The variances of the distributions of the combinations of the sexes within mammalian litters: Notes to mark the centenary of the problem

It is 100 years since Gini noted that in some samples of litters of mice and rabbits, the variances of the distributions of the combinations of the sexes are sub-binomial. In other words, in contrast with binomial expectation, there are too many litters in which the sexes are equally balanced, and there are too few unisexual litters. In the intervening years, this finding has been replicated in a number of further species, but no explanation has become established. Potential explanations are reviewed here, and it is suggested that the most likely cause is that, at the time of formation of the zygotes, p, the probability that a zygote will be male, varies from one zygote to another within litters, thus constituting an example of Poisson variation. And it is a standard result in probability theory that such variation causes sub-binomial variance.     

Design and statistical methods in studies using animal models of development

Experiments involving neonates should follow the same basic principles as most other experiments. They should be unbiased, be powerful, have a good range of applicability, not be excessively complex, and be statistically analyzable to show the range of uncertainty in the conclusions. However, investigation of growth and development in neonatal multiparous animals poses special problems associated with the choice of "experimental unit" and differences between litters: the "litter effect." Two main types of experiments are described, with recommendations regarding their design and statistical analysis: First, the "between litter design" is used when females or whole litters are assigned to a treatment group. In this case the litter, rather than the individuals within a litter, is the experimental unit and should be the unit for the statistical analysis. Measurements made on individual neonatal animals need to be combined within each litter. Counting each neonate as a separate observation may lead to incorrect conclusions. The number of observations for each outcome ("n") is based on the number of treated females or whole litters. Where litter sizes vary, it may be necessary to use a weighted statistical analysis because means based on more observations are more reliable than those based on a few observations. Second, the more powerful "within-litter design" is used when neonates can be individually assigned to treatment groups so that individuals within a litter can have different treatments. In this case, the individual neonate is the experimental unit, and "n" is based on the number of individual pups, not on the number of whole litters. However, variation in litter size means that it may be difficult to perform balanced experiments with equal numbers of animals in each treatment group within each litter. This increases the complexity of the statistical analysis. A numerical example using a general linear model analysis of variance is provided in the Appendix. The use of isogenic strains should be considered in neonatal research. These strains are like immortal clones of genetically identical individuals (i.e., they are uniform, stable, and repeatable), and their use should result in more powerful experiments. Inbred females mated to males of a different inbred strain will produce F1 hybrid offspring that will be uniform, vigorous, and genetically identical. Different strains may develop at different rates and respond differently to experimental treatments.     

Optimal offspring size in a small mammal: an exception to the tradeoff invariant life-history rule

Offspring size and number were examined in a captive population of wild guinea pigs ( Cavia aperea ), and findings were compared with models of optimal offspring size for small litters. Median and modal litter size was two, regardless of maternal size or parity. Females producing their second litter tended to have litters that were larger than average. In contrast, young females that were still growing never had litters that were larger than average. Mean offspring size decreased and variation in offspring size tended to decrease with increasing litter size. Optimal offspring size models, in which offspring survival depended on the amount of resources invested, as well as litter size, predict such a trend. Little support was found for Charnov and Downhower's (1995) tradeoff invariant life-history rule that the range in offspring sizes between litters is inversely proportional to the size of the litter. Cavia aperea may be an exception to this rule because pup mass at birth did not reflect total reproductive investment, because conversion of resources into litter mass may not be linearly related to litter size and because resources were not equally partitioned among offspring within large litters. Experimental data are needed to determine the relevance of these results among mammals in general.     

Reproductive biology of captive female Eurasian lynx, Lynx lynx

Studies on wild Eurasian lynx (Lynx lynx) have revealed variation in reproduction between areas, years and individuals. In order to explore potential causes for this variation other than food supply, we analysed data from captive lynx, which provide conditions with minimal environmental variation as all were fed ad libitum. Data from 37 individual female lynx were available from 20 zoos in Norway, Sweden, Finland, Switzerland and the Czech Republic. Data on 177 reproductive events (where a male was available to the female at mating time) are presented. Of these events, 85% resulted in litters being born. Average litter size was 1.95, with a variation from 1 to 4. The mean birth date was 26th May, and sex ratio was not significantly different from parity. The probability of reproduction was related to age, with fewer litters produced by the very young (2–3-year old), and no sign of a senescence effect. However, a clear effect of senescence on litter size was evident. The captive lynx did not have higher reproductive rates than wild lynx, indicating that either factors other than food supply are driving the variation in wild lynx reproduction, or that a factor such as stress may be causing additional variation in the captive population.     

Litter stoichiometric traits of plant species of high-latitude ecosystems show high responsiveness to global change without causing strong variation in litter decomposition

? High-latitude ecosystems are important carbon accumulators, mainly as a result of low decomposition rates of litter and soil organic matter. We investigated whether global change impacts on litter decomposition rates are constrained by litter stoichiometry. ? Thereto, we investigated the interspecific natural variation in litter stoichiometric traits (LSTs) in high-latitude ecosystems, and compared it with climate change-induced LST variation measured in the Meeting of Litters (MOL) experiment. This experiment includes leaf litters originating from 33 circumpolar and high-altitude global change experiments. Two-year decomposition rates of litters from these experiments were measured earlier in two common litter beds in sub-Arctic Sweden. ? Response ratios of LSTs in plants of high-latitude ecosystems in the global change treatments showed a three-fold variation, and this was in the same range as the natural variation among species. However, response ratios of decomposition were about an order of magnitude lower than those of litter carbon/nitrogen ratios. ? This implies that litter stoichiometry does not constrain the response of plant litter decomposition to global change. We suggest that responsiveness is rather constrained by the less responsive traits of the Plant Economics Spectrum of litter decomposability, such as lignin and dry matter content and specific leaf area.     

Analysis of dichotomous response data from certain toxicological experiments

In certain toxicological experiments with laboratory animals, littermate data are frequently encountered. It is generally recognized that one characteristic of this type of data is the "litter effect", i.e., the tendency for animals from the same litter to respond more alike than animals from different litters. In this paper attention is restricted to dichotomous response variables that frequently arise in toxicological studies, such as the occurrence of fetal death or a particular malformation. Various techniques for estimating the underlying probability of response are discussed. A number of generalized models that have recently been proposed to take the litter effect into account are breifly reviewed and compared to the simpler binomial and Poisson models. Various procedures for assessing the significance of treatment-control differences are presented and their relative merits discussed. Finally, future research needs in this area are outlined.     

Estimating a Key Parameter of Mammalian Mating Systems: The Chance of Siring Success for a Mated Male

Studies of multiple paternity in mammals and other animal species generally report proportion of multiple paternity among litters, mean litter sizes, and mean number of sires per litter. It is shown how these variables can be used to produce an estimate of the probability of reproductive success for a male that has mated with a female. This estimate of male success is more informative about the mating system that alternative measures, like the proportion of litters with multiple paternity or the mean number of sires per litter. The probability of success for a mated male can be measured both theoretically and empirically, and gives an estimate of the intensity of sperm competition and of a male's “confidence of paternity” upon mating. The probability of success for mated males for ten “exemplar” species of mammals is estimated and they are compared for insights into the functioning of their mating systems.     

四川红杉-岷江冷杉原始林凋落物K和Na的归还动态

以凋落物为载体的养分归还是生态系统物质循环的主要过程,也是林木生长所需养分的重要来源。相对于其他元素,钾(K)和钠(Na)在调节渗透压方面有着极其重要的作用,且淋溶作用强烈,极易流失,但缺乏必要关注。因此,以海拔3589 m高山峡谷区典型的四川红杉(Larix mastersiana)-岷江冷杉(Abies faxoniana)原始林为研究对象,在2015年9月到2016年8月期间调查了不同类型凋落物中K和Na元素在不同时期的归还特征。结果表明:1)凋落物K和Na元素年归还量分别为25.34和4.44 kg·hm^-2,表现为:凋落叶>凋落枝>其他凋落物>凋落皮>附生植物>繁殖器官。其中,凋落叶和枝占总凋落物K和Na元素归还的85%以上;2)总凋落物、凋落叶和枝的K、Na元素归还动态呈现"双峰型",最大值出现在5月和10月;凋落皮和繁殖器官K、Na元素归还动态呈现"单峰型",最大值出现在5月;3)乔木层树种凋落物的K和Na元素呈现"双峰型"的归还模式,最大值在5月和10月,灌木树种凋落物的K和Na元素呈现"单峰型"归还模式,最大值在9-10月。这些结果说明了高山峡谷区典型针叶林不同类型凋落物元素归还的季节性特征,为进一步认识区域森林物质循环及相关的生态学过程提供了基础数据。     

Microbial communities may modify how litter quality affects potential decomposition rates as tree species migrate

Background and aims

Climate change alters regional plant species distributions, creating new combinations of litter species and soil communities. Biogeographic patterns in microbial communities relate to dissimilarity in microbial community function, meaning novel litters to communities may decompose differently than predicted from their chemical composition. Therefore, the effect of a litter species in the biogeochemical cycle of its current environment may not predict patterns after migration. Under a tree migration sequence we test whether litter quality alone drives litter decomposition, or whether soil communities modify quality effects.

Methods

Litter and soils were sampled across an elevation gradient of different overstory species where lower elevation species are predicted to migrate upslope. We use a common garden, laboratory microcosm design (soil community x litter environment) with single and mixed-species litters.

Results

We find significant litter quality and microbial community effects (P?<?0.001), explaining 47 % of the variation in decomposition for mixed-litters.

Conclusion

Soil community effects are driven by the functional breadth, or historical exposure, of the microbial communities, resulting in lower decomposition of litters inoculated with upslope communities. The litter x soil community interaction suggests that litter decomposition rates in forests of changing tree species composition will be a product of both litter quality and the recipient soil community.     

Determinism of nonadditive litter mixture effect on decomposition: Role of the moisture content of litters

The mechanisms behind the plant litter mixture effect on decomposition are still difficult to disentangle. To tackle this issue, we used a model that specifically addresses the role of the litter moisture content. Our model predicts that when two litters interact in terms of water flow, the difference of evaporation rate between two litters can trigger a nonadditive mixture effect on decomposition. Water flows from the wettest to the driest litter, changing the reaction rates without changing the overall litter water content. The reaction rate of the litter receiving the water increases relatively more than the decrease in the reaction rate of the litter supplying the water, leading to a synergistic effect. Such water flow can keep the microbial biomass of both litter in a water content domain suitable to maintain decomposition activity. When applied to experimental data (Sphagnum rubellum and Molinia caerulea litters), the model is able to assess whether any nonadditive effect originates from water content variation alone or whether other factors have to be taken into account.     

Reproductive output, maternal age, and survivorship in captive common marmoset females (Callithrix jacchus)

Common marmosets (Callithrix jacchus) demonstrate significant variation in reproductive output on both a yearly and lifetime basis in comparison to other anthropoid primates. We explore the factors that may be most important in determining reproductive variation in captive common marmosets. Studies have found that maternal age, maternal condition, and dam survivorship are related to reproductive output; however, these reports are not in agreement and are far from conclusive. With the use of a large, multicolony, demographic database pooling data across five marmoset colonies, we examined litter information for 1,649 litters, and reproductive summaries for 400 dams to assess 1) how reproductive output variation (total production, total weaned production) is determined by litter size, interbirth interval (IBI), age at first birth, and dam survival age; 2) the relationship between maternal age and reproductive output variables; and 3) relationship between the reproductive output variables and survival. We used stepwise regression procedures to describe the amount of variation in lifetime reproductive output among dams, and found that mean litter size accounted for 18% of the variance in total production, survival age accounted for 10.6%, age at first birth accounted for 8.8%, and mean IBI accounted for 5%. For total (nonzero) weaned production, survival age accounted for 7.6% of variance, age at first birth accounted for 7.2%, mean IBI accounted for 2%, and mean litter size accounted for 1.6%. We identified significant effects (P<0.05) of maternal age on litter size and IBI length, but no effect of dam age on weaned litter size. Cox proportional hazards regression analyses revealed significant effects (P<0.01) of number of litters, age at first birth, and site on dam survivorship. Dams that produced more litters showed higher survivorship. Age at first birth showed a positive relationship with dam survivorship, i.e., dams that delayed first reproduction had higher survival. Our findings about reproductive variation in marmosets may have practical applications for the management of marmoset breeding colonies.     

The consequences of differences in litter size for the nursing cat and her kittens

Seventy-one litters of kittens (mean litter size 4.4) were studied from birth to eight weeks of age in order to measure kitten growth and maternal body condition. Few sex differences in growth occur; male and female kittens place a similar burden on their lactating mother. A mother's weight (non-pregnant, non-lactating) interacts with litter size to determine the fate of her growing kittens. A large litter places a burden on both the mother and on the kittens, whose growth is affected; small mothers with large litters are particularly at risk. An acceleration in kitten growth occurs at about 32 days as the kittens take more solid food. This change in growth rate is more marked in large litters. Kittens of light mothers and kittens in large litters are weaned at a lower weight, and kittens of light mothers are weaned earlier. Our results indicate that, under poor environmental conditions, large litters would be less successful than small litters; kitten growth and survival would be affected and providing milk for a large litter would have a detrimental effect on the mother's health. The cost of lactation appears to have been a major evolutionary factor in determining mean litter size.     

Non‐additive effects of litter mixing are suppressed in a nutrient‐enriched stream

Investigations of how species compositional changes interact with other aspects of global change, such as nutrient mobilization, to affect ecosystem processes are currently lacking. Many studies have shown that mixed species plant litters exhibit non‐additive effects on ecosystem functions in terrestrial and aquatic systems. Using a full‐factorial design of three leaf litter species with distinct initial chemistries (carbon:nitrogen; C:N) and breakdown rates (Liriodendron tulipifera, Acer rubrum and Rhododendron maximum), we tested for additive and non‐additive effects of litter species mixing on breakdown in southeastern US streams with and without added nutrients (N and phosphorus). We found a non‐additive (antagonistic) effect of litter mixing on breakdown rates under reference conditions but not when nutrient levels were elevated. Differential responses among single‐species litters to nutrient enrichment contributed to this result. Antagonistic litter mixing effects on breakdown were consistent with trends in litter C:N, which were higher for mixtures than for single species, suggesting lower microbial colonization on mixtures. Nutrient enrichment lowered C:N and had the greatest effect on the lowest‐ (R. maximum) and the least effect on the highest‐quality litter species (L. tulipifera), resulting in lower interspecific variation in C:N. Detritivore abundance was correlated with litter C:N in the reference stream, potentially contributing to variation in breakdown rates. In the nutrient‐enriched stream, detritivore abundance was higher for all litter and was unrelated to C:N. Thus, non‐additive effects of litter mixing were suppressed by elevated streamwater nutrients, which increased nutrient content of all litter, reduced variation in C:N among litter species and increased detritivore abundance. Nutrients reduced interspecific variation among plant litters, the base of important food web pathways in aquatic ecosystems, affecting predicted mixed‐species breakdown rates. More generally, world‐wide mobilization of nutrients may similarly modify other effects of biodiversity on ecosystem processes.     

氮-硫沉降对邓恩桉及杉木人工林凋落物C和N残留率的影响

采用二次正交回归旋转设计,以Na2S04为硫源、46％CO（NH2）2为氮源模拟氮一硫沉降,分析了不同氮一硫沉降水平下邓恩桉（Eucalyptus dunnii Maiden）和杉木[Cunninghamia lanceolata（Lamb．）Hook．]人工林凋落物中C和N残留率的动态变化,并采用Olson指数模型对c和N分解模型进行拟合。结果表明：在不同氮一硫沉降水平下,在1年内随处理时间延长邓恩桉和杉木凋落物的C和N残留率总体上均呈下降趋势;且N较难释放,总体表现为“释放一富集一释放”的动态过程;但在不同氮一硫沉降水平下及不同处理时间凋落物中C和N残留率均有极显著差异（P〈0．01）。凋落物中C和N分解的Olson指数模型的相关性总体上达到极显著或显著（P〈0．05）水平;邓恩桉和杉木凋落物中C和N的平均分解系数分别为0．877和0．208、0．704和0．600,平均周转期分别为3．148和15．877a,4．090和4．947a,显示凋落物中C释放速率大于N,杉木凋落物的C周转期大于邓恩桉但其N周转期则小于后者。在Na2SO4164kg·hm-1·a-1的水平下,氮沉降对邓恩桉凋落物的C和N释放及杉木凋落物的N释放有促进作用,但对杉木凋落物的C释放有抑制作用;在46％CO（NH：）：150或256kg·hm-2·a-1。的水平下,硫沉降也具有同样的作用。随分解时间的延长,邓恩桉凋落物的C／N值呈波动但总体减小的趋势,而杉木凋落物的C／N值呈波动趋势;但在不同氮一硫沉降水平下凋落物的C／N值均有极显著差异,且邓恩桉凋落物C／N值的变化幅度总体上大于杉木凋落物。     

Do non‐additive effects on decomposition in litter‐mix experiments result from differences in resource quality between litters?

Differences in resource quality between litter species have been postulated to explain why litter-mixtures may decompose at a different rate to that which would be predicted from single species litters (termed 'non-additive effects'). In particular, positive, non-additive effects of litter-mixing on decomposition have been explained by differences in initial nitrogen concentration between litter species. This interpretation is confounded because litter species that differ in nitrogen content also differ by a number of other resource quality attributes. Thus, to investigate whether initial nitrogen concentration does account for positive, non-additive effects of litter-mixing, we mixed grass litters that differed in initial nitrogen concentration but not species or structural plant part identity, and then followed mass loss from the litter-mixes over time. We used the litterbag technique and three grass species for which a gradient of four distinct initial nitrogen concentrations had been generated. We produced all no- to four-mix compositions of litter qualities for each species. Litter from different species was never mixed.
Contrary to what would be predicted, we found that when litters of the same species but with different initial nitrogen concentrations were mixed, that negative, non-additive effects on decomposition were generally observed. In addition, we found that once mixed, increasing litter quality richness from two to four mixtures had no significant, non-additive effect on decomposition. Litter quality composition explained little of the experimental variation when compared to litter quality richness, and different compositions generally behaved in the same manner. Our findings challenge the commonly held assumption that differences in nitrogen concentration between plant species are responsible for positive, non-additive effects of litter-mixing on decomposition.     

Variation in reproductive investment among and within populations of the scorpion Centruroides vittatus

Although information concerning variation among and within populations is essential to understanding an organism's life history, little is known of such variation in any species of scorpion. We show that reproductive investment by the scorpion Centruroides vittatus varied among three Texas populations during one reproductive season. Females from the Kickapoo population produced smaller offspring and larger litters than females from the Independence Creek or Decatur populations; this pattern remained when adjusting for among population variation in either female mass or total litter mass. Relative clutch mass (RCM) and within-litter variability in offspring mass (V*) did not differ among populations. Among-population variation may result from genetic differences or from phenotypically plastic responses to differing environments. Within populations, the interrelationships among reproductive variables were similar for Decatur and Independence Creek: females investing more in reproduction (measured by total litter mass, TLM) produced larger litters and larger offspring, and V* decreased with increased mean offspring mass (and with decreased litter size at Decatur). At Kickapoo, larger females produced larger litters and had larger TLM; females investing more in reproduction produced larger litters but not larger offspring. Within litter variability in offspring mass was not correlated with any reproductive variables in this latter population. These patterns may be explained by the fractional clutch hypothesis, the inability of females precisely to control investment among offspring or morphological constraints on reproduction.     

温带红松阔叶混交林凋落叶与主要大型土壤动物热值的季节变化

对温带红松阔叶混交林不同种类凋落叶、混合凋落叶和主要大型土壤动物的干质量热值及季节变化规律进行了研究.结果表明：不同种类凋落叶和3种大型土壤动物的干质量热值不同,且其季节变化规律存在一定的差异.红松凋落叶的干质量热值平均值最高(19.71 kJ·g^-1),枫桦(18.22 kJ·g^-1)、紫椴(18.13 kJ·g^-1)、混合凋落叶(17.91 kJ·g^-1)居中,水曲柳(16.94 kJ·g^-1)和色木槭(16.25 kJ·g^-1)最低.红松和色木槭凋落叶干质量热值随凋落叶分解进行呈逐渐降低趋势,水曲柳凋落叶干质量热值季节变化较小,而紫椴、枫桦和混合凋落叶干质量热值次年有上升的趋势.大型土壤动物中,蜈蚣(22.07 kJ·g^-1)的干质量热值最高,蚯蚓(16.72 kJ·g^-1) 次之,马陆(13.28 kJ·g^-1)最低.蚯蚓和马陆干质量热值的季节变化规律一致,蜈蚣干质量热值的季节变化规律则有所不同.凋落叶和3种大型土壤动物干质量热值的季节变化之间没有明显的相关性.     

降水量变化对蒙古栎落叶分解过程的间接影响

分析了在4种不同降水量条件下蒙古栎叶凋落物基质质量的变化,并应用分解袋法研究其凋落物在蒙古栎次生林内的分解过程.结果表明：与对照相比,降水量减少条件下,蒙古栎叶凋落物的初始N、P、K浓度显著升高,初始木质素浓度显著降低,凋落物分解速率大,N、P、K矿化率高,N和P固持时间缩短;降水量增加情况下,其凋落物初始N浓度显著降低、木质素浓度显著升高,N、P、K矿化率低,N和P固持时间延长.4种类型叶片凋落物的质量损失过程均符合指数降解模型,分解速率可以由凋落物木质素/N来预测.相关性分析显示,木质素浓度高、N浓度低的两种凋落物的分解速率与N浓度相关性最大;而木质素浓度低、N浓度高的两种凋落物的分解速率与木质素浓度相关性最大.说明降水量的变化显著地改变了蒙古栎叶凋落物的基质质量,进而间接地改变了凋落物的分解过程.     

Explaining the seasonal decline in litter size in European ground squirrels

In European ground squirrels Spermophilus citellus as in many ground squirrel species. late born litters are composed of fewer young than early born litters. Two alternative though not mutually exclusive hypotheses may explain this seasonal pattern of change in litter size. On the one hand. the production of few large young late in the season may be an adaptation to time limitations on the offspring. that have to complete growth and fattening prior to hibernation. Then one would expect a trade-off between offspring number and size as the breeding season progresses. At its extreme. this hypothesis would predict that total maternal effort should be equal independent of litter size. Alternatively. litter size may be determined by physiological limitations on the mother. in that highly constrained mothers breed later and produce smaller litters. Then one would expect reduced overall maternal effort in highly constrained mothers of smaller litters. In this case. a trade-off between litter size and offspring size would not be expected. We found that total maternal effort in terms of gestation length and the duration of lactation increased with increasing litter size. thus supporting the second hypothesis. Lactation was not terminated at natal emergence. It extended a relatively long period of time beyond the time of first litter emergence depending on litter size. During prolonged lactation. individual young of large litters made up body mass to young of small litters. As a consequence. juvenile weaning body mass was unaffected by litter size although offspring body mass at natal emergence was inversely related to litter size. This additional weight gain in young of large litters compensated for initial survival disadvantages and presumably affected fecundity at yearling age.     

Nitrogen addition drives convergence of leaf litter decomposition rates between <Emphasis Type="Italic">Flaveria bidentis</Emphasis> and native plant

Evidence is growing that invasive species can change decomposition rates and associated nutrient cycling within an ecosystem by changing the quality of the litter entering a system. However, the relative contribution of their distinct litter types to carbon turnover is less understood, especially in the context of enhanced N deposition. The objective of this study was to investigate the whole-plant responses of an invasive plant Flaveria bidentis in litter decay to simulated N eutrophication. A 1-year study was conducted to assess if N enhancement influenced decomposition and nutrient dynamics of litters from foliage, fine roots and twigs of F. bidentis compared to co-occurring native species Setaria viridis. N fertilization significantly decreased the decomposition rate of the foliage of the invasive F. bidentis by more than 25% relative to the water control, but had relatively minor effects on decomposition of its twigs and fine root litter or leaf litter from the native species. Collectively, decomposition rates of foliar litters of the invasive and native species become convergent over time in the presence of N addition. Moreover, net N loss was predominately influenced by litter species, followed by the litter type, while N addition had little effect on net N loss. Our study showed that the variation in litter decomposition was much greater between litter types of the invasive F. bidentis than between different plant species under the N addition and that the litter of invasive species with higher inherent decomposability did not always decompose more rapidly than the litter of native species in response to predicted N deposition enhancement.