth. This trend was also shown for the relationship between the cumulative stem‐volume growth during the 9‐yr period and growth allocation to height, suggesting that trees with a larger biomass increase depress the allocation of photosynthate to competition with a large expenditure for reproduction. In contrast to this, trees with a smaller biomass increase might allocate photosynthate to competition with surrounding trees. The results of this study suggest that an increase in reproductive organs during life history and annual variation in reproduction are closely associated with the growth patterns of the stem in A. mariesii trees.     

Seasonal and artificially elevated temperatures influence bioenergetic allocation patterns in the common pond snail, Physella virgata

Allocation of organic carbon (OC) to primary energetic pathways was estimated under seasonal and artificially elevated ambient temperatures for a field population of a freshwater pulmonate snail, Physella virgata. Allocation to respiration increased with temperature. Snails allocated most assimilated OC to reproduction within their natural temperature range (15 degrees -35 degrees C), where assimilation efficiencies remained relatively stable at 25%-35%. However, in artificially heated waters exceeding 35 degrees C, declining assimilation rates and increasing respiratory demands inhibited allocation to reproduction and growth. At the species' 40 degrees C upper thermal limit, assimilation efficiencies fell below 10%, while average consumption levels more than doubled relative to snails unaffected by the thermal effluent. Ambient temperature substantially influenced OC allocation over P. virgata's natural temperature range and negatively affected growth and reproduction at temperatures approaching or exceeding maximum natural levels.