make a list of the chilling models and the spring phenology models

[lizzieinvancouver]

In chillR and then in phenor packages

[ngoj1]

Here are the notes from the alternating, sequential, and parallel models from the phenor package:

Alternating model

• Cannell & Smith (1983)
• study system: Picea sitchensis
• "presents an empirical model for the timing of budburst...based solely on thermal time and winter chilling."
• Predictive model on 2 to 10 year old trees for most of the provenances grown in Britain
• thermal time: T_x = sum(t_m - x) where T_x = day degrees with a base temperature of x degC and t_m = mean daily temperature on those days, i.e. basically GDD
• Chill days = n days between 1 Nov to budburst date where t_m <= x
• observed relationship was that increased chilling during april-may decreased the thermal time required for budburst
• least squares method for finding the optimal balance between thermal time and chill day/unit requirements led to decreasing exponential models fitting the best
• as such the model is thermal time = 67.4 + 4401.8e(-0.042 x chill days)

Sequential model

• Kramer (1994)
• study system: Fagus sylvatica
• leaf unfolding data collected over the course of 57 years in the Netherlands was used as the data to fit 6 pre-existing models, which were developed to only require temperature as an input
• This species responds to photoperiod cues, however, and so this was incorporated into the models that were tested by inserting an additive argument (just appended to R_chl, the rate of chilling)
• The model that apparently fit the data best was the Sequential model posited by Sarvas (1974) which "considered rest and quiescence as two strictly separate phases." with no gradation between these two stages unless the chilling threshold is met, and "no transition from quiescence to the active phase" unless the forcing threshold is met
• "This model was called the sequential model, because the state of chilling and the state of forcing increase sequentially in time (Model I of Hanninen 1990)."

However, Hanninen (1990) argues that not even this sequential model posited by Sarvas (1974) is sufficient;

• Hanninen (1990)
• Study system: Pinus sylvestris and Picea abies
• From section 5, Synthesis model; based on previous models and experimental results
• C(t) = ((1 - C_min - deltaC(t))/(CU_crit - deltaCU(t) - CU_abs))*(S_chl(t)-CU_abs) + C_min + deltaC(t)
• The premise of this model is that it takes the data from many studies and also compares the accuracy of prior models and finds the model type that has the most empirical support
• they argue that "with increased chilling, the rate of ontogenetic development becomes less dependent on the forcing temperature."
• This paper argues that the prior models of all types from I to IV (outlined in Table 2 of this paper) are too extreme and/or insufficiently integrate environment cues in their predictions of effects of chilling

Parallel model

• Landsberg (1974) + Hanninen and Kramer
• study system: Malus domestica
• posits that apple bud development can be split into 3 phases, which are morphogenesis and dormancy induction, true dormancy, and burst to bloom
• from Kramer (1994): "even when the critical state of chilling has not yet been attained, response to forcing temperature must be possible."
• "This model was called the parallel model, because the state of chilling and the state of forcing increase together in time (Model II of Hanninen 1990)."
• this paper explicitly talks about endogenous factors that promote and inhibit growth, like GA, cytokinin, etc and cite a bunch of papers where these hormones are discussed
• Here they mention that base temperature is 5 degC because apparently below that threshold, "lower temperatures are not advantageous to the physiological processed leading to the condition in which growth can proceed at the maximum rate allowed by prevailing conditions."; no citation for this though because "the 5 degC limit is arbitrarily chosen as a convenient value at about the level below which growth is usually assumed to cease"
• they do later mention that 5 degC might not be correct, but they still chose to follow through with it regardless
• the model is laid out as G = A/(I + be^(-k(I),P)) where G is the number of growth units
• also note that Hanninen and Kramer both critique this model in their respective papers

I'll be adding these papers to the docs folder and also to the reference list.

[lizzieinvancouver]

@ngoj1 This is great! Can you add what models Luedeling has used? And try to combine Kramer figures with molecular understanding.

[ngoj1]

Here are the summaries for the three models explicitly mentioned in the Luedeling 2015 paper:

Chilling Hours

• Weinberger JH (1950) Chilling requirements of peach varieties. Proc Am Soc Hortic Sci 56, 122128 (Couldn’t access the paper )
• Bennett JP (1949) Temperature and bud rest period. Calif Agric 3 (11), 9+12
• Study system: Hardy pear i.e. some cultivar of Pyrus communis
• Summary: Cold temperatures of 37 F (2.8 degC) for between 56 to 81 days permitted full bud break, temperatures higher than 45 F and/or days shorter than 56 were unconducive and/or had a delaying effect

"The requirements are a temperature between freezing and about 45 F and a period of continuous exposure of two to three months.” “In the intermediate temperature range - 45" F to 60" F - the results of continuous exposure vary with the kind of plant, but in general, an incomplete ending of the rest occurs.” “The picture shows that trees which.had been stored at 37" F continuously for 56 to 81 days opened most of their buds, as they do after a normal winter outdoors” “With decreasing length of cold treatment below 56 days, an increasing proportion of buds remained inactive until at no exposure and at 10 days exposure only two injured buds grew feebly”

Utah Model

• Richardson EA, Seeley SD, Walker DR (1974) A model for estimating the completion of rest for Redhaven and Elberta peach trees. HortScience 9(4), 331-332
• Study system: Prunus persica ‘Elberta’ and P. persica ‘Redhaven’
• Summary: temperatures between 37 and 48 F were most conducive to acquiring chill units where 1 chill unit = 1 hour of exposure to temperatures below 6 degC, like a quantification of Erez & Lavee’s findings

^ I have the summaries for the two Erez papers that these experiments on peaches were based on also summarized in the notes document.

Dynamic Model

• Erez A, Fishman S, Linsley-Noakes GC, Allan P (1990) The dynamic model for rest completion in peach buds. Acta Hortic 276, 165-174
• Fishman S, Erez A, Couvillon GA (1987a) The temperature dependence of dormancy breaking in plants- computer simulation of processes studied under controlled temperatures. J Theor Biol 126(3), 309-321
• Fishman S, Erez A, Couvillon GA (1987b) The temperature dependence of dormancy breaking in plants- mathematical analysis of a two-step model involving a cooperative transition. J Theor Biol 124(4), 473-483
• From Zhang & Taylor (2011):

  “The Dynamic Model (Fishman et al., 1987a, 1987b) was developed in the 1980s and defined a new concept for the negation process. Winter chill is assumed to accumulate in a two-step process. Cold temperatures initially result in the formation of an intermediate chilling product; high temperatures can destroy this product. Once a critical amount of this chilling product has accumulated, it converts to a chill portion, which cannot be destroyed. A certain chill portion accumulation indicates fulfillment of chilling requirement.”

• Arose when it was observed that cyclic and intermittent exposures to cold and warm displayed different effects where longer cycles of cold and warm (that is, the exposure to cold lasted longer) displayed weaker warmth-induced negative of chill accumulation than plants that had frequent intervals of thermoperiodicity
• This was built upon data from Erez et al. (1979)

^ More information is in the notes document

[ngoj1]

Also, maybe I was too optimistic about the diagrams in the Kramer paper...

They really are just simple visualizations of the general structure of the models mentioned in this paper, though the glossary of the mathematical terms and arguments listed and formulae provided might be of good use.

[lizzieinvancouver]

@ngoj1 Wow! That was overly optimistic. I guess it's something and maybe some of. the experimental results from callose could be but on top (where x is temperature and y is something like 'callose degrades') ... but it seems to not show the accumulation or anything.