Plant growth analysis: towards a synthesis of the classical and the functional approach

A method of calculating relative growth rates (RGR) and net assimilation rates is presented. The method is based on the fitting of a polynomial through the relative growth rate values calculated by the 'classical' approach rather than through the In-transformed plant weights as in the 'functional' method. Additional ways of reducing the harvest-to-harvest variation characteristic of the classical approach are discussed. The main advantages of the present approach over the functional one are: (1) The degree of the polynomial can be increased (within certain limits) without inducing spurious fluctuations in RGR. Thus, quite complex trends in RGR can be described. (2) There is little interference between RGR values in different parts of the experiment. The main advantages over the classical approach are: (1) The erratic fluctuations in RGR are dampened. (2) As frequent small harvests are allowed, the workload at each harvest can be diminished and a more reliable impression of ontogenetic drift in RGR can be obtained. (3) RGR is described by a continuous function, thus facilitating further calculations and compilations.     

Effects of geminivirus infection and growth irradiance on the vegetative growth and photosynthetic production of Eupatorium makinoi

Eupatorium makinoi plants with or without geminivirus infection were grown in shading frames with 70, 15 and 5.5% sunlight. Growth characteristics of these plants in the early vegetative phase were compared by means of growth analysis. We also measured leaf photosynthetic gas exchange rates and examined relationships between leaf photosynthesis and whole-plant growth. Relative growth rate (RGR=(1/W)×(dW/dt), where W is plant dry mass) of virus-infected plants was lower than that of uninfected plants under all three light conditions. The reduction of RGR by infection was increased with irradiance. The net assimilation rate (NAR=(1/A)×(dW/dt), where A is total leaf area of the plant) was also reduced both by infection and shading. NARs that were estimated from light-response curves of leaf photosynthesis, in situ measurements of irradiance, and respiration rates of leaves, stems and below-ground parts, agreed very well with the values obtained by conventional growth analysis techniques. Decreases in the estimated NAR value from infection and shading were mostly explained by the decreases in leaf photosynthesis. These results clearly showed that lowered RGR in virus-infected plants was attributed mainly to impaired photosynthesis in virus-infected leaves.     

Explaining patterns of primary production from individual level traits

Question: Do species traits explain differences in productivity in grazed and ungrazed plots? Location: Río de la Plata grasslands, Uruguay (31°54′S, 58°15′W). Methods: In a greenhouse experiment, we measured the relative growth rate (RGR) of grasses with contrasting responses to grazing (increasers and decreasers). We performed six harvests at weekly intervals in order to calculate the RGR and assess 12 plant traits. We compared the RGR between increaser and decreaser species after 2 and 5 weeks using t‐tests. Linear and potential regression models were fitted to time versus natural logarithm of total dry biomass relationships. The RGR temporal trajectories of increaser and decreaser species were obtained from the derivatives of the best‐fit functions. Principal component analysis (PCA) was used to sort species according to their traits. Results: The RGR of decreaser grasses was higher than that of increasers at the second week, while at the fifth week the opposite was observed. The RGR of decreasers dropped through time, while the RGR of increaser species was constant. The PCA separated increaser from decreaser species. The attributes related to increaser species were: high specific leaf area, tillering rate, green leaf rate, total leaf number, root weight ratio and leaf weight ratio; while those associated with decreaser species were: high dead biomass, senescence rate, reproductive biomass, leaf elongation rate and total biomass. Conclusions: Traits possessed by decreasers reduce light availability and increase the reproductive investment, explaining the drop in RGR. Specific differences in RGR seem to scale up to the ecosystem level and would explain the pattern in aboveground net primary production observed in the field under contrasting grazing regimes.     

Effect of Photoperiod on Vegetative Growth in Two Natural Populations of Dactylis glomerata L.

The growth of two natural populations of cocksfoot from contrastingclimatic regions (Norway and Portugal) was studied at four temperaturesand two photoperiods. Serial harvests were taken and quadraticcurves were fitted to log dry weight and leaf area for eachreplicate in order to calculate growth attributes at a constantplant weight for all treatments. Interactions of population,temperature, and photoperiod on relative growth-rate (RGR) werefound, with the greatest population differences at 5 and 30°C in an 8-h photoperiod. Leaf-area ratio (LAR) played alarger part than net assimilation rate (NAR) in determiningthe differential population responses in RGR to daylength, andthese differences in LAR were primarily the result of differentpatterns of dry-matter distribution within the plant.     

A novel method of supplying nutrients permits predictable shoot growth and root : shoot ratios of pre-transplant bedding plants

BACKGROUND AND AIMS: Growth of bedding plants, in small peat plugs, relies on nutrients in the irrigation solution. The object of the study was to find a way of modifying the nutrient supply so that good-quality seedlings can be grown rapidly and yet have the high root : shoot ratios essential for efficient transplanting. METHODS: A new procedure was devised in which the concentrations of nutrients in the irrigation solution were modified during growth according to changing plant demand, instead of maintaining the same concentrations throughout growth. The new procedure depends on published algorithms for the dependence of growth rate and optimal plant nutrient concentrations on shoot dry weight W(s) (g m(-2)), and on measuring evapotranspiration rates and shoot dry weights at weekly intervals. Pansy, Viola tricola 'Universal plus yellow' and petunia, Petunia hybrida 'Multiflora light salmon vein' were grown in four independent experiments with the expected optimum nutrient concentration and fractions of the optimum. Root and shoot weights were measured during growth. KEY RESULTS: For each level of nutrient supply W(s) increased with time (t) in days, according to the equation DeltaW(s)/Deltat=K(2)W(s)/(100+W(s)) in which the growth rate coefficient (K(2)) remained approximately constant throughout growth. The value of K(2) for the optimum treatment was defined by incoming radiation and temperature. The value of K(2) for each sub-optimum treatment relative to that for the optimum treatment was logarithmically related to the sub-optimal nutrient supply. Provided the aerial environment was optimal, R(sb)/R(o) approximately W(o)/W(sb) where R is the root : shoot ratio, W is the shoot dry weight, and sb and o indicate sub-optimum and optimum nutrient supplies, respectively. Sub-optimal nutrient concentrations also depressed shoot growth without appreciably affecting root growth when the aerial environment was non-limiting. CONCLUSION: The new procedure can predict the effects of nutrient supply, incoming radiation and temperature on the time course of shoot growth and the root : shoot ratio for a range of growing conditions.     

Growth and shoot:root partitioning of spinach plants as affected by nitrogen supply

Spinach plants (Spinacia oleracea L.) were grown hydroponically in fixed environmental conditions either at full nitrate availability (11·8mol m^-3) or at a suboptimum relative nitrate addition rate of 0·20d^-1, 0·15d^-1 or 0·10d^-1 respectively, the other nutrients being adequately provided. The relative growth rate (RGR) of the plants varied significantly with the nutrition treatment and decreased during development in all treatments. The concentration of reduced nitrogen in the plants grown at full nitrate availability did not change significantly during the experimental growth period and nitrate accumulation was substantial. After an adaptation period, the concentration of reduced nitrogen in the plants at the suboptimum nitrate addition rates increased during growth and was lowest at the lowest relative nitrate addition rate. Nitrate uptake was almost complete in the suboptimum treatments and nitrate accumulation was negligible as long as the concentration of reduced nitrogen was below 2·0 mmol (g dry weight)^-1. The RGR of all plants was proportional to the concentration of reduced nitrogen in the plant minus a minimal tissue concentration required for growth. However, the proportionality factor was inversely related to the plant mass. This relationship was summarized in an empirical model which explained 98·7% of the variance of the dry weight (log scale) data of all treatments at all harvests. The model was compared with other growth models found in the literature. The shoot/root weight ratio increased from 2 to 4 if nitrate provision was not limiting, and initially, this ratio decreased at suboptimum nitrate provision but increased at higher growth stages. Possible explanations of the dynamics of dry matter partitioning are discussed in relation to models.     

Effects of sodium, potassium and calcium on salt-stressed barley. I. Growth analysis

Barley ( Hordeum vulgare L. cv. CM 72) was grown for a 28-day period and stressed with treatments of 125 mol m⁻³ NaCl or KC1 with low Ca²⁺ (0.4 mol m⁻³ Ca²⁺) or high Ca²⁺ (10 mol m⁻³ Ca²⁺). Plants were harvested periodically so that relative growth rate (RGR), net assimilation rate (NAR) and leaf area ratio (LAR) could be calculated using the functional approach to plant growth analysis. Relative growth rate declined with time for all treatments, including controls. Salinity inhibited RGR relative to control values by day 10. High Ca²⁺ improved the growth of salt-stressed plants in both NaCl-salinity and KCl-salinity. KC1 proved more toxic than NaCl, especially for KCI-salinity plants with low Ca²⁺, which died by day 28. Net assimilation rate, but not LAR, was highly correlated with RGR for all treatments. This indicates that the photosynthetic-assimilatory machinery was limiting RGR and not the leaf area of the plant.     

Relative growth rate,resource allocation and root morphology in the perennial legumes, <Emphasis Type="Italic">Medicago sativa</Emphasis>, <Emphasis Type="Italic">Dorycnium rectum</Emphasis> and <Emphasis Type="Italic">D. hirsutum</Emphasis> grown under controlled conditions

Perennial pastures are needed in farming systems in southern Australia to combat environmental problems such as dryland salinity. The mediterranean climate in southern Australia imposes constraints to the growth and survival of perennial plants. The aim of this study was to compare growth rates, resource allocation and root distribution in three perennial legumes, Medicago sativa L., Dorycnium hirsutum (L.) Ser. and Dorycnium rectum (L.) Ser., to identify different plant traits and their ecological and agronomic significance. Plants were grown in 1-m deep split tubes and destructive harvests were made every 2 weeks after plant emergence for 10 weeks. Leaf area and leaf, stem and root fresh and dry weights were measured. Maximum root depth and the root distribution were also determined. Seedlings of Dorycnium were slower to emerge and had a lower relative growth rate (RGR) than M. sativa. The slower RGR was associated with a lower specific leaf area (SLA) in D. hirsutum and a lower net assimilation rate (NAR) in D. rectum. Although all species allocated a similar proportion of biomass to roots, D. rectum had a shallower root distribution and took longer to produce deep roots. The slow growth rates of Dorycnium seedlings suggest that they are more prone to establishment problems due to competition from weeds or other pastures, and because they have less access to water at greater depth during summer drought. However, D. hirsutum displayed characteristics of a plant that is adapted to stressful environments and therefore may be able to grow in conditions where other perennial legumes cannot.     

Long-term responses of Melilotus segetalis to salinity. I. Growth and partitioning

Annual sweetclover plants [Melilotus segetalis (Brot) Ser.] were grown for a complete life cycle with and without saline (NaCl treatment of CE=15 dS m⁻¹). Growth and partitioning analyses were performed. Sequential harvests (every 15 d) during the life cycle, and separation of plant material into roots, stems, petioles, leaves and reproductive structures were carried out Salt treatment reduced growth during the early and middle stages of the life of the plant, but did not significantly affect RGR in the reproductive phase. The root–shoot allometric coefficient of salinized plants in the generative phase decreased more than in control plants. We suggest that salinity-induced growth reduction in M. segetalis was primarily a result of a lower unit leaf rate (ULR) despite an increased leaf area ratio (LAR). Earlier flowering, higher biomass allocation to shoot and greater reproductive investment, but similar relative growth rate (RGR), were some of the main characteristics of salt-stressed plants compared to controls during the reproductive phase, these apparently being associated with increased sink strength caused by developing flowers and fruits.     

The Evolution of Multilocus Systems under Weak Selection

The evolution of multilocus systems under weak selection is investigated. Generations are discrete and nonoverlapping; the monoecious population mates at random. The number of multiallelic loci, the linkage map, dominance, and epistasis are arbitrary. The genotypic fitnesses may depend on the gametic frequencies and time. The results hold for s << c(min), where s and c(min) denote the selection intensity and the smallest two-locus recombination frequency, respectively. After an evolutionarily short time of t(1) ~ (ln s)/ln(1 - c(min)) generations, all the multilocus linkage disequilibria are of the order of s [i.e., O(s) as s -> 0], and then the population evolves approximately as if it were in linkage equilibrium, the error in the gametic frequencies being O(s). Suppose the explicit time dependence (if any) of the genotypic fitnesses is O(s(2)). Then after a time t(2) ~ 2t(1), the linkage disequilibria are nearly constant, their rate of change being O(s(2)). Furthermore, with an error of O(s(2)), each linkage disequilibrium is proportional to the corresponding epistatic deviation for the interaction of additive effects on fitness. If the genotypic fitnesses change no faster than at the rate O(s(3)), then the single-generation change in the mean fitness is ΔW = W(-1)V(g) + O(s(3)), where V(g) designates the genic (or additive genetic) variance in fitness. The mean of a character with genotypic values whose single-generation change does not exceed O(s(2)) evolves at the rate ΔZ = W(-1)C(g) + O(s(2)), where C(g) represents the genic covariance of the character and fitness (i.e., the covariance of the average effect on the character and the average excess for fitness of every allele that affects the character). Thus, after a short time t(2), the absolute error in the fundamental and secondary theorems of natural selection is small, though the relative error may be large.     

Relative growth and nutrient accumulation rates for tobacco

Summary Tobacco plants (Nicotiana tabacum L.) were grown from transplanting until floral expression in the phytotron units of Southeastern Plant Environment Laboratories to evaluate the relationship between relative growth rate (RGR) and relative accumulation rates (RAR) of N, P, K, Ca, and Mg. RAR is calculated to be analogous to RGR. Plants were grown in both controlled-environment rooms with artificial light and air-conditioned greenhouses with natural light at three temperature conditions and three application rates of N-P-K. RGR and RAR were calculated only for the period of grand growth which occurred within the interval from 7 to 32 days after transplanting. In general, neither RGR nor RAR were affected by temperature or nutrient level. However, both temperature and nutrient level affected dry matter accumulation of the plants apparently by an influence on the rapidity with which plants adjusted to their new environment during the initial 7-day interval after transplanting. RAR for P and K were coequal with RGR of the whole plant; thus, the concentrations of P and K within the plant tended to remain constant during growth. RAR for N, Ca, and Mg were less than RGR for the whole plant; thus, internal concentrations of these nutrients declined during growth. RAR of N, Ca, and Mg for the whole plant were equivalent to RGR of the roots. As a rationale for the association of RGR of roots and RAR of N, it is proposed that the soluble carbohydrate pool in the roots concurrently influences both N absorption, as NO₃ ^-, and growth of new roots of immature plants. Research reported in this paper was supported in part by National Science Foundation (RANN) Grants GI-39229 and GI-39230. Operation of the Phytotron Units of Southeastern Plant Environmental Laboratories at Duke and North Carolina State Universities was supported by National Science Foundation Grants GB-28950-1A and GI-28951. Approved as Paper Number 4773 of the Journal Series of the North Carolina Agricultural Experiment Station, Raleigh, NC. Research reported in this paper was supported in part by National Science Foundation (RANN) Grants GI-39229 and GI-39230. Operation of the Phytotron Units of Southeastern Plant Environmental Laboratories at Duke and North Carolina State Universities was supported by National Science Foundation Grants GB-28950-1A and GI-28951. Approved as Paper Number 4773 of the Journal Series of the North Carolina Agricultural Experiment Station, Raleigh, NC.     

Latitudinal variation in plant size and relative growth rate in Arabidopsis thaliana

Latitude is an important determinant of local environmental conditions that affect plant growth. Forty ecotypes of Arabidopsis thaliana were selected from a wide range of latitudes (from 16°N to 63°N) to investigate genetic variation in plant size and relative growth rate (RGR) along a latitudinal gradient. Plants were grown in a greenhouse for 31 days, during which period three consecutive harvests were performed. Plants from high latitudes tended to have smaller plant size in terms of seed size, cotyledon width, rosette size, number of rosette leaves, size (leaf area) of the largest leaves, total leaf area, and total dry weight per plant than those from low latitudes. The mean (±SE) RGR across ecotypes was 0.229 (±0.0013) day⁻¹. There was, however, significant ecotypic variation, with RGR being negatively correlated with latitude. The two main components of RGR, leaf area ratio (LAR) and unit leaf rate (ULR), were also correlated with latitude: LAR increased with increasing latitude while ULR decreased with increasing latitude. It was also found that RGR tended to be negatively correlated with LAR, specific leaf area (SLA) and specific root length (SRL) but to be positively correlated with mean area per leaf (MAL) and ULR. The variation in RGR among ecotypes was relatively small compared with that in the other traits. RGR may be a conservative trait, whose variation is constrained by the trade-off between its physiological (i.e. ULR) and morphological (i.e. LAR) components. Received: 2 November 1997 / Accepted: 28 February 1998     

Plant functional traits shape growth rate for xerophytic shrubs

• Trade-offs exist for xerophytic shrubs between functional traits, involving in water loss and assimilate accumulation, can contribute to its survival and growth rate regulation in arid environments. However, growth analysis based on plant functional traits has been focused on the study of herbs and woody species. It is still unclear how the functional traits of xerophytic shrubs regulate their growth rate.
• In this study, we selectedeight xerophytic shrubs as samples to analyze the regulation process of the functional traits of shrubs on growth rate. Plants were cultivated for three years, and three harvests (every one year) were carried out. Factors explaining between-species differences in relative growth rate (RGR) varied, depending on whether different ages were considered.
• The results showed that RGR was positively correlated with net assimilation rate, but there was a significant negative correlation with leaf area ration (LAR), specific leaf area (SLA), and leaf biomass ratio in the age 1. However, in the age 2, RGR showed a significant positive correlation with the morphological traits (i.e., leaf area ration and specific leaf area), but not with physiological traits (i.e., net assimilation rate) and leaf biomass allocation.
• Our results suggested that the fluctuation of environmental factors affects the regulation path of the plant functional traits on RGR of xerophytic shrubs. However, the analysis of causality model showed that no matter in which age, net assimilation rate and leaf area ration principally drive the variation in RGR among xerophytic shrubs.

     

The 48 kDa Ca2+-binding protein of bovine brain.

The integrated rate equation for reactions with stoichiometry A----P + Q is: e0t = -Cf . ln(1-delta P/A0) + C1 delta P + 1/2C2(delta P)2 where the coefficients C are linear or quadratic functions of the kinetic constants and the initial substrate and product concentrations. I have used the 21 progress curves described in the accompanying paper [Cox & Boeker (1987) Biochem. J. 245, 59-65] to develop computer-based analytical and statistical techniques for extracting kinetic constants by fitting this equation. The coefficients C were calculated by an unweighted non-linear regression: first approximations were obtained from a multiple regression of t on delta P and were refined by the Gauss-Newton method. The procedure converged in six iterations or less. The bias in the coefficients C was estimated by four methods and did not appear to be significant. The residuals in the progress curves appear to be normally distributed and do not correlate with the amount of product produced. Variances for Cf, C1 and C2 were estimated by four resampling procedures, which gave essentially identical results, and by matrix inversion, which came close to the others. The reliability of C2 can also be estimated by using an analysis-of-variance method that does not require resampling. The final kinetic constants were calculated by standard multiple regression, weighting each coefficient according to its variance. The weighted residuals from this procedure were normally distributed.     

A model relating the maximum nitrate inflow of lettuce (Lactuca satvia L.) to the growth of roots and shoots

The net inflow of nitrate can be calculated from the nitrate concentration at the root surface by means of the Michaelis-Menten equation. Because of maximum inflow (Imax) is not constant but varies with plant age and growing conditions, a model for calculating Imax during plant growth was derived. Lettuce was grown in nutrient solution. Variations in temperature, radiation and plant age were used to vary growth rates and N-demand of plants. There was a linear relationship between relative growth rates (RGR) and maximum nitrate inflow (Imax), that could be described by the following regression function: Imax = 0.24 + 6.57 RGR. A residual analysis showed a further influence on Imax from the root:shoot-ratio (RSR), the effects of which could be accounted for by including an e-function in the relationship: Imax = (0.27 + 10.63 RGR) e^{(–0.0017 RSR)}. This model for calculating Imax was validated in two further experiments.     

The contribution of roots and shoots to whole plant nitrate reduction in fast- and slow-growing grass species

The hypothesis was tested that slow-growing grass species perform a greater proportion of total plant NO3- reduction in their roots than do fast-growing grasses. Eight grass species were selected that differed in maximum relative growth rate (RGR) and net NO3- uptake rate (NNUR). Plants were grown with free access to nutrients in hydroponics under controlled-environment conditions. The site of in vivo NO3- reduction was assessed by combining in vivo NO3- reductase activity (NRA) assays with biomass allocation data, and by analysing the NO3- to amino acid ratio of xylem sap. In vivo NRA of roots and shoots increased significantly with increasing NNUR and RGR. The proportion of total plant NO3- reduction that occurs in roots was found to be independent of RGR and NNUR, with the shoot being the predominant site of NO3- reduction in all species. The theoretical maximum proportion of whole plant nitrogen assimilation that could take place in the roots was calculated using information on root respiration rates, RGR, NNUR, and specific respiratory costs associated with growth, maintenance and ion uptake. The calculated maximum proportion that the roots can contribute to total plant NO3- reduction was 0.37 and 0.23 for the fast-growing Dactylis glomerata L. and the slow-growing Festuca ovina L., respectively. These results indicate that slow-growing grass species perform a similar proportion of total plant NO3- reduction in their roots to that exhibited by fast-growing grasses. Shoots appear to be the predominant site of whole plant NO3- reduction in both fast- and slow-growing grasses when plants are grown with free access to nutrients.     

棉花苗期棉蚜的二项式抽样设计及其精度分析

基于棉花苗期棉蚜（Ａｐｈｉｓ ｇｏｓｓｙｐｉｉ）的２４组调查数据,利用每样方虫口不超过数阈值Ｔ（为０,１,２,…,９,１０,１５,２０,３０）头蚜虫的植株比例（ＰＴ）与种群密度（ｍ,头／株）的关系,拟合经验关系式１ｎ（ｍ）＝α＋ｂ１ｎ〔－１ｎ（ＰＴ）〕设计二项式抽样。通过对不同数阈值Ｔ的决定系数（ｒ＾２）、估计方差（Ｖａｒ（ｍ））和抽样精度（ｄ估计）等进行综合分析,结果表明该蚜虫在数阈值Ｔ为１５时     

A Single Equation to Quantify the Hierarchy in Plant Size Induced by Competition Within Monocultures

The following empirical model: Ra(i) = r(1+ln(w(i)/wm)Kn)(1–(w(i)/W))(1–(y/Y)) which is based on the logistic growth equation, is developedto describe the growth of differently sized individuals withinplant communities. The model is tested against extensive setsof carrot (Daucus carota L.) and red beet (Beta vulgaris L.)data and is shown to fit well. The model was used to predictindividual plant weights in independent data. The agreementsbetween observed and predicted weights were often close butsome systematic deviations did occur. Thus, a single equationdescribed most of the complex interactions that occurred withinmonocultures of annual crop plants. Carrot, Daucus carota L., red beet, Beta vulgaris L., model, growth, variation     

Variation in the components of relative growth rate in 10 Acacia species from contrasting environments

In this study we assessed the inherent relative growth rate (RGR) under controlled environment conditions of 10 contrasting Acacia species from semi-arid and mesic environments. For several of the species, compound pinnate leaves produced early in the seedling stage, were gradually replaced by phyllodes (expanded petioles that form simple lamina). Other species either did not form phyllodes, or only did so to a minor degree by the end of the study. Phyllode production was dominant in the four slow-growing Acacia species from semi-arid environments (A. aneura, A. colei, A. coriacea and A. tetragonophylla), with leaf production being exclusive or dominant in five (A. dealbata, A. implexa, A. mearnsii, A. melanoxylon and A. irrorata) of the six faster-growing species from mesic environments. The exception was A. saligna which was fast growing but did produce phyllodes. From a carbon economy perspective, slow growth in the semi-arid species was not associated with lower net assimilation rates or less plant mass allocated to foliage. Rather, the primary factor associated with their slow growth was a smaller foliage area per unit foliage mass. This was true for comparisons based on the mean over all harvests or at set plant masses. The production of phyllodes by the semi-arid species substantially reduced foliage area per unit foliage mass, as this was lower for phyllodes than leaves in all species. To assess the impact that phyllode production had on ontogenetic changes in RGR, we modelled the situation where only leaves were formed. This analysis showed that changing from leaves to phyllodes substantially reduced the RGR. There was little difference in plant nitrogen concentration or the ratio of foliage nitrogen to plant nitrogen between the species. This resulted in foliage nitrogen productivity (dry mass gain per unit foliage nitrogen and time) being directly proportional to foliage area per unit foliage mass between species. We concluded that a smaller foliage area per unit foliage mass and phyllode production are the primary factors associated with lower RGR in contrasting Acacia species.     

Effects of sample size on estimates of population growth rates calculated with matrix models

Background

Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (λ) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of λ–Jensen''s Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of λ due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of λ.

Methodology/Principal Findings

Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating λ for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of λ with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography.

Conclusions/Significance

We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities.