Ovule and Ovary Culture in Doritis Pulcherrima

Pollination resulted in an increase in size of ovary, the development of the ovules and fertilization in Doritis pulcherrima. The growth curve of percentage increase in total growth of ovary width was bimodal. The first dip was at 40 days after pollination which was correlated with the time of megaspore formation inside the ovary. The growth curve of increase in percentage of ovary length was trimodal. These growth curves did not show a strong relationship with the development of ovule and embryo. However, the incremental growth in width and length of ovary was highest during rudimentary ovule formation and before embryo sac maturation. The mature pod dehisced at about 210 days after pollination, while the incremental growth in width and length stopped at about 90 to 110 days after pollination. Wilting of perianth occurred 2 days after pollination, which is the first observable morphological change in Doritis. The placental ridge started to proliferate at about 20 days after pollination. Approximately 60 days was required to form the mature embryo sac and almost half of that time was occupied in placental growth. Although the pollen tubes existed around developing ovules at 10 days after pollination, they entered the micropyle after the embryo sac was fully formed at about 60 days after pollination. Fertilization occurred soon after the embryo sac was fully formed containing mature egg at 60-65 days after pollination. Therefore, approximately 1/4 of the period between pollination and pod maturity was required for fertilization. Between 40 to 50 days after pollination, the megaspore mother cell underwent meiosis. After the first division, the two dyads were formed, and after the second division two megaspores and the degenerating dyad was formed. The megaspore enlarged and formed the 8-nucleate embryo sac at about 60 days after pollination. At about 65 days after pollination, the zygote and the endosperm initial cell were formed through double fertilization. However, the endosperm initial cell degenerated soon thereafter. At about 70 days after pollination, the zygote divided to form a 2-celled embryo which consisted of a terminal cell and a basal cell. Thin middle and suspensor initial cells were produced from the basal cell. The seed coat was also formed at about 70 days after pollination from the integuments. At about 80 days after pollination, the suspensor initial cell produced eight suspensor cells, and the terminal cell produced a multi-celled embryo. Histochemical study showed that deoxyribonucleic acid (DNA), ribonucleic acid (RNA), total proteins and total carbohydrates decreased during megasporogensis. An interesting point was that RNA was more dense in the terminal cell than in the basal cell, which suggested that the initial differentiation had already occurred in the 2-celled embryo This is the first case of obtaining seedlings of orchids directly from ovules through ovary and ovule culture with ovules collected prior to the occurrence of fertilization. Approximately 150 days were reduced to obtain seedlings of Doritis pulchcrrima from pollination through ovary and ovule culture over the traditional method of sowing "mature" seeds. Seedlings were obtained from ovules 45 days prior to normal fertilization time through ovary and ovule culture, which suggested that fertilization must have occurred in vitro during ovary and ovule culture to obtain seedlings. In the 20-day-old ovule culture, young seedlings were obtained from the treatments of sucrose; naphthaleneacetic acid (NAA) + coconut water; and NAA + 6-benzlaminopurine (BA) + coconut water. However, the growth rate of ovules during culture was not high in these treatments. In the 40-day-old ovule culture, the treatments of sucrose; coconut water; and NAA + BA + sucrose + coconut water were highly effective on both ovule growth rate and seedling formation. In the 60-day-old ovule culture, seedlings were obtained from all treatments except NAA; BA; and NAA + BA. Good growth of ovules did not always induce good seedling formation. Seedlings were obtained from 20-, 40- and 60-day-old ovule cultures if media contained sucrose or coconut water. Sucrose must be necessary for seedling formation during ovule culture, since coconut water contains sucrose. However, if we compare the time required to obtain seedlings, coconut water promoted faster growth than sucrose alone in ovule culture. Maleic hydrazide, tryptophan, casein hydrolysate, NAA and BA were not effective on seedling formation without sucrose or coconut water. The best hormonal conditions for obtaining seedlings in ovary culture were 1.0 ppm BA in 20-day-old ovary culture, 1.0 ppm NAA in 40-day-old ovary culture, and 1.0 ppm NAA in 60-day-old ovary culture. BA was more effective than NAA in forming seedlings in early stage (20 days after pollination) during ovary culture. Coconut water was also effective in ovary culture to obtain seedlings. However, it also increased callus formation rate. Sucrose was necessary in ovule culture to obtain seedlings. However, even without sucrose seedlings were obtained through ovary culture with NAA or BA treatments. Therefore, sucrose might be necessary for ovule development and seedling formation, but in the case of ovary culture sucrose might be obtained from the ovary wall tissues. Sucrose was also necessary for seed germination, but coconut water can be substituted effectively for seed germination and protocorm formation. Sucrose appears to have a very important role in ovule and embryo developments and seedling formation

Computability of Probability Distributions and Distribution Functions

We define the computability of probability distributions on the real line as well as that of distribution functions. Mutual relationships between the computability notion of a probability distribution and that of the corresponding distribution function are discussed. It is carried out through attempts to effectivize some classical fundamental theorems concerning probability distributions. We then define the effective convergence of probability distributions as an effectivization of the classical vague convergence. For distribution functions, computability and effective convergence are naturally defined as real functions. A weaker effective convergence is also defined as an effectivization of pointwise convergence